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+paracol (v1.35): a multi-column package to typeset columns in "parallel".
+===
+Copyright (C) 2005-2018
+  Hiroshi Nakashima <h.nakashima@DOMAIN;  DOMAIN=media.kyoto-u.ac.jp>
+  (Kyoto Univerisity)
+This package 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.
+===
+
+[Contents]
+
+- README ............ this document
+- paracol.ins ....... for docstrip
+- paracol.dtx ....... main dtx for manual and implementation document
+- man.dtx ........... source of Section 1 to 6 of user's manual
+- ref.dtx ........... source of Section 7 of user's manual
+- pwfnote.dtx ....... source of Section 8 of user's manual
+- ppts.dtx .......... source of Section 9 of user's manual
+- bgpaint.dtx ....... source of Section 10 of user's manual
+- probs.dtx ......... source of Section 11 of user's manual
+- impl.dtx .......... source of implementation document
+- paracol-man.pdf ... PDF of user's manual
+
+[How to "make"]
+
+  % tex paracol.ins     # you'll have paracol.sty and paracol-man.tex
+
+# to have user's manual (its PDF is included in the distribution)
+  % latex paracol-man
+  % latex paracol-man   # you need do it twice to make index correct.
+  % makeindex -s gind.ist -o paracol-man.ind paracol-man.idx
+  % latex paracol-man
+
+# to have implementation document of almmost 300 pages(!!)
+  % latex paracol.dtx
+  % latex paracol.dtx   # you need do it twice to make index correct.
+  % makeindex -s gind.ist -o paracol.ind paracol.idx
+  % makeindex -s gglo.ist -o paracol.gls paracol.glo
+  % latex paracol.dtx
+
+Note that if you want LaTeXing paracol-man.tex and/or paracol.dtx,
+you need newvbtm.sty being also available in CTAN.
+
+[Features]
+
++ "paracol" environment in which you may "switch" and "synchronize columns
+  by \switchcolumn(*).
+
++ "column", "nthcolumn", "leftcolumn" and "rightcolumn" environments used in
+  "paracol" to enclose texts to appear in a column.
+
++ Counters are "local" to each column in default but you may make some of
+  them global to all columns by \globalcounter{<ctr>}.
+
++ \definethecounter{<ctr>}{<col>}{<rep>} to give <ctr> its <rep>resentaion
+  specific to <col>-th column.
+
++ \addcontentsonly{<file>}{<col>} to allow contents output for <file> only
+  from <col> (new for v1.00).
+
++ \columnratio{<r_0>,<r_1>,...} to control the width of each column rather
+  than splitting columns evenly (new for v1.1).
+
+- \columncolor[<mode>]{<color>}[<col>] to give the default <color> (with
+  <mode>) to the column <col> (new for v1.2).
+
+- \footnotelayout{<layout>} to choose ordinary column-wise footnote
+  typesetting or page-wise typesetting to gather footnotes in all columns
+  (new for v1.2 and *NEW* for v1.3 with better API).
+
+- \twosided{<t_1><t_2>...} to enable ordinary two-sided typesetting
+  (<t_i>=p), reversal of printing order of columns in even-numbered pages
+  (<t_i>=c), reversal of margins where marginal notes go to (<t_i>=m),
+  and/or mirroring background painting (<t_i>=b) ('m' and 'b' and better API
+  are *NEW* for v1.3).
+
+- "paracol" environment has options for "parallel-paging" to typeset
+  parallel-columns in adjacent page pairs (*NEW* for v1.3).
+
+- \thecolumn to let your macros know which columns they are in (*NEW* for
+  v1.3).
+
+- \ensurevspace{<len>} to force a page break if a synchronization point
+  would be set leaving a small space less than <len> (*NEW* for v1.3).
+
+- \setcolumnwidth{<s_1>,<s_2>,...}[<s'_1>,<s'_2>,...] to specify widths of
+  columns and column-separating gaps more detailedly than \columnratio
+  (*NEW* for v1.3).
+
+- \marginparthreshold{<k>}[<k'>] to specify the minimum ordinal <k> of
+  columns whose marginal notes go to right margin (*NEW* for v1.3).
+
+- \[no]coloredwordhyphenated to allow/disallow hyphenating the first word
+  following a coloring command (*NEW* for v1.3).
+
+- \colseprulecolor[<mode>]{<color>}[<col>] to specify the color of rules
+  drawn in gaps separating columns, i.e., now they can be drawn (*NEW* for
+  v1.3).
+
+- \backgroundcolor{<regino>}{<color>}[<mode>] to paint the background of a
+  <region> by <color> (*NEW* for v1.3).
+
+- \globalcounter* to make all counters global (*NEW* for v1.32).
+
+- Compatible with the new implemenatation of LaTeX (2015/01/10 or
+  later) now (*NEW* for v 1.32).
+
+- \belowfootnoteskip to add space below non-merged pre-environment footnotes
+  (*NEW* for v 1.35).
+
+- \definecolumnpreamble{<col>}{<pream>} to define the column preamble
+  <pream> for the column <col> (*NEW* for v 1.35).
+
+- Emulation of \marginnote[<left>]{<right>}[<voffset>] given by marginnote
+  package (*NEW* for v 1.35).
+
+- Bugs found in v1.3 and successors up to v1.34 has been fixed.
+
+Enjoy!
+
+Hiroshi Nakashima <h.nakashima@DOMAIN;  DOMAIN=media.kyoto-u.ac.jp>
diff --git a/macros/latex/contrib/paracol/bgpaint.dtx b/macros/latex/contrib/paracol/bgpaint.dtx
new file mode 100644
index 0000000000..ac79f4e9a9
--- /dev/null
+++ b/macros/latex/contrib/paracol/bgpaint.dtx
@@ -0,0 +1,601 @@
+% \backgroundcolor{t}[rgb]{0.7,0,0}
+% \backgroundcolor{b}[rgb]{0.8,0.6,0}
+% \backgroundcolor{l}[rgb]{0,0,0.7}
+% \backgroundcolor{r}[rgb]{0,0.7,0}
+% \backgroundcolor{c[0]}[rgb]{1,0.8,1}
+% \backgroundcolor{c[1]}[rgb]{1,1,0.8}
+% \backgroundcolor{g}[rgb]{0.8,1,1}
+% \backgroundcolor{f}[rgb]{0.8,0,1}
+% \backgroundcolor{n}[rgb]{0.8,0.6,1}
+% \backgroundcolor{p}[rgb]{0.8,1,0.6}
+% \backgroundcolor{s}[rgb]{0.8,0.8,0.8}
+% \pagerim5pt
+% 
+% \section{Examples of Background Painting}
+% \label{sec:bgpaint}
+% \subsection{Fundamental Painting}
+% \label{sec:bgpaint-fund}
+% \twosided[pcm]
+% 
+% As you undoubtedly notice, this page and a few pages following it are
+% colorfully painted.  For this and the next three pages, the author
+% declared the \bground{} color of each region as follows.
+% 

+% \begin{itemize}\item[]
+% |\backgroundcolor{t}[rgb]{0.7,0,0}       % dark red for top margin|\\
+% |\backgroundcolor{b}[rgb]{0.8,0.6,0}     % dark orange for bottom margin|\\
+% |\backgroundcolor{l}[rgb]{0,0,0.7}       % dark blue for left margin|\\
+% |\backgroundcolor{r}[rgb]{0,0.7,0}       % dark green for right margin|\\
+% |\backgroundcolor{c[0]}[rgb]{1,0.8,1}    % pink for colunmn-0|\\
+% |\backgroundcolor{c[1]}[rgb]{1,1,0.8}    % cream yellow for column-1|\\
+% |\backgroundcolor{g}[rgb]{0.8,1,1}       % light blue for the gap|\\
+% |\backgroundcolor{f}[rgb]{0.8,0,1}       % purple for page-wise floats|\\
+% |\backgroundcolor{n}[rgb]{0.8,0.6,1}     |

+%     |% light purple for page-wise footnotes|\\
+% |\backgroundcolor{p}[rgb]{0.8,1,0.6}     |

+%     |% pale green for pre/post-environment|\\
+% |\backgroundcolor{s}[rgb]{0.8,0.8,0.8}   % light gray for spanning texts|
+% \end{itemize}
+% 

+% \SpecialUsageIndex{\backgroundcolor}

+% 

+% Therefore, the \bground{} of this |p|re-environment paragraph and other
+% stuff above is painted by pale green.
+% 

+% \Index{pre-environment stuff}

+% 

+% Since the author set \Uidx{\!\pagerim!} to be 5\,|pt|, you will see
+% unpainted strips of 5\,|pt| wide at all paper edges surrounding painted
+% regions.  For this and the next three pages, \Uidx{\!\twosided!}|[pcm]| is
+% declared to enable |p|, |c| and |m| features but to disable the |b|
+% feature.  Therefore, though this page \pageref{sec:bgpaint} is even and
+% thus the left outside margin is wider than the right inside one, the
+% \bground{}s of |l|(eft) and |r|(ight) margins are painted by dark blue and
+% dark green respectively.
+% \par\bigskip
+% 

+% \begin{paracol}{2}
+% This column-0 is now right and inside because of the |c| feature of
+% \!\twosided! is enabled.  On the other hand, the \bground{} is this column
+% is painted by pink because \!\backgroundcolor! for |c[0]| specifies so.
+% That is, the column ordinals optionally given to |c|(olumn) (and |g|(ap))
+% regions are \emph{logical} ones not always corresponding to their
+% \emph{physical} positions in a page.
+% 
+% \switchcolumn
+% \begingroup\it
+% As explained in the right column-0, the \bground{} of this left and
+% outside column-1 is painted by cream yellow as
+% {\rm\!\backgroundcolor!|{c[1]}|} specifies.  Now we have a
+% {\rm\!\switchcolumn!|*|} with a \mctext{} to show the \bgpaint{} for
+% it\footnote{

+% 

+% Since the footnotes in this \env{paracol} environment are \scfnote{} and
+% \mgfnote{}, and \!\backgroundcolor!\texttt{\char`\{n\char`\}} specifies
+% light purple, the \bground{} of this (foot)|n|(ote) region is painted by
+% the color.}.
+% 

+% \par\endgroup
+% \switchcolumn*[\subsection*{The background of this |s|(panning text)
+% region is painted by light gray}\medskip]
+% 
+% \begin{figure*}\nosv
+% \def\arraystretch{0.8}
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     \texttt{f}(loat) region for this page-wise figure is painted by purple\\ 
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Page-Wise Figure}
+% \end{figure*}
+% 
+% This paragraph is to show how the first line of a paragraph just below a
+% \mctext{} is placed in the painted region.
+% \par\vfill
+% 
+% \switchcolumn
+% \begingroup\it
+% See the right column for the reason why this paragraph is here.
+% \par\vfill
+% 
+% See the right column for what we are now doing.
+% \par\endgroup
+% \switchcolumn
+% 
+% Now we have a \!\flushpage! to see the \bgpaint{} for a material not shown
+% in the page, i.e., a page-wise float.
+% \flushpage
+% 
+% Since we are now in an odd-numbered page \pageref{page:bgpaint2}, this
+% column-0 is now a left one and is still painted by pink of course.
+% \par\vfill\label{page:bgpaint2}
+% 
+% This paragraph is to show how the last line of a page without \Scfnote{}s
+% is placed in the painted region.
+% \par\newpage
+% 
+% This page is to show how the page without any \pwstuff{} looks like.
+% \par\vfill
+% 
+% Shortly we will close this \env{paracol} environment in the next page.
+% \par\newpage
+% 
+% Now we are closing this \env{paracol} environment to show how its
+% \postenv{} is painted.
+% 
+% \switchcolumn
+% \begingroup\it
+% As expected, the \bground{} of this column-1 is still painted by cream
+% yellow.
+% \par\vfill
+% 
+% See the comment in the left column.
+% \par\newpage
+% 
+% See the right column for the reason why we have this almost blank page.
+% \par\vfill
+% 
+% See the right column for what will happen shortly.
+% \par\newpage
+% 
+% See the left column for the reason why we are now closing the environment.
+% \endgroup
+% \end{paracol}
+% \bigskip
+% 

+% The \bground{} of this paragraph in |p|(ost-environment) region is also
+% painted by pale green, because \postenv{} can be \preenv{} at the same
+% time as we see shortly.  \par\bigskip
+% 
+% \begin{paracol}{2}
+% This short \env{paracol} environment illustrates how the \preenv{} of this
+% environment, or the \postenv{} of the last environment in other words, is
+% painted.
+% 
+% \switchcolumn
+% \begingroup\it
+% Therefore, the author does not have much to say in this column, except for
+% giving a footnote here\footnote{

+% 

+% Since this footnote is \mgfnote{} with that in the \postenv{}, it is
+% considered as a part of \postenv{} and thus painted by pale green rather
+% than light purple.\label{fn:bgpaint1}}.
+% \endgroup
+% \end{paracol}
+% \bigskip
+% 
+% Before moving to the next example, one caution is given for \bgpaint{} of
+% \Mgfnote{}s.  As the footnote \ref{fn:bgpaint1} itself says, \Mgfnote{}s
+% given in the \lpage{} of a \env{paracol} environment are considered as
+% belonging to \postenv{}.  Therefore, the footnote \ref{fn:bgpaint1} is
+% painted by pale green as well as another footnote given now\footnote{

+% 

+% Since this footnote really belongs to \postenv{}, its \bground{} is painted
+% by pale green naturally.}.
+% \par\label{page:bgpaint4}
+% 
+% 
+% 
+% \newpage
+% \backgroundcolor{t(0pt,0pt)(0pt,-4pt)}[rgb]{0.7,0,0}
+% \backgroundcolor{b(0pt,-4pt)(0pt,0pt)}[rgb]{0.8,0.6,0}
+% \backgroundcolor{l(0pt,4pt)(-4pt,4pt)}[rgb]{0,0,0.7}
+% \backgroundcolor{r(-4pt,4pt)(0pt,4pt)}[rgb]{0,0.7,0}
+% \backgroundcolor{c[0](4pt,4pt)}[rgb]{1,0.8,1}
+% \backgroundcolor{c[1](4pt,4pt)}[rgb]{1,1,0.8}
+% \backgroundcolor{g(-4pt,4pt)}[rgb]{0.8,1,1}
+% \backgroundcolor{f(4pt,4pt)(4pt,-4pt)}[rgb]{0.8,0,1}
+% \backgroundcolor{n(4pt,-4pt)(4pt,4pt)}[rgb]{0.8,0.6,1}
+% \backgroundcolor{p(4pt,4pt)}[rgb]{0.8,1,0.6}
+% \backgroundcolor{s(4pt,-4pt)}[rgb]{0.8,0.8,0.8}
+% 
+% \subsection{Mirrored Painting and Enlarging/Shrinking/Shifting Regions}
+% \label{sec:bgpaint-me}
+% \twosided
+% 
+% At a glance, this and the next three pages look painted similarly to
+% previous four pages, but by a careful examination you should notice
+% two important differences.  The first one is found in the colors
+% of left and right margins.  As the author enabled all features of
+% \Uidx{\!\twosided!} including |b| for \mirror{}ing and we are now in an
+% even-numbered page \pageref{sec:bgpaint-me}, the left and outside margin
+% is painted by dark green for the region |r|(ight margin), while the right
+% and inside one is painted by dark blue for |l|(eft margin).
+% 
+% The other is that regions are enlarged, shrunk or shifted by 4\,|pt| by
+% the following \!\backgroundcolor! commands with extensions.
+% 

+% \begin{itemize}\item[]
+% |\backgroundcolor{t(0pt,0pt)(0pt,-4pt)}[rgb]{0.7,0,0}   |

+%     |% B up|\\
+% |\backgroundcolor{b(0pt,-4pt)(0pt,0pt)}[rgb]{0.8,0.6,0} |

+%     |% T down|\\
+% |\backgroundcolor{l(0pt,4pt)(-4pt,4pt)}[rgb]{0,0,0.7}   |

+%     |% R left T/B outside|\\
+% |\backgroundcolor{r(-4pt,4pt)(0pt,4pt)}[rgb]{0,0.7,0}   |

+%     |% L right T/B outside|\\
+% |\backgroundcolor{c[0](4pt,4pt)}[rgb]{1,0.8,1}          |

+%     |% all edges outside|\\
+% |\backgroundcolor{c[1](4pt,4pt)}[rgb]{1,1,0.8}          |

+%     |% all edges outside|\\
+% |\backgroundcolor{g(-4pt,4pt)}[rgb]{0.8,1,1}            |

+%     |% L/R inside & T/B outside|\\
+% |\backgroundcolor{f(4pt,4pt)(4pt,-4pt)}[rgb]{0.8,0,1}   |

+%     |% L/R outside & T/B up|\\
+% |\backgroundcolor{n(4pt,-4pt)(4pt,4pt)}[rgb]{0.8,0.6,1} |

+%     |% L/R outside & T/B down|\\
+% |\backgroundcolor{p(4pt,4pt)}[rgb]{0.8,1,0.6}           |

+%     |% all edges outside|\\
+% |\backgroundcolor{s(4pt,-4pt)}[rgb]{0.8,0.8,0.8}        |

+%     |% L/R outside & T/B inside|
+% \end{itemize}
+% 

+% \SpecialUsageIndex{\backgroundcolor}

+% 

+% In the comments above, |L|(eft), |R|(ight), |T|(op) and |B|(ottom) mean
+% edges moved by a given extension.  Therefore, for example,
+% ``|L/R outside & T/B up|'' for |f|(loat) region means it is enlarged
+% horizontally and shifted up vertically by the asymmetric extension
+% |(4pt,4pt)(4pt,-4pt)|.  These a little bit complicated setting of
+% extensions are to solve the problems in the fundamental example shown in
+% previous four pages, namely too strict definition of the regions to be
+% painted.  That is, both vertical edges of regions having texts, e.g.,
+% |c|(olumn) regions, should look too close to the first and last letters.
+% Similarly both horizontal edges of those regions seem too close especially
+% when the first line is tall (e.g., the section title in
+% p.\Tie\pageref{sec:bgpaint} and the page-wise figure in
+% p.\Tie\pageref{page:bgpaint2}) and the last line of a column is followed by
+% \mctext{} or \postenv.  Therefore, the author made fine tuning moving
+% inside edges of margins outside, and so on.  We will come back this issue
+% after exemplifying the effect of the tuning.
+% \par\bigskip
+% 

+% \advance\skip\footins4pt\relax
+% \begin{paracol}{2}
+% By the tuning to enlarge this |c|(olumn) region, this paragraph has
+% comfortable spaces above and below it, as well as at the both side edges.
+% 
+% \switchcolumn
+% \begingroup\it
+% This paragraph is surrounded by spaces of a small but comfortable amount as
+% well.\footnote{

+% 

+% Shifting this (foot)|n|(ote) region down a little bit, the space below this
+% footnote and above the top edge of the |b|(ottom margin) region is enlarged.}.
+% 

+% \par\endgroup
+% \switchcolumn*[\subsection*{The background of this |s|(panning text)
+% region is painted by light gray and enlarged horizontally but shrunk
+% vertically}\par\medskip]
+% 
+% \begin{figure*}\nosv
+% \def\arraystretch{0.8}
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     shifting up this \texttt{f}(loat) region gives us a small space above
+%     the top edge of the rectangle\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Page-Wise Figure}
+% \end{figure*}
+% 
+% This paragraph is to show how well the first line of a paragraph just below a
+% \mctext{} is separated from the boundary of two painted regions.
+% \par\vfill
+% 
+% \switchcolumn
+% \begingroup\it
+% See the right column for the reason why this paragraph is here.
+% \par\vfill
+% 
+% See the right column for what we are now doing.
+% \par\endgroup
+% \switchcolumn
+% 
+% By enlarging this |c|(olumn) region and shift the (foot)|n|(ote) region
+% down, this paragraph has a comfortable amount of space below it.
+% \flushpage
+% 
+% Similarly to other paragraphs below \pwstuff, this paragraph is well
+% separated from the bottom edge of the |f|(loat) region above.
+% 
+% \par\vfill\label{page:bgpaint-me2}
+% 
+% As in the case of the line above \Scfnote{}s, the last line of this
+% paragraph has a sufficient space separating it from the top edge of the
+% |b|(ottom margin) region.
+% \par\newpage
+% 
+% This page is to show how the page without any \pwstuff{} looks like.  As
+% you are seeing, the space above this paragraph is sufficient and
+% comfortable.
+% \par\vfill
+% 
+% Shortly we will close this \env{paracol} environment in the next page.
+% \par\newpage
+% 
+% Now we are closing this \env{paracol} environment to show how this
+% paragraph is separated from the boundary of |c|(olumn) and
+% |p|(ost-environment) regions.
+% 
+% \switchcolumn
+% \begingroup\it
+% See the comment in the left column for the intention of placing this
+% paragraph here.
+% \par\vfill
+% 
+% See the comment in the left column, too.
+% \par\newpage
+% 
+% See the right column for the reason why we have this almost blank page.
+% \par\vfill
+% 
+% See the right column for what will happen shortly.
+% \par\newpage
+% 
+% See the left column for the reason why we are now closing the environment.
+% \endgroup
+% \end{paracol}
+% \bigskip
+% 

+% The \bground{} of this paragraph in |p|(ost-environment) region is
+% painted by pale green as done in p.\Tie\pageref{page:bgpaint4}, but its top
+% and bottom edges \emph{look} shifted down and up to give spaces below and
+% above the last and first paragraphs in \env{paracol} environments,
+% respectively.
+% \par\bigskip
+% 
+% \begin{paracol}{2}
+% This short \env{paracol} environment illustrates how the \preenv{} of this
+% environment, or the \postenv{} of the last environment in other words, is
+% painted.
+% 
+% \switchcolumn
+% \begingroup\it
+% Therefore, the author does not have much to say in this column, except for
+% giving a footnote here\footnote{

+% 

+% As the footnote \ref{fn:bgpaint1} in p.\Tie\pageref{fn:bgpaint1}, this
+% \Mgfnote{} is a part of \postenv{} and thus painted by pale green rather
+% than light purple.\label{fn:bgpaint-me1}}.
+% \endgroup
+% \end{paracol}
+% \bigskip
+% 
+% In the setting with \!\backgroundcolor! commands in
+% p.\Tie\pageref{sec:bgpaint-me}, the author carefully moved contacting edges
+% of regions.  For example, to enlarge |c|(olumn) regions, the inside edges
+% of |l|(eft margin) and |r|(ight margin) regions are moved outside, and both
+% vertical edges of the |g|(ap) region shifted toward its inside.  As for
+% the horizontal edges, the bottom edges of |t|(op margin) and |f|(loat)
+% regions are moved up, the top edges of |b|(ottom margin) and
+% (foot)|n|(ote) regions are moved down, and both top and bottom edges of
+% the |s|(panning text) region are shifted toward its inside.
+% 
+% These edge shifting could make a region too narrow or too much shifted
+% resulting in a material in it overreaching its boundary, especially in
+% vertical shifting of horizontal edges.  However we can exploit some large
+% space automatically or manually inserted above and/or below the material
+% to avoid overreaching.  That is the author exploited the following spaces;
+% \!\headsep! below the page head (though it is empty in this document);
+% \!\dbltextfloatsep! below the bottom-most page-wise float; spaces that
+% \!\subsection!|*| inserts above and below it together with manually
+% inserted \!\medskip! below it; \!\skip!\!\footins!\footnote{

+% 

+% This is a kind of ``length command'' maybe not widely known.}
+% 

+% above the first footnote which the author enlarged by 4\,|pt| temporarily
+% for this and the next subsections; and \!\footskip! from the bottom edge
+% of text area to that of the page number.
+% 
+% Now you might notice that the explanation above does not mention the |p|
+% region for \Preenv{} and \postenv.  As you should find in the settings,
+% this region is enlarged horizontally \emph{and vertically} so that its top
+% and bottom edges are moved up and down when the region is at the top or
+% bottom of a page, as you are seeing now and find in
+% p.\Tie\pageref{sec:bgpaint-me}.  However, this enlargement of course has a
+% side effect that the region collides against |c|(olumn) and |g|(ap) regions
+% also enlarged vertically making them overlapped.  This overlap will be
+% invisible with most of \emph{printers} because, as shown in
+% Section\Tie\ref{sec:ref-bgpaint}, |p| region is painted \emph{before} |c|
+% and |g| regions are painted.  In addition, since relatively large spaces
+% of \!\bigskip! are manually inserted before each \beginparacol{} and after
+% each \Endparacol{}, texts in \Preenv{} and \postenv{} are well separated
+% from region boundaries.
+% 
+% This overlay painting |c| and |g| over |p|, however, might produce an
+% unexpected result with some printer with which, for example, two colors
+% are \emph{blended} in the thin overlapped strip\footnote{

+% 

+% For example, a dvi previewer |dviout| produces such a blended result with
+% the default setting of coloring.}.
+% 

+% Unfortunately, this overlay painting is inevitable in the current version
+% 1.3, but in a future version, hopefully 1.4, more sophisticated
+% \emph{position-dependent} region definition, for example, to shift the top
+% edge of |p| region only when the region is at the top of page, could be
+% introduced.
+% 
+% Another remark is that the \mirror{}ing specified by the |b| feature of
+% \!\twosided! works not only on the colors of side margins but also on
+% their asymmetric shrinkage.  That is, the asymmetric shifts of vertical
+% edges of |l| and |r| regions correctly performed irrespective of their
+% physical positions, i.e., even when the |l| (resp.\ |r|) region is at
+% the right (resp.\ left) margin and the edge to be shift is the left
+% (resp.\ right) one rather than right (resp.\ left).
+% 
+% 
+% 
+% \newpage \suppressfloats
+% \nobackgroundcolor{t}
+% \nobackgroundcolor{b}
+% \nobackgroundcolor{l}
+% \nobackgroundcolor{r}
+% \nobackgroundcolor{g}
+% \backgroundcolor{c[0](4pt,4pt)(0.5\columnsep,4pt)}[rgb]{1,0.8,1}
+% \backgroundcolor{c[1](0.5\columnsep,4pt)(4pt,4pt)}[rgb]{1,1,0.8}
+% \backgroundcolor{C[0](10000pt,10000pt)(0.5\columnsep,10000pt)}[rgb]{1,0.8,1}
+% \backgroundcolor{C[1](0.5\columnsep,10000pt)(10000pt,10000pt)}[rgb]{1,1,0.8}
+% 
+% \subsection{Regions with Infinite Extensions}
+% \label{sec:bgpaint-inf}
+% 
+% You are now seeing another \bgpaint{} much different from previous two
+% examples.  That is, after disabling painting of |t|, |b|, |l|, |r| and |g|
+% regions by \Uidx{\!\nobackgroundcolor!}, the author gave the followings
+% for painting this and the next pages.
+% 

+% \begin{itemize}\item[]
+% |\backgroundcolor|

+%     |{c[0](4pt,4pt)(0.5\columnsep,4pt)}[rgb]{1,0.8,1}|\\
+% |\backgroundcolor|

+%     |{c[1](0.5\columnsep,4pt)(4pt,4pt)}[rgb]{1,1,0.8}|\\
+% |\backgroundcolor|

+%     |{C[0](10000pt,10000pt)(0.5\columnsep,10000pt)}[rgb]{1,0.8,1}|\\
+% |\backgroundcolor|

+%     |{C[1](0.5\columnsep,10000pt)(10000pt,10000pt)}[rgb]{1,1,0.8}|
+% \end{itemize}
+% 

+% \SpecialUsageIndex{\backgroundcolor}

+% 

+% The first two lines above is different from the previous declaration
+% because inside edges of |c[0]| and |c[1]| regions are shifted toward
+% outside of them and thus inside of unpainted |g| region so that the edges
+% are contacted.  On the other hand, the last two lines are for
+% \emph{under-painting} of columns and has \emph{\bginfext} to make top,
+% bottom and outside edges of |C| regions reaching to the corresponding
+% paper edges.  Since this under-painting is done with colors same as those
+% of over-painting of |c| regions, you will have an impression that the
+% paper is two-toned and \pwstuff{} are pasted on the paper\footnote{

+% 

+% This footnote is given outside \env{paracol} environment but its
+% \bground{} is painted by light purple because it is merged with the
+% footnote \ref{fn:bgpaint-inf2}.\label{fn:bgpaint-inf1}}.
+% 

+% \par\bigskip
+% 

+% \begin{figure}\nosv
+% \def\arraystretch{0.8}
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     \parbox{.8\textwidth}{

+% 	This \texttt{f}(loat) region could be extended to both side edges
+%	and the top edge of the paper if its extension were
+%	\texttt{(10000pt,10000pt)(10000pt,-4pt)}.}\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Page-Wise Figure \emph{Imported} from Pre-Environment}
+% \label{fig:bgpaint-inf}
+% \end{figure}
+% 

+% \begin{paracol}{2}
+% Though you cannot see, the right edge of this over-painted |c[0]| region
+% is shifted right by 4\,|pt| to hide the small patch at the right bottom
+% corner of the |p| region above by overlaying.
+% 
+% \switchcolumn
+% \begingroup\it
+% As explained in the right column, this {\rm|c[1]|} region also has an
+% invisible left edge shifted left by {\rm4\,|pt|}\footnote{

+% 

+% This (foot)|n|(ote) region could be extended to both side edges and the
+% bottom edge of the paper if its extension were
+% \texttt{(10000pt,-4pt)(10000pt,10000pt)}.\label{fn:bgpaint-inf2}}.
+% \endgroup
+% 
+% \switchcolumn*[\subsection*{This \texttt{s}(panning text) region could be
+% extended to both side edges of the paper if its extension were
+% \texttt{(10000pt,-4pt)}.}\par\medskip]
+% 
+% The author does not have much to say now for this column chunk.
+% \par\vfill
+% 
+% Still nothing to say particular to the page break we will have shortly.
+% \par\newpage
+% 
+% This paragraph is just for keeping the \env{paracol} environment alive in
+% this page.
+% \switchcolumn
+% 
+% \begingroup\it
+% Little to say as well.
+% \par\vfill
+% 
+% Nothing to say as well.
+% \par\newpage
+% 
+% This paragraph is not necessary for keeping alive the environment but is
+% given for consistent view.
+% \endgroup
+% 
+% \begin{figure*}\nosv
+% \def\arraystretch{0.8}
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     \parbox{.8\textwidth}{

+% 	This figure is given in the \env{paracol} environment closed in the
+%	previous page but its background is not painted.}\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Page-Wise Figure \emph{Exported} to Post-Environment}
+% \label{fig:bgpaint-inf2}
+% \end{figure*}
+% \end{paracol}
+% \bigskip
+% 
+% Note that overlay painting is inevitable for two-toned page painting, as
+% far as you want to paint \bground{} of \pwstuff.
+% 
+% The last issue of \bgpaint{} is about painting materials given outside
+% \env{paracol}.  As you have seen, \Preenv{} and \postenv{} are painted but
+% it is done only when they reside in a page having a portion of a
+% \env{paracol} environment (maybe) of course.  Therefore, the next page is
+% \emph{not} painted because the page does not have any parallel-columned
+% stuff.  Therefore, even if you wish to paint the whole of your document
+% including pages without \env{paracol} stuff, you cannot do it just with
+% \Paracol{} package, at least so far.
+% 
+% On the other hand, some materials given outside \env{paracol} environments
+% are painted as if they are given in the environment when they are
+% \emph{imported} into the environment.  One category has footnotes given in
+% \preenv{} when \!\footnotelayout!|{m}| is specified for merging, as
+% exemplified by the footnote \ref{fn:bgpaint-inf1} in the previous page.
+% Note that such a footnote is painted by the color for |n| region rather
+% than |p| region even when there are no footnotes in the \env{paracol}
+% environment.  The other category has ordinary floats given by \env{figure}
+% and/or \env{table}
+% (i.e., neither \env{figure*} nor \env{table*}) environments outside
+% \env{paracol} and then \emph{deferred} to a page having (a portion of)
+% stuff produced by \env{paracol}.  Since such a float, e.g.,
+% Figure\Tie\ref{fig:bgpaint-inf} in this page, is considered as a page-wise
+% float given in the \env{paracol} environment in this section, its
+% background is painted by the color for the |f| region, rather than that
+% for the |p| region which would be used if the float were is placed in the
+% previous page.  Note that such a deferred float import could occur not
+% only from the page having \beginparacol{} but also from pages preceding
+% it.  For example, if you have three \env{figure} environments in a page
+% $p-1$ just preceding the page $p$ in which you start a \env{paracol}
+% environment, it could happen that first one is placed in $p-1$ without
+% painting, the second is placed in $p$ and painted by the color for |p|,
+% and the third is placed in $p+1$ and painted by the color for |f|.
+% 
+% Finally some materials \emph{exported} from a \env{paracol} environment
+% are painted as if they are in \postenv.  In previous two subsections, we
+% saw \Mgfnote{}s (e.g., \ref{fn:bgpaint1} in p.\Tie\pageref{fn:bgpaint1}
+% and \ref{fn:bgpaint-me1} in p.\Tie\pageref{fn:bgpaint-me1}) are painted by
+% the color of |p| rather than |n|.  The other kind of exportation is of
+% page-wise floats given in a \env{paracol} environment but deferred to the
+% page next to the page having \Endparacol, or further.  For example,
+% Figure~\ref{fig:bgpaint-inf2} is given in the \env{paracol} environment
+% above in this page, but its \bground{} is not painted because the next page
+% in which the figure is placed does not have any parallel-columned
+% stuff\footnote{

+% 

+% If it has, the background is painted by the color for |p|.}.
+% 

+% \newpage\vspace*{\fill}
+% \centerline{(intentionally blanked page to show this page is \emph{not}
+% painted)}
+% \vfill
+% \advance\skip\footins-4pt\relax
+% \endinput
diff --git a/macros/latex/contrib/paracol/impl.dtx b/macros/latex/contrib/paracol/impl.dtx
new file mode 100644
index 0000000000..4d7893f019
--- /dev/null
+++ b/macros/latex/contrib/paracol/impl.dtx
@@ -0,0 +1,19562 @@
+% \section{Overview}
+% \label{sec:imp-ovv}
+% 
+% \subsection{Column-Pages}
+% \label{sec:imp-ovv-colpage}
+% 
+% In our parallel multi-column typesetting, a column may grow independently
+% of other columns and may cross its page boundary asynchronously with
+% others.  Therefore, we cannot throw away the contents of a column in a
+% page, or a {\em\Uidx\colpage} in short, when a page break occurs in the
+% column.  Instead, we have to keep \colpage{}s until all columns are
+% {\em\Uidx\sync{}ed} implicitly or explicitly.
+% 
+% An {\em\Uidx\imsync} takes place when all columns in a page see
+% page-breaks to let the page is shipped out.  In general, all columns but
+% the last one which arrives the page-break have completed \colpage{}s in the
+% page in question and some of them may have succeeding \colpage{}s.
+% Therefore, we maintain the list of completed \colpage{}s
+% $\Uidx\S_c=|\pcol@shipped|{\cdot}c$
+% 

+% \SpecialArrayMainIndex{c}{\pcol@shipped}

+% 

+% for each column $c\In0\C$, where $\Uidx\C=\!\pcol@ncol!$ is the number of
+% columns given through the argument of \env{paracol} environment, and the
+% set of them $\Uidx\SS=\Set{\S_c}{c\In0\C}$.
+% 
+% Each element $\Uidx\s_c(p)$ of a list $\S_c$ is an \!\insert! whose
+% \!\vbox! contains the 
+% $p$-th completed \colpage\footnote{

+% 

+% Other registers such as \cs{count} are not used.},
+% 

+% where $p=0$ for the first \colpage{} produced in \env{paracol}
+% environment or that following a page flushing macro \!\flushpage!,
+% \!\clearpage! or \!\cleardoublepage!.  That is, $\S_c$ is defined as
+% follows, where $\Uidx\pbase=\!\pcol@basepage!$ is the zero-origin ordinal
+% of the {\em\Uidx\bpage} being the oldest page not shipped out yet.
+% 

+% \begin{eqnarray*}
+% \S_c&=&(\s_c(\pbase),\s_c(\pbase{+}1),\ldots,\s_c(\pbase{+}k{-}1))\\
+% &=&\!\@elt!\,\s_c(\pbase)\;\!\@elt!\,\s_c(\pbase{+}1)\;\cdots\;
+% 	\!\@elt!\,\s_c(\pbase{+}k{-}1)
+% \end{eqnarray*}
+% 

+% Note that a list $\S_c$ can be empty and all members in $\SS$ may be empty.
+% 
+% The other type of \sync{}ation, {\em\Uidx\exsync}, takes place by
+% \!\switchcolumn!|*| or the beginning of starred \csenv{}s, by
+% \Endparacol, or by one of page flushing macros \!\flushpage!, 
+% \!\clearpage! and \!\cleardoublepage!.  A flushing \exsync{} ships out the
+% pages from $\pbase$ to $\Uidx\ptop=\!\pcol@toppage!$ being the ordinal of
+% the {\em\Uidx\tpage} to which the most advanced {\em\Uidx\lcolumn} has
+% reached.  On the other hand, other non-flushing \exsync{} keeps the page
+% $\ptop$ from being shipped out because the \colpage{}s in it or the page
+% itself will grow further.
+% 
+% 
+% 
+% \subsection{Current Column-Pages and Their Contexts}
+% \label{sec:imp-ovv-ccol}
+% \changes{v1.3-4}{2013/09/17}
+%	{Remove $\mu$ for \cs{@mparbottom} from column-context because it is
+%	 now in page context.}

+% 
+% We also have to maintain another type of \colpage{}s which are currently
+% built, or {\em\Uidx\ccolpage{}s} in short, to switch from a column to
+% another.  Since each column may have its own {\em context} for the
+% typsetting of it, or {\em\Uidx\cctext} in short, it were perfect to save
+% the context when we leave from a 
+% column and to restore that when we revisit the column if we could.
+% However, \TeX{} and \LaTeX{} has a tremendously large number of context
+% variables and the number becomes virtualy boundless when we take variables
+% defined in various styles and by users themselves into account.
+% Therefore, we had to abandon to keep the whole context of the column but
+% carefully chose a small subset comprising variables automatically modified
+% outside of users' control.  That is, the \cctext{}
+% $\Uidx\cc_c=|\pcol@col|{\cdot}c$
+% 

+% \SpecialArrayMainIndex{c}{\pcol@col}

+% 

+% of a column $c$ consists of the following elements, each of which named
+% $e$ is referred to as $\cc_c(e)$ hereafter.
+% 

+% \begin{itemize}
+% \item $\Uidx\vb$
+% represents $\!\insert!{\cdot}\vb$ containing the followings.
+% 

+% \begin{itemize}
+% \item
+% $\vb^b=\!\box!{\cdot}\vb=\!\@holdpg!$ is the \!\vbox! containing the main
+% vertical list which has already contributed to the \ccolpage{}.
+% 
+% \item
+% $\vb^p=\!\count!{\cdot}\vb=\!\pcol@page!$ means the \ccolpage{} belongs to
+% the page $\vb^p$.
+% 
+% \item
+% $\vb^r=\!\dimen!{\cdot}\vb=\!\@colroom!$ is the room of the column.
+% \end{itemize}
+% 
+% \item $\Uidx\ft=\Midx{\!\pcol@currfoot!}$
+% is the \!\insert! containing the footnotes added in the \ccolpage, if
+% \Mcfnote{} typesetting is in effect.  Its constituent \!\box!, \!\count!,
+% \!\dimen! and \!\skip! are denoted as $\ft^b$, $\ft^c$, $\ft^d$ and
+% $\ft^s$ respectively.  On the other hand, if \Scfnote{} typesetting is in
+% effect, $\ft$ is always empty\footnote{

+% 

+% But the macro \cs{pcol@currfoot} is used to keep \Scfnote{}s temporarily.}.
+% 
+% \item $\Uidx\pd=\!\pcol@prevdepth!$
+% is the depth of the last vertical item in $\vb^b$ obtained by
+% \!\prevdepth!.
+% 
+% \item $\Uidx\tl=\!\@toplist!$
+% is the list of top floats inserted in the \ccolpage.
+% 
+% \item $\Uidx\ml=\!\@midlist!$
+% is the list of mid floats inserted in the \ccolpage.
+% 
+% \item $\Uidx\bl=\!\@botlist!$
+% is the list of bottom floats inserted in the \ccolpage.
+% 
+% \item $\Uidx\dl=\!\@deferlist!$
+% is the list of \cwise{} floats deferred to the next \colpage.
+% 
+% \item $\Uidx\tf=\!\pcol@textfloatsep!$
+% is the vertical skip used instead of \!\textfloatsep! for top floats in the
+% \ccolpage{} if it has \sync{}ation points, or $\infty$ otherwise.
+% 
+% \item $\Uidx\fh=\!\@textfloatsheight!$
+% is the total height of mid floats and their separators in the \ccolpage.
+% 
+% \item $\Uidx\tn=\!\@topnum!$
+% is the maximum number of top floats which the \ccolpage{} can accommodate
+% further.
+% 
+% \item $\Uidx\tr=\!\@toproom!$
+% is the room for top floats in the \ccolpage.
+% 
+% \item $\Uidx\bn=\!\@botnum!$
+% is the maximum number of bottom floats which the \ccolpage{} can accommodate
+% further.
+% 
+% \item $\Uidx\br=\!\@botroom!$
+% is the room for bottom floats in the \ccolpage.
+%
+% \item $\Uidx\cn=\!\@colnum!$
+% is the maximum total number of floats which the \ccolpage{} can accommodate
+% further.
+% 
+% \item $\Uidx\sw$
+% is the following encoding of \CSIndex{if@nobreak} and
+% \CSIndex{if@afterindent} at the time we left from the column $c$.
+% $$
+% \sw=\cases{0&$\CSIndex{if@nobreak}=\false$\cr
+%            1&$\CSIndex{if@nobreak}=\true\;\land\;
+%               \CSIndex{if@afterindent}=\true$\cr
+%            2&$\CSIndex{if@nobreak}=\true\;\land\;
+%               \CSIndex{if@afterindent}=\false$}
+% $$
+% Note that we have only three states because \CSIndex{if@afterindent} is
+% meaningful only when $\CSIndex{if@nobreak}=\true$\footnote{

+% 

+% If only with the standard \LaTeX{} and so far.}.
+% 
+% \item $\Uidx\ep=\!\everypar!$
+% is the tokens stored in \!\everypar! at the time we left from the column
+% $c$.
+% \end{itemize}
+% 

+% \changes{v1.1}{2012/05/11}
+% 	{Add description of $w_c\EQ\cs{pcol@columnwidth}{\cdot}c$.}

+% 

+% In addition, we have special context variables
+% $\Uidx\w_c=|\pcol@columnwidth|{\cdot}c$
+% 

+% \SpecialArrayMainIndex{c}{\pcol@columnwidth}

+% 

+% in which we keep \!\columnwidth! for the column $c$.
+% 
+% Note that we could add other variables to the saved context and/or provide
+% some API macro to define them by users, but abandon them because it should
+% be too complicated for users\footnote{

+% 

+% And for the author if we include save/restore of macros, though it could
+% be done with a \cs{toks} containing the \cs{def}initions of macros.}.
+% 

+% Also note that we provide a save/restore mechanism for \lcounter{}s as
+% discussed in \secref{sec:imp-ovv-counter}.
+% 
+% 
+% 
+% \subsection{Pages and Their Contexts}
+% \label{sec:imp-ovv-page}
+% \changes{v1.2-2}{2013/05/11}
+%	{Redesign page context and its implementation.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add $\pi^s(p)$ to the page context of $p$ for column-separating
+%	 rule drawing and background painting.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add $\pi^m(p)$ to the page context of $p$ for marginal note
+%	 placement.}

+% 
+% Besides the \colpage{}s, we have to keep track each whole page not yet
+% shipped out but has some complete or incomplete (i.e., current) \colpage{}s.
+% We maintain the list;

+% 

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

+% \begin{eqnarray*}
+% \Uidx\PP
+% &=&\!\pcol@pages!=(\Uidx\pp(\pbase),\pp(\pbase{+}1),\ldots\pp(\ptop{-}1))\\
+% &=&\!\@elt!\,\pp(\pbase)\;\!\@elt!\,\pp(\pbase{+}1)\;\cdots\;
+%    \!\@elt!\,\pp(\ptop{-}1)\\
+% \pp(p)&=&|{|\pp^p(p)|}|\pp^i(p)\pp^f(p)|{|\pp^s(p)|}||{|\pp^m(p)|}|
+% \end{eqnarray*}
+% 

+% where $\pp(p)$ is the {\em\Uidx\pctext} of $p$ and its elements $\pp^p(p)$,
+% $\pp^i(p)$, $\pp^f(p)$, $\pp^s(p)$ and $\pp^m(p)$ have the followings.
+% 

+% \begin{itemize}
+% \item
+% $\pp^p(p)=\Uidx\page(p)$ is the value of the counter \counter{page}
+% (i.e. \!\c@page!) for the page $p$.
+% 
+% \item
+% Iff $\pp^i(p)\neq\bot$, the page $p$ has \pwise{} floats or the
+% single-column {\em\Uidx\preenv} preceeding \beginparacol{} in the
+% {\em\Uidx\spage} where it resides and spannig all columns.  In this case
+% $\pp^i(p)=i$ represents $\!\insert!{\cdot}i$, often {\em cached}
+% in the macro \!\pcol@spanning!, for such {\em\Uidx\spanning}
+% whose registers have the followings.
+% 

+% \begin{itemize}
+% \item
+% $\pp^b(p)=\!\box!{\cdot}i$ contains the \spanning.
+% 
+% \item
+% $\pp^h(p)=\!\dimen!{\cdot}i=\!\@colht!$ if positive for the height of
+% columns shrunk by the \spanning.  If negative, the page is only for
+% the \spanning, i.e. a {\em\Uidx\fpage}.  We use the notation $\pp^h(p)$
+% for the pages $\pp^i(p)=\bot$ to mean \!\textheight!.
+% 
+% \item
+% $\pp^t(p)=\!\skip!{\cdot}i=\!\pcol@topskip!$ being the value of
+% \!\topskip! at \beginparacol{} to be inserted at the top of each column in
+% each non-first page.  Otherwise, i.e., for the columns in the \spage{}
+% following the \preenv{}, it has 0 to prevent the \!\topskip! insertion.
+% We use the notation $\pp^t(p)$ for the pages $\pp^i(p)=\bot$ to
+% mean \!\pcol@topskip!.
+% \end{itemize}
+% 
+% \item
+% Iff $\pp^f(p)\neq\bot$, \Scfnote{} typesetting, discussed in
+% \secref{sec:imp-ovv-scfnote}, is in effect and the page $p$ has some
+% footnotes in $\!\box!\cdot\pp^f(p)$.  This element is often {\em cached}
+% in the macro \Midx{\!\pcol@footins!}.

+% 

+% \SpecialMainIndex{\pcol@pages}
+% 
+% \item
+% $\pp^s(p)=(\Uidx\spt(H_1,h_1),\ldots,\spt(H_n,h_n))=
+% \!\@elt!\Arg{H_1,h_1}\ldots\!\@elt!\Arg{H_n,h_n}$ is the list of \mctext{}s
+% in the page $p$, where $i$-th one's top edge is at $H_i$ from the top of
+% the page (excluding \spanning) and its height-plus-depth is $h_i$, where
+% $H_i$ and $h_i$ are represented in the form of integers.  Therefore, it is
+% emptied by \!\pcol@startpage!, and then the elements are added by
+% \!\pcol@makecol! (only for the last one) and \!\pcol@output@switch!
+% whenever they find a \mctext{} completes.  The element is often {\em
+% cached} in the macro \!\pcol@sptextlist! and is referred to by
+% \!\pcol@buildcolseprule! to draw \cseprule{} and to paint columns and
+% \csepgap{} leaving spaces for \mctext{}s.  The usage of this element is
+% discussed in \secref{sec:imp-ovv-cswap} a little bit more detailedly.
+% 
+% \item
+% $\pp^m(p)=\Arg{\Uidx\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$
+% is the set of lists of marginal notes in the left ($l$) and right
+% ($r$) margins and in the left ($L$) and right ($R$) \parapag{}es.  The
+% words left and right of margins mean physical left and right, while left
+% and right of \parapag{}es mean the logical ones, i.e., the page where the
+% column-0 resides is left.  Each element $\mpb_{\{L,R\}}^{\{l,r\}}$ has a
+% list $(\Uidx\mpar(t_1,b_1),\ldots,\mpar(t_n,b_n))=
+% \!\@elt!\Arg{t_1}\Arg{b_1}\ldots\!\@elt!\Arg{t_n}\Arg{b_n}$ of marginal
+% notes whose top and bottom are at $t_i$ and $b_i$ from the top of the
+% column area, where $t_i$ and $b_i$ are represented in the form of
+% integers.  Each element can be empty of course, and $\pp^m(p)$ itself can
+% be so as well to mean all elements are empty\footnote{

+% 

+% To minimize the possibility of miscoding for emptying and save a small
+% amount of memory for pages having no marginal notes.}.
+% 

+% Therefore, $\pp^m(p)$ is emptied by
+% \!\pcol@startpage!, and then examined and modified by
+% \!\pcol@addmarginpar! when it adds a marginal note through macros
+% \!\pcol@getmparbottom! and \!\pcol@setmpbelt!.  Another modifier
+% \!\pcol@output@start! initializes one of the element $\mpb_L^{\{l,r\}}$
+% with the value representing the last marginal note in \preenv{}, while
+% another examiner \!\pcol@output@end! lets the outside \!\@mparbottom! have
+% a value based on $b_n$ of one of the element, according to \LaTeX's
+% setting of marginal note placement.  The whole elemnt $\pp^m(p)$ is often
+% {\em cached} in the macro \!\pcol@mparbottom!.  The usage of this
+% element is discussed in \secref{sec:imp-ovv-cswap} a little bit more
+% detailedly.
+% \end{itemize}
+% 

+% Note that even in \parapag{}ing and in \npaired{} one in particular,
+% a page $p$ consists of all columns $c\In0\C$.  Therefore, the term {\em
+% left\slash right \parapag{}e} $p$ always mean the left and right component
+% of a \parapag{}e (pair) $p$.
+% 
+% The reason why we keep track of $\page(p)$ is that page numbering is not
+% necessrary to be consecutive.  If such a {\em jump} occurs randomly in any
+% columns explicitly updating \counter{page}, it is very tough to give a
+% consistent view of the page number of a specific page to all columns.
+% Therefore we suppose jumps occur only in the leftmost column 0\footnote{

+% 

+% But we neither inhibit nor nullify a jump in non-leftmost column and thus
+% the update can be seen referring to \texttt{page} counter explicitly.}
+% 

+% which controls the page numbering, while non-leftmost columns are expected
+% to refer the \counter{page} passively.
+%
+% This page numbering is implemented as follows.  Each time a \colpage{} at
+% $p$ of the leftmost column is completed to start a new \colpage{},
+% $\page(p)$ is fixed to be the value of \counter{page} and
+% $\page(q)=\pp^p(q)$ for all $q\in[p,\ptop]$ are let be $\page(p)+(q-p)$ in
+% usual cases but $\page(p)+2(q-p)$ in \npaired{} \parapag{}ing.
+% This update also takes place on \cswitch{} from the leftmost \colpage{} at
+% $p$ to another column so that a jump happning before the switching is
+% notified to other columns.  On the other hand, starting or \cswitch{} to a
+% non-leftmost \colpage{} at $p$ lets \counter{page} have $\page(p)$
+% referring to $\pp(p)$, unless the column starts the most advanced \tpage.
+% In this new \tpage{} case, $\pp(\ptop{+}1)$ is added to $\PP$ with the
+% temporary setting $\pp^p(\ptop+1)=\page(\ptop+1)=\page(\ptop)+1$ usually but
+% $\pp^p(\ptop+1)=\page(\ptop+1)=\page(\ptop)+2$ in \npaired{}
+% \parapag{}ing, and $\ptop$ is incremented.
+% 
+% Note that this management is imperfect because direct references of
+% \counter{page} in non-leftmost columns can give inconsistent results if 
+% \counter{page} is modified in a non-leftmost column or the reference occurs
+% in a page $p$ after that the leftmost column modifies \counter{page} in a
+% page $q$ such that $q\leq p$.  In addition to them, this mechanism in
+% \npaired{} \parapag{}ing always gives incorrect page number to the
+% columns in a right \parapag{}e because $\pp^p(p)$ always has $\page(p)$
+% for the left \parapag{}e.  However, it is expected that the progress of
+% the leftmost column usually preceeds other columns to give consistent
+% \counter{page} reference even with jumps, unless the reference is made by
+% a column in a right \npaired{} \parapag{}e.  More importantly, it is
+% assured that indirect refereces through |.aux| records and page numbers
+% recorded in |.toc|, |.idx|, and so on are always consistent because of the
+% lazy evaluation of $\counter{page}=\page(p)$ at ship-out of an ordinary
+% page $p$ or a left \parapag{}e $p$, while the counter is let have
+% $\page(p)+1$ when a right \npaired{} \parapag{}e $p$ is shipped out.
+% 
+% Also note that we also keep $\pp(\ptop)$ in \Midx{\!\pcol@currpage!}
+% which is initialized by \!\pcol@output@start! to let $\pp^i(\ptop)$ have
+% the \preenv.  Then the macro is redefined to have the value representing
+% the new page possibly with $\pp^i(\ptop)$ for \pwise{} floats in
+% \!\pcol@startpage! by the macro \!\pcol@defcurrpage!.  Another
+% \!\def!inition is done in \!\pcol@output@switch! also with
+% \!\pcol@defcurrpage! to let $\pp^f(\ptop)$ have \Scfnote{}s built in
+% \!\footins! if \scfnote{} typsetting is in effect and the \cswitch{}
+% leaves the column in $\ptop$\footnote{

+% 

+% The \!\def!inition of \!\pcol@currpage! in \!\pcol@setpnoelt!, and
+% emptying it in \!\pcol@output@start! and \!\pcol@freshpage! are for coding
+% trick and thus not for giving a really new \!\def!initions.}.
+% 

+% We denote the concatenation of $\PP$ and $\pp(\ptop)$ as $\Uidx\PPP$ to
+% represent all pages {\em on-the-fly}.
+% 
+% 
+% 
+% \subsection{Counters}
+% \label{sec:imp-ovv-counter}
+% 
+% Besides the context variables discussed in \secref{sec:imp-ovv-ccol}, we
+% need to make counters local to each column except for those declared to be
+% global by \!\globalcounter!.  Let $\Uidx\CC$ be the set (list) of all
+% counters declared before \beginparacol, i.e., $\CC=\!\cl@@ckpt!$, and
+% $$
+% \Uidx\CG=\!\pcol@gcounters!=\{\Uidx\cg_1,\ldots\}=\!\@elt!|{|\cg_1|}|\cdots
+% $$
+% be the set of {\em\Uidx\gcounter{}s} which have declared so by
+% \!\globalcounter!|{|$\cg_i$|}|.  Then the set of {\em\Uidx\lcounter{}s}
+% $\Uidx\CTL$ is defined as follows.

+% 

+% \SpecialMainIndex{\pcol@counters}
+% $$
+% \CTL=\CC-\CG=\!\pcol@counters!=\{\Uidx\cl_1,\ldots\}=\!\@elt!|{|\cl_1|}|\cdots
+% $$
+% 
+% Since each column has its own values in \lcounter{}s, we have to keep the
+% set of counter\slash value pairs
+% 

+% \SpecialArrayMainIndex{c}{\pcol@counters}

+% $$
+% \Uidx\Cc_c=\!\pcol@counters!{\cdot}c=\{\<\cl_1,\val_c(\cl_1)\>,\ldots\}
+% =\!\@elt!|{|\cl_1|}||{|\val_c(\cl_1)|}|\cdots
+% $$
+% for each column $c$, where $\Uidx\val_c(\cl_i)$ is the value of a counter
+% $\cl_i$ local to $c$.  That is, whenever we switch from a column $c$ to
+% $d$, we save $\<\cl_i,\val_c(\cl_i)\>$ in $\Cc_c$ and restore $\cl_i$ for
+% $d$ by letting it have $\val_d(\cl_i)$ in $\Cc_d$, for all $\cl_i\in\CTL$.
+% 
+% A \gcounter{} is free from these save\slash restore operations but needs
+% another special operation when it is incremented by \!\stepcounter!.  That
+% is, the invocation of \!\stepcounter! for a \gcounter{} $\cg_i$ may clear
+% \lcounter{}s in its set of descendant counters
+% $\Uidx\clist(\cg_i)=|\pcol@cl@|{\cdot}\cg_i$
+% 

+% \SpecialArrayMainIndex{\theta}{\pcol@cl@}

+% 

+% and this clearing must be performed on the all instances of
+% $\cl_j\in\clist(\cg_i)$ saved in $\Cc_c$ for all $c\In0\C$.  Therefore, on
+% the \!\stepcounter!, we do the followings for all $c\In0\C$; temporarily
+% restore all $\cl_k\in\CTL$ from $\Cc_c$; clear all $\cl_j\in\clist(\cg_i)$;
+% and then save $\<\cl_k,\val_c(\cl_k)\>$ back to $\Cc_c$.
+% 
+% The other item we maintain for a \lcounter{} $\cl$ is its {\em\Uidx\lrep}
+% $\arg{rep}$ in a column $c$ defined by
+% $\!\definethecounter!\<\cl\>\<c\>\arg{rep}$.  The \lrep{} $\arg{rep}$ is
+% kept in $|\pcol@thectr@|{\cdot}\cl{\cdot}c$ and is made \!\let!-equal to
+% $|\the|{\cdot}\cl$ when the column $c$ is visted.
+% 

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

+% \SpecialArrayIndex{\theta}{\the}

+% 
+% 
+% 
+% \subsection{Page-Wise and Merged Footnotes}
+% \label{sec:imp-ovv-scfnote}
+% \changes{v1.2-2}{2013/05/11}
+%	{Add the subsection ``Single-Columned and Merged Footnotes''.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Change the title from ``Single-Columned and Merged Footnotes'' to
+%	 ``Page-Wise and Merged Footnotes'' according to the new naming.}
+% 
+% \Uidx{\Index{page-wise footnote}}{\em Page-wise footnote}
+% typesetting is completely different from ordinary {\em\Mcfnote}
+% typesetting.
+% 
+% When a \colpage{} in the \tpage{} is built, \!\footins! keeps all footnotes
+% \!\insert!ed by \!\footnote! or \!\footnotetext! in {\em any} columns in
+% the page.  Therefore, \!\footnote! and \!\footnotetext! in the \tpage{}
+% act as usual to add the footnote to \!\footins!.  Then if a \cswitch{}
+% takes place to leave the column, \!\footins! is saved into $\pp^f(\ptop)$
+% by \!\pcol@output@switch!, so that $\pp^f(\ptop)$ is \!\insert!ed to
+% \!\footins! again by \!\pcol@restartcolumn! when it visits a column in
+% $\ptop$, or by \!\pcol@startcolumn! when it finds a column proceeds to
+% $\ptop$.
+% 
+% Then, when a \colpage{} in the \tpage{} completes advancing $\ptop$,
+% \!\footins! is kept in $\pp^f(\ptop{-}1)$ by \!\pcol@startpage!, rather
+% than being combined with the \colpage{}.  This saving into
+% $\pp^f(\ptop{-}1)$ {\em fixes} the footnotes in $\ptop{-}1$ so that
+% $\pp^f(\ptop{-}1)$ is combined with other materials in the page by
+% \!\pcol@outputelt! or \!\pcol@makeflushedpage! through \!\pcol@putfootins!
+% when the page is shipped out.
+% 
+% Fixing $\pp^f(p)$ for $p<\ptop$ makes it impossible to add footnotes in a
+% column in the page $p$ not only to $\pp^f(p)$ but also to \!\footins!
+% for the page $p$ becaues we have at least one fixed \colpage{} $\s_c(p)$
+% unable to shrink to have such additional footnotes in $p$\footnote{

+% 

+% The \colpage{} $\s_c(p)$ could have some space at its bottom produced by,
+% for example, \cs{newpage}, but exploitation of such space is extremely
+% hard.}.
+% 

+% Therefore, such a footnote addition is {\em deferred} and is thrown into
+% $\pp^f(\ptop)$ through a list;
+% $$
+% \Uidx\df=\!\pcol@topfnotes!=
+% (f_1,f_2,\ldots,f_n)=\!\vbox!|{|f_1\;f_2\;\cdots\;f_n|}|
+% $$
+% where $f_i$ is a \!\vbox! containing the deferred footnote preceded by
+% \!\penalty!\!\interlinepenalty! to allow \TeX{} to break footnotes to place
+% them in two (or more) pages.  That is, \!\footnote! or \!\footnotetext! in
+% $p<\ptop$ adds an element for the footnote to $\df$, then all the elements

+% 

+% \footnote{More accurately, some trailing elements may be left in $\df$ if
+% its total height is too large, as discussed in
+% \secref{sec:imp-sout-scfnote}.}
+% 

+% are \!\insert!ed to \!\footins! by \!\pcol@deferredfootins! invoked in
+% \!\pcol@restartcolumn! when it visits a column in $\ptop$, or in
+% \!\pcol@startcolumn! when it starts a \colpage{} in $\ptop$.  The macro
+% \!\pcol@output@end! also do the \!\insert!ion by itself with \Mgfnote{}
+% typesetting to let deferred footnotes be a part of \postenv.
+% 
+% The reference to $\pp^f(p)$ for $p<\ptop$ is also made in
+% \!\pcol@restartcolumn! and \!\pcol@flushcolumn!.  The former \!\insert!s
+% $\pp^f(p)$ to \!\footins! so that the \colpage{} which the macro restarts
+% is built as if it has the footnotes in $\pp^f(p)$ to make the \colpage{}
+% broken leaving the space for the footnotes.  However, \!\footins! is never
+% grown because it has been fixed and thus additional footnotes will go
+% to $\df$ as discussed above.  Then \!\footins! is discarded by
+% \!\pcol@makecol! when the \colpage{} completes, or by
+% \!\pcol@output@switch! when it leaves the column.
+% 
+% The reference to $\pp^f(p)$ by the latter macro \!\pcol@flushcolumn! is to
+% build the ship-out image of the \colpage{} to be flushed.  When this macro
+% and other macros, namely \!\pcol@makecol! and \!\pcol@makeflushedpage!,
+% build the ship-out image in a page $p$ having $\pp^f(p)$ using
+% \!\@makecol!, we have to be careful of the fact that the \colpage{} has
+% been build as if it has footnotes in $\pp^f(p)$ but the footnotes are not
+% included in its ship-out image but that of the page.  Therefore,
+% \!\@colht! referred in \!\@makecol! should be shrunk by the sum of
+% height and depth of $\pp^f(p)$ and $\!\skip!\cdot\pp^f(p)$ by
+% \!\pcol@shrinkcolbyfn!.  Other and more subtle adjustment is to add the
+% stretch and shrink factors of $\!\skip!\cdot\pp^f(p)$ at the tail of the
+% \colpage{} by \!\pcol@unvbox@cclv!.  This is necessary because \TeX{} has
+% broken the \colpage{} taking account of the stretch and, more essentially,
+% shrink factors, and thus without the factors the main vertical list in the
+% \colpage{} could be a little bit taller than \!\@colht! causing overfull.
+% 
+% The feature gathering footnotes in all columns in a page brings a problem
+% to \exsync{}, because a column whose contents fit the \tpage{} at the
+% last visit may be too tall on the \sync{}ation because other columns have
+% put some footnotes after the last visit.  That is, we cannot simply build
+% the \tpage{} combining $\s_c(\ptop)$ for all $c\In0\C$ and $\pp^f(\ptop)$
+% because there could be $\s_c(\ptop)$ too tall to reside in $\ptop$ with
+% $\pp^f(\ptop)$.
+% 
+% To solve this problem, we perform the following operations prior to fix
+% the contents of $\ptop$ having an \exsync{} point in it.  First one is
+% {\em\Uidx\cscan} to visit all columns by \cswitch{} prior to the
+% \sync{}ation so that \TeX's page builder has opportunities to break too
+% tall \colpage{}s.  Since this scan could merely break footnotes rather
+% than the main vertical lists in the \colpage{}s and the broken footnotes
+% will be reconnected when the \!\output!-routine is invoked for the
+% \sync{}ation, we then examine if all $\s_c(\ptop)$ are accommodated in
+% $\ptop$ with $\pp^f(p)$.
+% 
+% This examination for a \sync{}ation by \!\switchcolumn!|*| or its
+% relatives is done as a part of the inherent \sync{}ing procedure to see if
+% the combination of the tallest {\em top} items, i.e., top floats and the
+% main vertical list, and the tallest {\em bottom} items, i.e., bottom
+% floats and \Mcfnote{}s, is too large causing page flushing.  As for page
+% flushing and environment closing, this {\em\Uidx\pfcheck} requires a
+% special kind of \sync{}ed \cswitch{} by which we flush pages up to
+% $\ptop-1$ and examine if there is a too tall column.
+% 
+% Then if too tall columns are found, in either cases, we move to the {\em
+% tallest} column to force a page break in the column so that we have a new
+% page with shorter columns and shorter \Scfnote{}s as well.  In the
+% \sync{}ation by \!\switchcolumn!|*| or its relatives, this forced page
+% break is then applied to all other columns so that new \colpage{}s have
+% top floats, if any, below which we should place the \sync{}ation point.
+% This examination and forced page break is repeated until we have a page
+% without any too tall columns, because a page break may bring deferred
+% floats and footnotes which may result in a too tall column.
+% 
+% 
+% 
+% \subsection{Text Coloring}
+% \label{sec:imp-ovv-color}
+% \changes{v1.2-1}{2013/05/11}
+%	{Add the subsection ``Coloring''.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Change the subsection title from ``Coloring'' to ``Text Coloring''
+%	 to distinguish it from background painting clearly.}

+% 
+% \subsubsection{Fundamental Mechanism}
+% \label{sec:imp-ovv-color-fundamental}
+% \changes{v1.34}{2018/05/07}
+% 	{Revise the description of \Sec1.6.1 according to the new
+%	 implementation with \cs{insert}.}
+% 
+% Text coloring done by \textsf{color} package and its relatives using
+% \!\special! stands on the fact that the main vertical list is {\em
+% printed} in the order of occurrence in the source |.tex|.  That is, a
+% command such as \!\color!|{red}| puts
+% \!\special!|{color push [1 0 0]}|\footnote{

+% 

+% If \texttt{.dvi} is processed by \texttt{dvips}, or other
+% printer-dependent command corresponding to it.}
+% 

+% into |.dvi| to make all stuff in the main vertical list colored red until
+% other coloring \!\special! inserted by other coloring macro appears in
+% |.dvi|.  This simple mechanism works well even when the pair of coloring
+% \!\special!s are in different pages and/or columns because, with respect
+% to the main vertical list, everything between them in |.tex| is also
+% surrounded by the \!\special! pair in |.dvi|.  As for other stuff such as
+% header, footer, floats and footnotes, \LaTeX{} surrounds them by
+% \!\color@begingroup! and \!\color@endgroup! or other similar constructs so
+% that they are colored without interference with the coloring of the main
+% vertical list.
+% 
+% In \env{paracol} environment, however, the orders of the main vertical list
+% in |.tex| and |.dvi| are not always same.  When a column encounters a page
+% break, in |.dvi| the other column should intervene between the stuff in
+% the broken pair of \colpage{}s possibly changing the color of the second
+% \colpage.  A \cswitch{} from $c_1$ to $c_2$ also makes the main vertical
+% list out-of-order to cause another unexpected coloring because a coloring
+% command in $c_2$ will have no effect when $c_1$ is revisited after that
+% following its pre-switching stuff in |.dvi| which was put before the
+% coloring.  Therefore, we have to make {\em\Uidx\colorctext{}s} in both
+% |.tex| and |.dvi| coherent inserting appropriate \!\special!s into |.dvi|
+% whenever an out-of-order {\em jump} occurs in |.dvi| by a page break or in
+% |.tex| by a \cswitch{}.
+%
+% The \textsf{color} package and its relatives\footnote{

+% 

+% And all other coloring mechanism compliant with \LaTeXe{}, hopefully and
+% believingly.}
+% 

+% assume that {\em printers} have a stack for coloring and thus a coloring
+% \!\special! pushes the new color into the stack while it is popped by
+% another \!\special! which will be inserted by \!\aftergroup!  mechanism
+% when a group surrounding the coloring \!\special! is closed.  Therefore we
+% have to keep track of the \colorctext{} with {\em\Uidx\colorstack}
+% $$
+% \Uidx\cst=
+% (\Uidx\celt_1,\celt_1,\ldots,\celt_n)=
+% \!\vbox!|{|\celt_1\;\celt_2\;\ldots\;\celt_n|}|
+% $$
+% where $\celt_i$ is a \!\vbox! of 1\,|sp| tall, 0 deep and 0 wide containing
+% a coloring \!\special! which \!\set@color! puts into the main vertical
+% list.  That is, when \!\set@color! is invoked we push $\celt$ to the tail
+% of $\cst$, while when the corresponding \!\reset@color! appears we pop it
+% from $\cst$\@.  Then when we encounter an out-of-order jump, at first we
+% rewind the \colorstack{} in |.dvi| by putting \!\special!s which
+% \!\reset@color! would put, and then reestablish the \colorstack{} by
+% putting \!\special!s in $\celt_i$ as if \!\set@color! for it is invoked
+% for all $\celt_i\in\cst$.  Therefore from the viewpoint of a {\em
+% printer}, it will see stack-rewinding at the end of each \colpage{} and
+% the leaving points of \cswitch{}, while the beginning of each \colpage{}
+% and the entry points of \cswitch{} should have the sequence of coloring
+% \!\special!s to regain the \colorstack{} which the {\em printer} must have
+% at each of the points.
+% 
+% \SpecialArrayMainIndex{c}{\pcol@columncolor@box}

+% 

+% In addition, for each column $c$ we keep
+% $\Uidx\Celt^c=|\pcol@columncolor@box|\cdot c$ as the {\em default} color
+% of the column $c$, optionally given by the API macro \!\columncolor! or
+% \!\normalcolumncolor!.  If given for $c$, it is assumed to be at the bottom
+% of the \colorstack{} denoted by
+% $\Uidx\CST^c=(\Celt^c,\celt_1,\ldots,\celt_n)$ which we rewind\slash
+% reestablish at each out-of-order jump in the column $c$.
+% 
+% 
+% 
+% \subsubsection{Coloring in Horizontal Mode}
+% \label{sec:imp-ovv-color-hmode}
+% \changes{v1.22}{2013/06/30}
+%	{Add the subsection ``Coloring in Horizontal Mode''.}

+% \changes{v1.34}{2018/05/07}
+% 	{Revise the description of \Sec1.6.2 according to the new
+%	 implementation with \cs{insert}.}
+% 
+% We have to pay attention to the fact a coloring command can appear in
+% horizontal mode of course, and thus push/pop operations in a \colpage{}
+% would be done {\em before} the \colpage{} starts when \!\set@color! or
+% \!\reset@color! is in the second half of a page-crossing paragraph and if
+% we immediately performed push\slash pop of the \colorstack{} in these
+% macros.  In addition, even in vertical mode these macros can appear before
+% \TeX{} finds a page break after which they must be in effect, if they are
+% preceded by a sequece of non-breakable vertical items by which \TeX{}'s
+% examination of the page break is {\em delayed} as well as the invocation
+% of \!\output! at the break.
+% 
+% In order to solve the problem of push/pop timing, we perform push\slash
+% pop operations through \!\insert! to our own register set
+% \!\pcol@colorins!.  That is, we \!\insert! $\celt$ to \!\pcol@colorins!
+% when we encounter a \!\set@color! for $\celt$, while its corresponding
+% \!\reset@color! also \!\insert!s another \!\vbox! $\Uidx\celtpop$ of
+% null-height\slash depth\slash width having a \!\special! which the
+% \!\reset@color! puts into the main vertical list.  Since we let
+% $\!\count!\!\pcol@colorins!=0$ and $\!\skip!\!\pcol@colorins!=0$ to keep
+% the \!\insert!iion from affecting the growth of \!\pagetotal!, it is
+% guaranteed that an inserted $\celt$ or $\celtpop$ is given to \!\output!
+% through \!\pcol@colorins! together with |\box255| containing the
+% corresponding \!\special!.
+% 
+% When \!\output! is invoked, \!\pcol@colorins! has $\Uidx\cstraw$
+% containing $\celt_i$ and possibly its corresponding $\celtpop_i$.
+% Therefore, if \!\output! is for a page break or a \cswitch, we remove all
+% pairs of $\celt_i$ and $\celtpop_i$ from \!\pcol@colorins! to let it have
+% $\cst$ only with $\celt_j$ whose corresponding $\celt_j^-$ is not in
+% $\cstraw$.  For this removal, we scan $\cstraw$ from its tail
+% incrementing\slash decrementing a counter $\Uidx\npop$ which we initialize
+% to 0 before scanning.  In the scan, we remove all $\celtpop$
+% unconditionally incrementing $\npop$, and $\celt$ such that $\npop>0$ on
+% the encounter with it decrementing $\npop$.  This scan is done by
+% \!\pcol@clearcolorstack!, invoked from \!\pcol@opcol! for a page break and
+% \!\pcol@output@switch! for a \cswitch{} through \!\pcol@clearcst@unvbox!,
+% and is for rewinding the \colorstack{}
+% $(\Celt^c,\cstraw)=\Uidx\CSTraw^c$.  Therefore, for each $\celt$ to be kept
+% because of $\npop=0$ on the encoutner with it we put \!\special! for
+% \!\reset@color!.  Note that on another scan for stack reestablishment,
+% \!\pcol@colorins! has $\cst$ and is kept unchanged.  Also note that other
+% \!\output!  invocations such as that for floats do not touch $\cstraw$ to
+% allow it grows with $\celt$ and $\celtpop$ corresponding to \!\set@color!
+% and \!\reset@color! in the \colpage{} in which the invocation
+% happens\footnote{

+% 

+% Unlike \cs{footins} which becomes void by putting its contents back to the
+% main vertical list to reexamine the footnote placement possibly with
+% splitting.}.
+% 
+% The mechanism above especially for horizontal mode has subtle issues as
+% follows.
+% 

+% \begin{itemize}
+% \item
+% If \!\set@color! appears in a \!\vbox!, the \!\insert!ion for pushing
+% is not effective but corresponding \!\reset@color! can be outside of the
+% \!\vbox! to make pushes and pops unbalanced because \!\aftergroup! for it
+% inserts it just after the closing of the \!\vbox! if \!\set@color! is not
+% surrounded by an inner group.
+% 
+% \item
+% If we are in vertical mode, we can know if we are in a \!\vbox! by
+% \CSIndex{ifinner}.  However, in horizontal or math mode, \CSIndex{ifinner}
+% cannot help us because it is true iff we are in a \!\hbox! or in an
+% in-text math.  In short, \TeX{} does not provide us with any convenient
+% means to know if we are in a \!\vbox!.
+% \end{itemize}
+% 

+% To solve the problem above, we introduced a trick with \!\everyvbox! to
+% turn a switch $\CSIndex{ifpcol@inner}=\true$ at the beginning of every
+% \!\vbox! in a \env{paracol} environment, by which we supress the
+% \!\insert!ion for \!\set@color! because a \!\vbox! cannot cross a
+% page boundary.  As for that of \!\reset@color!, we suppress it by not
+% reserving our own macro \!\pcol@reset@color@pop! for the \!\insert!ion by
+% \!\aftergroup!.  That is, we reserve both \!\reset@color! and
+% \!\pcol@reset@color@pop! with \!\aftergroup! if we are outside of any
+% \!\vbox!es, while does the former only otherwise.  By the same reason, we
+% supress the \!\insert!ion if we are in restricted horizontal mode, i.e.,
+% if both \CSIndex{ifhmode} and \CSIndex{ifinner} are true.  On the other
+% hand, we cannot supress the \!\insert!ion when we are in an in-text math
+% because it can cross a page boundary\footnote{

+% 

+% If an in-text math is in a \cs{hbox}, \cs{insert}ion is not
+% necessary because the math cannot cross a page boundary.  Though we can
+% detect it by a trick with \!\everyhbox!, we abandon this idea because the
+% request is not harmful.  Another and more serious issue of coloring in
+% math mode will be discussed shortly.}.
+% 

+% Note that the detailed implementation shown in \secref{sec:imp-startenv}
+% does not interfere the use of \!\everyvbox! inside/outside of
+% \env{paracol} environments or is not affected by the use.
+% 
+% Another attention we should pay is that \!\color! will leave \!\aftergroup! 
+% tokens of \!\reset@color! and thus they are invoked just after
+% \Endparacol.  However, since we have completed all \colpage{}s in the
+% \lpage, the \colorstack{} in |.dvi| should be empty.  Therefore to avoid
+% stack underflow, we should reestablish $\cst$ (not $\CST^c$) so that
+% elements in the stack are popped by \!\reset@color! invoked with the
+% \!\aftergroup! mechanism.  We also take care of our own \colorstack{}
+% popper \!\pcol@reset@color@pop! which must do nothing, i.e., must not make
+% an \!\insert!ion, after we completed the \lpage, i.e., if
+% \CSIndex{ifpcol@output} is $\false$.
+% 
+% 
+% 
+% \subsubsection{Changing Default Column Color}
+% \label{sec:imp-ovv-color-colcolor}
+% \changes{v1.34}{2018/05/07}
+% 	{Split the description of \cs{columncolor} from \Sec1.6.2 to have
+%	 new \Sec1.6.3 ``Changing Default Column Color'' because we have
+%	 serveral new issues in the new implementation with \cs{insert}.}
+% 
+% The implemntation of \!\columncolor! and \!\normalcolumncolor! is
+% relatively easy for the cases that they appear outside
+% \env{paracol} environment or they define the default color of a
+% column different from the current column.  That is, for the default color
+% of a column $c$ we simply \!\def!ine
+% ${\Uidx\Celtshadow}^c=|pcol@columncolor|\cdot c$ to let it have what
+% \!\current@color! has for the color.  Then, in \beginparacol{} in the
+% former case or immediately in the latter, we let
+% $\Celt^c=|pcol@coloumncolor@box|\cdot c$ have the coloring \!\special! for
+% the color acquiring an \!\insert! from \!\@freelist! if the box is
+% $\bot$.
+% 

+% \SpecialArrayMainIndex{c}{\pcol@columncolor}

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% 
+% On the other hand, when the API commands are to define the default color
+% of the current column $c$, we need to place the coloring at the bottom of
+% \colorstack{}s in terms of |.tex| and |.dvi|.  That is, for the former we
+% have to rewind and reestablish the stack which can be different from
+% $\CST^c$ because the API command can follow a page break which \TeX{} does
+% not yet find.  Therefore, we maintain a {\em shadow} of $\cst$ namely;
+% $$
+% {\Uidx\cstshadow}={\Midx{\!\pcol@colorstack@shadow!}}
+% =({\Uidx\celtshadow}_1,\celtshadow_2,\ldots,\celtshadow_n)
+% =\!\@elt!\Arg{\celtshadow_1}\;\!\@elt!\Arg{\celtshadow_2}\;\cdots\;
+%  \!\@elt!\Arg{\celtshadow_n}
+% $$
+% to which our version of \!\set@color! pushes $\celtshadow_i$ being
+% \!\current@color! which the original one defines, while popping is done
+% automatically by \TeX's grouping mechanism because pushes are done by
+% \!\edef! rather than \!\xdef!.  Then before we \!\def!ine $\Celtshadow^c$
+% we rewind
+% ${\Uidx\CSTshadow}^c=(\Celtshadow^c,\celtshadow_1,\ldots,\celtshadow_n)$
+% putting \!\special! for pop to the main vertical list for each elements,
+% and then after the \!\def!initon of $\Celtshadow^c$ we reestablish
+% $\CSTshadow^c$ putting coloring \!\special! for each element.
+% 
+% As for placing $\Celt^c$ at the bottom of $\CST^c$, we must ensure that
+% the placement is done for the \colpage{} in which the API command
+% belongs to, as we did in ordinary push\slash pop of the \colorstack.
+% Therefore the API command \!\insert!s $\Celt^c$ to $\cstraw$ in the form
+% of a \!\vbox!, whose height and depth are 1\,|sp| and width is 0,
+% containing the coloring \!\special! for $\Celt^c$.  Then when $\cstraw$ is
+% scanned for rewinding in \!\output!, this \!\vbox! is found to let
+% $\Celt^c$ have the \!\special! acquiring an \!\insert! from \!\@freelist!
+% it was $\bot$.  Note that $\cstraw$ may have multiple \!\vbox!es to update
+% $\Celt^c$ and if so the last one is effective.
+% 
+% 
+% 
+% \subsubsection{Coloring in Math Mode}
+% \label{sec:imp-ovv-color-mmode}
+% \changes{v1.24}{2013/07/27}
+%	{Add the subsection ``Coloring in Math Mode''.}

+% \changes{v1.34}{2018/05/07}
+% 	{Revise the description of \Sec1.6.4 according to the new
+%	 implementation with \cs{insert}.}
+% 
+% Unfortunately the solution above is imperfect because \TeX{} builds an
+% implicit \!\hbox! for a |{|\textit{math stuff}|}| construct in math mode
+% and an \!\insert! in the construct does not contribute to
+% the main vertical list at all\footnote{

+% 

+% The contents is not thrown away but \cs{insert}ion itself is added
+% to the list rather than given to \cs{output}.}.
+% 

+% Since the implicit \!\hbox! does not care about \!\everyhbox!, we cannot
+% use the trick similar to that with \!\everyvbox!.  Another bad news is
+% that built-in \cs{if}s for mode checking cannot help us because we always
+% have $\CSIndex{ifvmode}=\CSIndex{ifhmode}=\false$ and
+% $\CSIndex{ifmmode}=\true$ while $\CSIndex{ifinner}$ is $\true$ or $\false$
+% when we are in in-text or displayed math mode respectively.  Therefore, we
+% have to take care of the potential loss of \!\insert!ion for pushes and
+% thus unmatched pops in $\cstraw$.
+% 
+% For example, we have to remember that, in the cases like
+% |${|\!\color!$\Arg{c}\textit{text}$|}$| or
+% |$|\!\textcolor!$\~\Arg{c}\ARg{text}$|$| expanded to the former, the
+% \!\insert!ion for push is lost while its counterpart for pop survives
+% making it necessary to check the existance of pushing counterpart for each
+% pop in $\cstraw$\footnote{

+% 

+% Since a pop is always in a group one level outer from its push
+% counterpart, the pop request should be presented if the push does.}.
+% 

+% Note that the fact that the pop in the examples is in the in-text math
+% does not help us, because the pop in
+% |$|\!\begingroup!\!\color!\Arg{c}\textit{text}\!\endgroup!|$| is also in
+% the in-text math while its pushing counterpart performs an effective
+% \!\insert!ion, and two \!\insert!ions must be presented in $\cstraw$
+% because we can have a page-break in \textit{text}.  Therefore, we have to
+% find a means to examine whether a pop $\celtpop_i$ has its counterpart
+% $\celt_i$ in $\cstraw$ to remove $\celt_i$ from $\cstraw$ if exists or to
+% igonore $\celtpop_i$ otherwise.  That is, we have to attach an identifier
+% $m$ to $\celt_i$ and $\celtpop_i$, i.e., to make them $\Uidx\mcelt_{i,m}$
+% and $\Uidx\mceltpop_{i,m}$.
+% 
+% Since the only means we have for the communication with \!\output! routine
+% is what we \!\insert! to $\cstraw$, the \!\insert!ed \!\vbox! must carry an
+% identifier $m$ for a push\slash pop in math mode.  To do that, we make
+% \!\vbox! $m$\,|sp| wide ($m>0$) if our version of \!\set@color! is in math
+% mode to represent $\mcelt_{i,m}$ and $\mceltpop_{i,m}$, while the width is
+% 0 otherwise as described in \secref{sec:imp-ovv-color-hmode}.  Then in the
+% scan of $\cstraw$ for rewinding in \!\output!, we supress
+% incrementing\slash decrementing $\npop$ for $\mcelt_{i,m}$ and
+% $\mceltpop_{i,m}$, but remove $\mcelt_{i,m}$ if $\mceltpop_{i,m}$ is in
+% $\cstraw$ as a successor while we keep it in $\cstraw$ otherwise putting a
+% \!\special! of pop for it to the main vertical list.
+% 
+% To ensure that $\mcelt_{i,m}$ has its counterpart $\mceltpop_{i,m}$ in
+% $\cstraw$ iff the push and pop are in a \colpage, we maintain the counter
+% \!\pcol@mcid! incremented before (the attempt of) the \!\insert!ion of
+% $\mcelt_{i,m}$ with $m=\!\pcol@mcid!$ and the \!\aftergroup! reservaion
+% for that of $\mceltpop_{i,m}$.  Then the counter is zero-cleared by
+% \!\output! routine in order to keep it less than
+% $\!\pcol@mcpushlimit!=1000$ unless, roughly speaking, a \colpage{} has a
+% unexpectedly large number of math constructs having coloring commands in
+% them.  Note that this zero-clearing does not ensure that an identifier $m$
+% is unique in $\cstraw$.  That is, it can happen that $\cstraw$ has
+% $\mcelt_{i,m}$, $\mceltpop_{i,m}$, $\mcelt_{j,m}$ and/or $\mceltpop_{j,m}$
+% in this order for $i<j$, when two math constructs with coloring for $i$
+% and $j$ are in different paragraphs and \!\output! is invoked at or after
+% the end of the paragraph with the math for $i$.  This potential
+% duplication is, however, unharmful because of the following.
+% 

+% \begin{itemize}
+% \item
+% Since a math construct cannot have immediate \!\output! invocations in it,
+% the order of the elements in $\cstraw$ must be $\mcelt_{i,m}$,
+% $\mceltpop_{i,m}$, $\mcelt_{j,m}$ and $\mceltpop_{j,m}$ from its bottom to
+% top, though some of them could be missing.  Therefore, if
+% $\mceltpop_{i,m}$ is in $\cstraw$, $\mcelt_{j,m}$ must follow it if
+% exsits not causing accidental matching with $\mceltpop_{i,m}$.
+% 
+% \item
+% If $\mcelt_{i,m}$ is in $\cstraw$ but $\mceltpop_{i,m}$ is not, it means
+% we have a page break between vertical items corresponding to
+% $\mcelt_{i,m}$ and $\mceltpop_{i,m}$ to keep the \!\insert!ion of
+% $\mceltpop_{i,m}$ and anything following it from appended into $\cstraw$.
+% Therefore, $\cstraw$ cannot have $\mceltpop_{j,m}$ not causing accidental
+% matching with $\mcelt_{i,m}$.
+% \end{itemize}
+% 
+% 
+% 
+% \subsubsection{Emptiness of a Column-Page}
+% \label{sec:imp-ovv-color-emptycol}
+% 
+% The mechanism above works well with respect to coloring, but it has a
+% problem that a \colpage{} created by, for example, a forced page break may
+% not be perfectly empty but can have some coloring \!\special!s for
+% \colorstack{} reestablishing and rewinding.  They are of course invisible
+% but affect the examination of \colpage{} emptiness for \exsync.  That is,
+% we examine if a \colpage{} does not have anything by a tricky way by
+% \!\pcol@ifempty! but the existence of coloring \!\special!s makes the
+% examination failed even if no other ordinary stuff such as boxes and skips
+% are in the \colpage.
+% 
+% Therefore we need to put coloring \!\special!s for \colorstack{}
+% establishing and rewinding a little bit more carefully to avoid empty
+% \colpage{}s just having such \!\special!s as follows.  When we start a new
+% \colpage{}, we don't put \!\special!s for establishing immediately but
+% save the \colorstack{} $\CST^c$ into
+% $\Uidx\csts=\!\pcol@colorstack@saved!$.  Then when we leave the
+% \colpage{} by switching or page breaking, we examine the emptiness of the
+% \colpage{} and if so we do nothing, while otherwise we put the
+% \!\special!s for reestablishing $\csts$ at the top of the \colpage{} and
+% those for rewinding $\cstraw$ at the bottom.  Similary, when we revisit a
+% \colpage, we examine its emptiness and if so we save $\CST^c$ into
+% $\csts$, while otherwise we put \!\special!s for reestablishing $\CST^c$
+% and nullify $\csts$ so that nothing will be put at the top of the
+% \colpage{} when we leave it.  By these mechanisms, an empty \colpage{}
+% should not have coloring \!\special!s, while non-empty ones should have a
+% sequence of triples; reestablishing \!\special!s; ordinary main vertical
+% list items including coloring \!\special!s inserted by \!\color! etc.; and
+% then rewinding \!\special!s.
+% 
+% 
+% 
+% \subsection
+% [Parallel-Paging, Column-Swapping, Column-Separating Rule
+%   Drawing and Background Painting]
+% {Parallel-Paging, Column-Swapping, Column-Separating\\Rule
+%   Drawing and Background Painting}
+% \label{sec:imp-ovv-cswap}
+% \changes{v1.2-4}{2013/05/11}
+%	{Add the subsection ``Column-Swapping''}

+% \changes{v1.3-1}{2013/09/17}
+%	{Change the section title from ``Column-Swapping'' to
+%	 ``Parallel-Paging, Column-Swapping, Column-Separating Rule Drawing
+%	 and Background Painting'' to discuss related issues together''.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add overview description of parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add overview description of column-separating rule drawing and
+%	 background painting.}

+% 

+% We have the following four extensions, which are correlated to each other,
+% from the basic parallel-columning.
+% 

+% \paragraph{\em Parallel-paging}\UsageIndex{parallel-paging}\hskip-.5em
+% to extend the concept of parallel-columning in a page to a pair of
+% adjacent pages.  A {\em left} \parapag{}e starts from column-0, has
+% $\Uidx\CL$ columns where $\CL$ is given by the first optional argument of
+% \beginparacol, while a {\em right} \parapag{}e starts from column-$\CL$
+% and has $\C-\CL$ columns.  Since we let $\CL=\C$ when \parapag{}ing is not
+% in effect, we may ship out columns $c\In0\CL$ always and then, if
+% $\CL<\C$, ship out columns $c\In\CL\C$ as a right \parapag{}e.
+% 
+% The pair of \parapag{}es can be {\em\Uidx\paired} to comprise a virtual
+% page $p$ and thus has common page number $\page(p)$, while
+% {\em\Uidx\npaired} \parapag{}ing produces two individual pages from a
+% internal page $p$ (i.e., set of all columns $\Set{c}{c\In0\C}$) whose
+% left and right components have page numbers $\page(p)$ and $\page(p)+1$
+% respectively.  Since a page $p$ is internally considered as the set of all
+% columns $c\In0\C$ always, regardless of \paired{} or \npaired{}
+% \parapag{}ing, the difference between them arises only in two-sided
+% ship-out process in which the header, footer and left-margin are common
+% for left\slash right \paired{} \parapag{}s while they have to depend on
+% the parity of the number of each \npaired{} \parapag{}e.  Note that
+% \textsf{paracol} does not specify the parity of a left \npaired{}
+% \parapag{}e number, but the number is decided by the page from which a
+% \parapag{}ed \env{paracol} environment starts.
+% 
+% In ship-out process, we build the ship-out image of a right \parapag{}e in
+% our own \!\box! register \!\pcol@rightpage! instead of the usual
+% \!\@outputbox!.  The register, however, must {\em survive} after
+% \Endparacol{} to keep the columns in the last right \parapag{}e,
+% 

+% \Index{last page}
+% 

+% so that it is shipped out when the whole of last page including \postenv{}
+% is shipped out, or, more complicatedly, to be passed to the next
+% \env{paracol} environment as a part of its \preenv.
+% 
+% {\em Page-wise stuff}
+% \UsageIndex{page-wise stuff}

+% spanning all columns, i.e., \spanning{} being \preenv{} or \pwise{}
+% floats, \mctext{}s, \scfnote{} footnotes and \postenv{} are always placed
+% in a left \parapag{}e, while the corresponding regions for them in a right
+% \parapag{}e are always blank\footnote{

+% 

+% So far.  In some future, we could implement a special setting to let
+% \preenv{}, \postenv{} and \scfnote{} footnotes are split into both
+% \parapag{}es, and to make it possible that a \pwise{} float or a
+% \mctext{} has its counterpart placed in the corresponding right
+% \parapag{}e.}
+% 

+% unless \preenv{} has the \lpage{} of the previous \env{paracol}
+% environment.
+%
+% \paragraph{\em Column-swapping}\UsageIndex{column-swapping}\hskip-.5em
+% to reverse the order of columns in even numbered pages from left-to-right
+% to right-to-left.  It is enabled by the specifier `|c|' of
+% \!\twosided!\footnote{

+% 

+% Or the backward compatible macro \!\swapcolumninevenpages!.}.
+% 

+% Though it is fundamentally simple because we just need to reverse the
+% scanning order of columns from left-to-right (i.e., 0 to $\C-1$) to
+% right-to-left (i.e., $\C-1$ to 0) in the ship-out process of an even
+% numbered page, there are a few complications in the implementation of
+% related functionalities.
+% 
+% First, a \paired{} \parapag{}e should also be swapped so that a
+% \emph{physical} left (resp.\ right) \parapag{}e has columns $\C-1$ to
+% $\CL$ (resp.\ $\CL-1$ to 0) in this order.  Note that this \parapag{}e
+% swapping also swaps the page in which \pwstuff{} are placed.  That is, if
+% both \paired{} \parapag{}ing and \cswap{} are in effect, \pwstuff{} are
+% placed in the physical right \parapag{}e, or in other words they always
+% placed in the page in which column-0 resides.  Note that since \cswap{}
+% with \npaired{} \parapag{}ing is meaningless and thus \cswap{} is
+% disabled.
+% 
+% Second, the side margin to which a marginal note goes can be swapped but
+% enabling this swap is independent of \cswap{} and done by the specifier
+% `|m|' of \!\twosided!, though almost all users will specify both swapping
+% consistently.  Since the side margin for a marginal note is decided in
+% \!\output! routine by \!\pcol@addmarginpar! being our own version of
+% \LaTeX's macro for maginal notes \!\@addmarginpar!, the page in which the
+% margial note resides has been fixed.  However, the number of the page and
+% thus its parity may not have been fixed yet due to the possible jump in
+% column-0 taking place afterward, unlike \cswap{} for which the page number
+% has been fixed because it is performed in ship-out process.  Since it is
+% too costly to avoid this possibly wrong placement, we have to accept the
+% possibility as \LaTeX{} itself does.  Also unlike \cswap, the swapping of
+% marginal notes is not disabled in \npaired{} \parapag{}ing because it is
+% meaningful.
+% 
+% Another remark for marginal notes is that two ore more columns may {\em
+% share} a margin, inevitably if a (parallel) page has three or more columns
+% or intentionally with a setting of \!\marginparthreshold!.  Therefore, the
+% context of marginal notes cannot be in \cctext{} but should be in \pctext,
+% or cannot simply give the bottom of the last marginal note (i.e., \LaTeX's
+% \!\@mparbottom!) but should show all marginal notes in margins in a
+% page\footnote{

+% 

+% Before version 1.3, we have \!\@mparbottom! in \cctext{} because a column
+% has its own area for marginal notes, which can be the gap between columns
+% rather than a margin of a page.}.
+% 

+% Therefore, each \pctext{} has all marginal notes in the form of lists of
+% their top and bottom positions in all margins as $\pp^m(p)$, so that we
+% find a space for a marginal note in a column to add it to not only to the
+% bottom but also into a space between two marginal notes having already
+% been put by other columns.
+% 
+% Third and finally, we have to take care the placement of \mctext{}s.  In
+% version 1.2 to which \cswap{} is introduced, we let a \mctext{} belong to
+% column-$(\C-1)$ instead usual column-0 so that its left edge is aligned to
+% the left edge of the leftmost column, i.e., that of the text area.
+% However this simple solution has a severe problem that, if a \mctext{} is
+% broken into two pages, its second half should be put in the rightmost
+% column.  In addition, even when a \mctext{} does not have page break in
+% it, such wrong placement may happen if the text is followed by \!\nobreak!
+% and thus a page break is made above the text but {\em after} the text is
+% processed.
+% 
+% In version 1.3, this problem is solved by capturing the first half of a
+% \mctext{} in \!\output! routine for the page break in the text, and the
+% second half or the whole of it in that for \sync{}ed \cswitch{} to close
+% the text.  Since an invocation of \!\output! routine means that it has been
+% fixed which page the \mctext{} or its part resides in, we can place the
+% text much more reliably expecting the parity of the page number has also
+% been fixed.  In addition, this decision making in \!\output! routine allows
+% (or forces) us to let \mctext{}s always belong to column-0 preserving the
+% consistency of, for example, local counter values referred to in them,
+% while we need to shift a text to the left edge of the text area if it
+% resides in an even numbered page.  Furhtermore, this \mctext{} capturing
+% enables to measure the vertical size of the captured text together with the
+% vertical position of its top edge to record them in the list $\pp^s(p)$,
+% so that we draw \cseprule{}s skipping the text and painting its \bground{}
+% with a specific color different from colors of columns and \csepgap{}s, as
+% discussed shortly.
+% 
+% \paragraph{\em Column-separating rule drawing}

+% \UsageIndex{column-separating rule}\hskip-.5em
+% to draw a vertical rule in {\em\Uidx\csepgap} is correlated with a part of
+% {\em\bgpaint} to paint each region in a page with a color specific to the
+% region.  Thanks to the list of \mctext{}s $\pp^s(p)=(\spt(H_i,h_i))_i^n$, we
+% can draw \cseprule{}s skipping \mctext{}s in the page $p$ as the sequence
+% of;
+% 

+% \begingroup
+% \def\RULE{\mathit{rule}}\def\GAP{\mathit{gap}}
+% \begin{eqnarray*}
+% &&\RULE(H'_1),\GAP(h_1),\ldots,\RULE(H'_n),\GAP(H'_n),\RULE(H'_{n+1})\\
+% &&H'_i=H_i-(H_{i-1}+h_{i-1})
+% \qquad H_0=h_0=0
+% \qquad H_{n+1}=\pp^h(p)
+% \end{eqnarray*}
+% \endgroup
+% 

+% where $\mathit{rule}(H')$ is a vertical rule of $H'$ high and
+% $\mathit{gap}(h)$ is a vertical space of $h$.  A rule may be colored with
+% the color specified by \!\colseprulecolor! for each \csepgap{} or all
+% of them.  Note that if \cswap{} is in effect, a column $c$ is {\em
+% preceded} by $c$-th \csepgap{} which may have its own width and color for
+% its rule, rather than being followed by it.
+% 
+% \paragraph{\em Background painting}\UsageIndex{background painting}\hskip-.5em
+% also uses the list $\pp^s(p)$ to paint the \bground{} of each column-$c$
+% with the color $\Uidx\bgc_c^c$, each \csepgap{} following the column-$c$
+% with $\bgc_g^c$, and \mctext{}s with $\bgc_s$ and $\bgc_S$, where
+% $\bgc_a^{[c]}$ is specified by the second argument of
+% $\!\backgroundcolor!\Arg{\hbox{\ttfamily\itshape a}|[|c|]|}\~\Arg{color}$
+% ($\hbox{\ttfamily\itshape a}\in\{|c|,|g|,|s|,|S|\}$) and kept in the macro
+% $|\pcol@bg@color@|{\cdot}a[|@|{\cdot}c]$.
+% 

+% \SpecialArrayMainIndex{a}{\pcol@bg@color@}

+% \SpecialArrayMainIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% 

+% The region to be painted for each item is as follows where
+% $[(x_0,y_0)(x_1,y_1)]$ means the region
+% $\Set{(x,y)}{x\In{x_0}{x_1},\;y\In{y_0}{y_1}}$ of the top-down
+% $xy$-coordinate whose origin is at the left-top corner of the leftmost
+% column.
+% 

+% \begingroup\def\sS{{\{s,S\}}}
+% \begin{eqnarray*}
+% \Uidx\bgr_c^c(i)&=&[(\Uidx\W_c,\;H_{i-1}+h_{i-1})\;
+%   (\W_c+w_c,\;H_i+d_{c/g})]\\
+% \bgr_g^c(i)&=&[(\W_c+w_c,\;H_{i-1}+h_{i-1})\;(\W_{c+1},\;H_i+d_{c/g})]\\
+% \bgr_\sS(i)&=&[(0,\;H_i)\;(\Uidx\WT,\;H_i+h_i+d_s)]\\
+% \W_{c}&=&\sum_{d=c_0}^{c-1}(w_c+g_c)\qquad
+%     c_0=\cases{0&$c<\CL$\cr
+%		 \CL&$c\geq\CL$}\qquad
+%     \WT=\!\textwidth!\\
+% d_{c/g}&=&\cases{\!\maxdepth!&$i=n+1\;\land\;H'_{n+1}>0\;\land\;$non-\lpage\cr
+%                0&otherwise}\\[1ex]
+% d_s&=&\cases{H_{n+1}-(H_n+h_n)+\!\maxdepth!&
+%                $i=n\;\land\;H'_{n+1}=0\;\land\;$non-\lpage\cr
+%              0&otherwise}
+% \end{eqnarray*}
+% \endgroup
+% 

+% In the specifications above, $\w_c$ and $\Uidx\gap_c$ is the width of the
+% column $c$ and that of the \csepgap{} following it, defined by
+% \!\columnratio! or \!\setcolumnwidth! and stored in
+% $|\pcol@columnwidth|{\cdot}c$ and $|\pcol@columnsep|{\cdot}c$
+% respectively.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% \SpecialArrayMainIndex{c}{\pcol@columnsep}

+% 

+% The additions of $d_{c/g}$ and $d_s$ are to extend the bottom edge of each
+% region down to the bottom of text area.  In addition, for each
+% $\bgr_a^{[c]}=[(x_0,y_0)(x_1,y_1)]$, {\em\Uidx\bgext}s
+% $\Uidx{\bge}_a^{[c]}(\{x,y\}^\pm)$ can be specified to shift the base
+% points $x_0$, $y_0$, $x_1$ and $y_1$ left ($x^-$), right ($x^+$), upward
+% ($y^-$) and downward ($y^+$) respectively.  That is, a region is defined
+% as;
+% $$
+% \bgr_a^{[c]}=[(x_0-\bge_a^{[c]}(x^-),\;y_0-\bge_a^{[c]}(y^-))\;
+%               (x_1+\bge_a^{[c]}(x^+),\;y_1+\bge_a^{[c]}(y^+))]
+% $$
+% \begingroup\par\hfuzz0.9pt\noindent
+% with the optional shifts specified by the first argument of
+% \!\backgroundcolor!  as
+% \Arg{\hbox{\ttfamily\itshape{a}}\oarg{c}$|(|x^\pm|,|y^\pm|)|$} (for both
+% $x^-$/$y^-$ and $x^+$/$y^+$) or \Arg{\hbox{\ttfamily\itshape
+% a}\oarg{c}$|(|x^-|,|y^-|)||(|x^+|,|y^+|)|$} and kept in macros
+% $|\pcol@bg@ext@|{\cdot}\~d{\cdot}|@|{\cdot}a[{\cdot}|@|{\cdot}c]$
+% 

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% \SpecialArrayIndex
+%   {d{\cdot}\string\texttt{@}{\cdot}a{\cdot}\string\texttt{@}{\cdot}c}

+%   {\pcol@bg@ext@}

+% 

+% where $d\in\{|l|,|r|,|t|,|b|\}$ for $x^-$ (|l|), $x^+$ (|r|), $y^-$ (|t|)
+% and $y^+$ (|b|).  Note that $\bge_a^{[c]}(\{x,y\}^\pm)$ can be extremely
+% large, namely greater than or equal to 9000pt, to mean the region is
+% extended to a border near by the corresponding paper edge.  More
+% specifically, by this {\em\Uidx\bginfext}, each $xy$ coordinate in
+% $[(x_0,y_0)(x_1,y_1)]$ is defined as follows to represent a coordinate
+% being $10000\PT-\bge_a^{[c]}(\{x,y\}^\pm)+\!\pagerim!$ inside from the page
+% edge;
+% \par\endgroup
+% 

+% \begingroup \def\feven{f_{\mathit{even}}}
+% \begin{eqnarray*}
+% x_0&=&-\WM+(10000\PT-\bge_a^{[c]}(x^-)+\WR)\\
+% y_0&=&-(\HS+\HM)+(10000\PT-\bge_a^{[c]}(y^-)+\HR)\\
+% x_1&=&(\WP-\WM)-(10000\PT-\bge_a^{[c]}(x^+)+\WR)\\
+% y_1&=&(\HP-\HS-\HM)-(10000\PT-\bge_a^{[c]}(y^+)+\HR)\\
+% \Uidx\WP&=&\!\paperwidth!\\
+% \Uidx\WM&=&1|in|+\cases{\!\oddsidemargin!&$\lnot\feven$\cr
+%                         \!\evensidemargin!&$\feven$}\\
+% \Uidx\WR&=&\Uidx\HR=\!\pagerim!\\
+% \Uidx\HP&=&\!\paperheight!\\
+% \Uidx\HM&=&\!\headsep!+\!\headheight!+\!\topmargin!+1|in|\\
+% \Uidx\HS&=&\mathit{height}(\pp^b(p))+\mathit{depth}(\pp^b(p))
+% \end{eqnarray*}
+% \endgroup
+% 

+% where $f_{\mathit{even}}$ is $\true$ iff we are in an even numbered page
+% and two-sided typesetting is specified by the optional argument of
+% \!\documentclass! or by the specifier `|p|' of \!\twosided! explicitly or
+% implicitly.
+% 
+% Another remark is that \cswap{} affects $\bgr_c^c(i)$ and $\bgr_s^c(i)$ to
+% {\em\Uidx\mirror} the region making a reflection-symmetric transformation
+% on it using a vertical edge of a page as the axis.  That is,
+% $[(x_0,y_0)(x_1,y_1)]$ for a region is transformed to
+% $[(\WT-x_1,y_0)(\WT-x_0,y_1)]$ if $x_{\{0,1\}}$ is not extended infinitely.
+% With \bginfext{} on the other hand, before this transformation $x_0$ and/or
+% $x_1$ are calculated by the rule above replacing $\WM$ with
+% $\WP-(\WM+\WT)$ to represent the width of the right margin rather than the
+% left.
+% 
+% On the other hand, the \mirror{}ing of $\bgr_{\{s,S\}}$ is enabled by the
+% specifier `|b|' of \!\twosided!, together with other regions being top
+% margin ($t,T$), bottom margin ($b,B$), left margin ($l,L$), right margin
+% ($r,R$), \pwise{} floats ($f,F$) and \scfnote{} footnotes ($n,N$).  The
+% geometical specifications $\bgr_a$ for those regions are given as follows,
+% but the coordinate origin is at the top-left corner of text area (rather
+% than the leftmost column).
+% 

+% \begin{eqnarray*}
+% \bgr_{\{t,T\}}&=&[(-\WM+\WR,\;-\HM+\HR),\;(\WP-\WM-\WR,\;0)]\\
+% \bgr_{\{b,B\}}&=&[(-\WM+\WR,\;\HT-\HM),\;(\WP-\WM-\WR,\;\HP-\HM-\HR)]\\
+% \bgr_{\{l,L\}}&=&[(-\WM+\WR,\;0),\;(0,\HT)]\\
+% \bgr_{\{r,R\}}&=&[(\WT,\;0),\;(\WP-\WM-\WR,\;\HT)]\\
+% \bgr_{\{f,F\}}&=&[(0.\;0),\;(\WT,\;\HS)]\\
+% \bgr_{\{n,N\}}&=&[(0,\;\HT-\HN)\;(\WT,\;\HT)]\\
+% \Uidx\HT&=&\!\textheight!+\!\maxdepth!\\
+% \Uidx\HN&=&\!\skip!\!\footins!+\!\ht!\!\footins!+\!\dp!\!\footins!
+% \end{eqnarray*}
+% 

+% Note that, since we use text area coordinates, in the calculation of
+% \bginfext{} $\HS$ is let be 0.
+% 
+% We have other regions for columns and \csepgap{}s, namely $\bgr_C^c$ and
+% $\bgr_G^c$, which vertically span all over text area regardless exsistance
+% of any \pwstuff.  Therefore, their geometical specifications are as
+% follows with text area coordinates.
+% 

+% \begin{eqnarray*}
+% \bgr_C^c&=&[(\W_{c-1},\;0),\:(\W_{c-1}+w_c,\;\HT)]\\
+% \bgr_G^c&=&[(\W_{c-1}+w_c,\:0),\;(\W_c,\;\HT)]
+% \end{eqnarray*}
+% 

+% In addition, we have to paint \preenv{} and \postenv{} with color
+% $\bgc_{\{p,P\}}$.  The region $\bgr_{\{p,P\}}$ for them is defined as
+% follows with text area coordinates where $\Uidx\HB$ is the $y$-coordinate
+% of the bottom of previous \env{paracol} environment if any, or 0
+% otherwise.
+% $$
+% \bgr_{\{p,P\}}=\cases{
+%	[(0,\;\HB)\;(\WT,\;\HS)]&	\preenv\cr
+% 	[(0,\;\HB)\;(\WT,\;\HT)]&	\postenv}
+% $$
+% Note that paiting of \postenv{} is done {\em outside} \env{paracol}
+% environment when the \postenv{} encounters a page break, unless another
+% \env{paracol} environment starts in the page and thus the \postenv{}
+% becomes \preenv{} of the second (or subsequent) environment.
+% 
+% Finally, we define the order of \bgpaint{} as follows, where $a$, $a(i)$,
+% $a^c$ and $a^c(i)$ mean $\bgr_a$, $\bgr_a(i)$, $\bgr_a^c$ and
+% $\bgr_a^c(i)$ respectively, so that a succeding region is {\em overlaid}
+% on preceding regions.
+% 

+% \begin{eqnarray*}
+% T&\to&B\to L\to R\\
+% &\to&G^0\to\cdots\to G^{\C-2}\to C^0\to\cdots\to C^{\C-1}\\
+% &\to&t\to b\to l\to r\to N\to n\to\{F,P\}\to\{f,p\}\footnotemark\\
+% &\to&S(1)\to\cdots\to\S(n)\\
+% &\to&g^0(1)\to\cdots\to g^{\C-2}(1)\to c^0(1)\to\cdots\to c^{\C-1}(1)\to
+% 	s(1)\\
+% &\to&\cdots\\
+% &\to&g^0(n)\to\cdots\to g^{\C-2}(n)\to c^0(n)\to\cdots\to c^{\C-1}(n)\to
+% 	s(n)\\
+% &\to&g^0(n{+}1)\to\cdots\to g^{\C-2}(n{+}1)
+%  \to c^0(n{+}1)\to\cdots\to c^{\C-1}(n{+}1)
+% \end{eqnarray*}
+% 

+% \footnotetext{In column flushing, the order is $\{F,P\}\to\{f,p\}\to N\to
+% n$ but this reversion should have no effect (almost always).}
+%
+% 
+% 
+% \subsection{Page-wise Float Placement}
+% \label{sec:imp-ovv-float}
+% \changes{v1.32-3}{2015/10/10}
+% 	{Add the section ``Page-wise Float Placement'' to discuss the
+%	 page-wise float problem.} 
+% 
+% In the release on 2015/01/10, \LaTeX{}'s float placement mechanism was
+% drastically changed to avoid {\em out-of-order\/} appearance of \pwise{}
+% floats as follows.  Since the cause of overtaking of a \pwise{} float by a
+% \cwise{} float is that they are in two separated lists \!\@dbldeferlist!
+% for the former and \!\@deferlist! for the latter, in the new implemenation
+% the two lists are merged to let all floats go to \!\@deferlist!.  To
+% distinguish \pwise{} and \cwise{} floats in the list, \!\end@dblfloat!
+% lets the \pwise{} float processed by the macro have a special depth of
+% |1sp|, while depth of \cwise{} floats are 0 since \!\@endfloatbox! add a
+% \!\vskip! of 0 at the end of the box of floats.
+% 
+% Then all float placement macros invoked in \!\output!-routine examine the
+% depth of floats in the list they are working on against a newly introduced
+% macro \!\f@depth! by also newly introduced \!\@testwrongwidth!, so that
+% they process only floats of a page/column category specified by
+% \!\f@depth!, while those not matching to \!\f@depth! are let go to
+% \!\@deferlist! to inhibit succeeding floats of the same type from
+% overtaking them.  The \!\def!inition of \!\f@depth! is done only by
+% modified \!\@dblfloatplacement!, always invoked in a group, to let it have
+% |1sp| so that float placement macros usually work on \cwise{} ones with
+% the default setting of $\!\f@depth!=\!\z@!$ except for special occasions
+% in which the placement of \pwise{} floats is tried.
+% 
+% Though the mechanism should work well with {\em ordinary\/} multi-columned
+% documents, it is incompatible with \Paracol{} almost inherently.  That is,
+% in the first place we have to separate float-related lists into the sets
+% of them corresponding to columns as we do\footnote{

+% 

+% If counters \counter{figure} and \counter{table} are global and we have to
+% avoid inter-column overtaking with respect to, for example, the partial
+% ordering rooted by the top-left corner, merging \cwise{} lists together
+% with the merge of \cs{@deferlist} and \cs{@dbldeferlist} might be a
+% solution to let the depth of a \cwise{} float be $c\,\texttt{sp}$ while
+% that of \pwise{} is $\C$\,\texttt{sp}.  However such implementation is not
+% only tough but also doubtful to be worthwhile.}.
+% 

+% Therefore, it is obviously nonsense to merge the list for  \pwise{} floats,
+% i.e., \!\@dbldeferlist!, to \!\@deferlist! of a particular column, and
+% thus we have to stick with the conventional implementation to process
+% \pwise{} and \cwise{} floats separately as follows.
+% 

+% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
+% \item
+% \label{item:ovv-float-end@dblfloat}
+% We \!\def!ine our own \!\end@dblfloat! namely \!\pcol@end@dblfloat!
+% whose definition is exactly same as the old version of \!\end@dblfloat!,
+% and replace the new version with it by \!\let!ting them equivalent in
+% \!\pcol@zparacol! by which start \env{paracol} environments.  Therefore,
+% \pwise{} floats composed in a \env{paracol} environment is processed in
+% the traditional way, i.e., being inclueded in \!\@dbldeferlist! rather than
+% \!\@deferlist! and having ordinary depth 0.
+% 
+% \item
+% \label{item:ovv-float-@dblfloatplacement}
+% Each invocation of \!\@dblfloatplacement! in our own \!\output!-routine is
+% followed by a \!\let! to nullify the setting of $\!\f@depth!=|1sp|$ done
+% by \!\@dblfloatplacement! by doing \!\f@depth!=\!\z@!.  By this setting,
+% \!\@tryfcolumn! in \!\pcol@startpage!  and \!\@makefcolumn! in
+% \!\pcol@output@clear! work on their argument \!\@dbldeferlist! in the way
+% exactly same as in 2014 or before.
+% 
+% \item
+% \label{item:ovv-float-@addtodblcol}
+% Among \LaTeX's macros in its \!\output!-routine which we use in our own
+% one as well, only \!\@addtodblcol! changed its target from
+% \!\@dbldeferlist! to \!\@deferlist!.  That is, if the macro fails to put a
+% \pwise{} float to the page we just have started by \!\pcol@startpage!,
+% the float is added to \!\@deferlist! rather than \!\@dbldeferlist!.
+% Therefore, when we apply \!\@sdblcolelt! to the copy of \!\@dbldeferlist!
+% to invoke \!\@addtodblcol! for each of its element float, we have to save
+% \!\@deferlist! somewhere, to \!\reserved@c! in reality, and clear it prior
+% to the application.  Then after all elements are processed, we have to let
+% \!\@dbldeferlist! have what \!\@deferlist! have, while \!\@deferlist!
+% should regain its origial contents from the saved place.  A subtle issue
+% is that we might work with \LaTeX{} of 2014 or older in which the floats
+% are returned to \!\@dbldeferlist!.  Therefore to make \Paracol{}
+% compatible with both of new and old versions, we have to {\em add}
+% \!\@deferlist! to \!\@dbldeferlist! rather than replacing
+% \!\@dbldeferlist! with \!\@deferlist!.  This addition should work well,
+% because we clear both lists before the application of \!\@sdblcolelt!  and
+% then one of them will have the still-deferred floats after the application
+% while the other remains empty.
+% 
+% \item
+% \label{item:ovv-float-@output@start}
+% We convert \!\@deferlist! to \!\@dbldeferlist! in \!\pcol@output@start! to
+% start a \env{paracol} environment, and perform the reverse operation in
+% \!\pcol@output@end! to close the environment.  Though it is very unlikely
+% (or maybe impossible) that the \!\@deferlist! {\em imported\/} in the
+% former operation has \LaTeX's (i.e., not \Paracol's) double-column floats
+% of |1sp| deep, we make such floats old-fashioned making their depth 0 so
+% that they can be put in a page built in the \env{paracol} environment.  On
+% the other hand, the latter cannot {\em export\/} a list having floats of
+% |1sp| deep because they have been produced in the closing \env{paracol}
+% environment or have passed our {\em custom\/} \!\pcol@output@start! when
+% they were imported\footnote{

+% 

+% Therefore, if one try to {\em smuggle\/} a double-column float of the new
+% scheme into a \env{paracol} and to pass it through the environment to
+% another double-column world, the float will become a single-column one.
+% Even if such guy a really exists and complains abount this transformation,
+% however, we have good right to say ``don't do that''.}.
+% \end{enumerate}
+% 

+% Note that the operations (1), (2) and (4) are fully compatible with 2014
+% or older version of \LaTeX{}, because with the old version; (1) 
+% \!\pcol@end@dblfloat! is equivalent to \!\end@dblfloat!; (2) modification
+% of \!\f@depth! cannot be seen because it does not exist;  and (4) we
+% virtually do nothing in the importation.  As for (3), we explicitly take
+% care of the compatibility as shown above.
+% 
+% 
+% 
+% \section{Interaction with \TeX{} and \LaTeX{}}
+% \label{sec:imp-tex}
+% 
+% The macros of \Paracol{} interacts with \TeX{} and \LaTeX{} through
+% various registers and macros as discussed in this section.
+% 
+% \subsection{Registers}
+% \label{sec:imp-tex-reg}
+% 
+% \subsubsection{Insertion Registers}
+% 
+% \begin{description}
+% \item[\Uidx{\!\footins!}]
+% is used to \!\insert! footnotes through it by \!\footnote! and
+% \!\footnotetext!, and then in \!\output! routine the footnotes
+% \!\insert!ed in a page is presented in the register.  The register is
+% referred to by the following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! examines if the register has \Scfnote{}s and, if so,
+% saves it into $\pp^f(p)$ if $p=\ptop$ or discards it otherwise.
+% 
+% \item
+% \!\pcol@startcolumn! \!\insert!s $\pp^f(p)$ into the \colpage{} to be
+% created through the register.
+% 
+% \item
+% \!\pcol@specialoutput! logs the contents of the register for debugging.
+% 
+% \item
+% \!\pcol@output@start! examines if the register has footnotes to be merged
+% with those in \env{paracol} environment, refers to its height plus depth to
+% calculate effective \!\@colht!, and/or \!\insert!s its contents through
+% itself to the main vertical list as the first part of \Mgfnote{}s.
+% 
+% \item
+% \!\pcol@makenormalcol! combines footnotes in the register to other
+% \preenv{} to make a \spanning, or makes save\slash restore of the register
+% to/from \!\@tempboxa! to exclude footnotes from \spanning{} when
+% \mgfnote{}-footnote typesetting is specified.
+% 
+% \item
+% \!\pcol@output@switch! saves the register into $\pp^f(p)$ or $\cc_c(\ft)$,
+% or discards its contents, when we leave from the column $c$ with footnotes.
+% 
+% \item
+% \!\pcol@restartcolumn! restores $\cc_d(\ft)$ or $\pp^f(p)$ to the register
+% and then \!\insert!s the contents of \!\box!\!\footins! into itself so
+% that it contributes to the main vertical list to be rebuilt for the column
+% $d$.
+% 
+% \item
+% \!\pcol@getcurrfoot! for column $d$ lets the register have $\cc_d(\ft)$.
+% 
+% \item
+% \!\pcol@savefootins! saves the register into an \!\insert! for $\pp^f(p)$
+% or $\cc_c(\ft)$.
+% 
+% \item
+% \!\pcol@deferredfootins! refers the \!\skip! component of the register to
+% have the vertical skip above \Scfnote{}s and \!\insert!s deferred
+% footnotes through the register.
+% 
+% \item
+% \!\pcol@output@end! \!\insert!s $\pp^f(p)$ into the \lpage{} through the
+% register.
+% 
+% \item
+% \!\pcol@fntexttop!\marg{text} \!\insert!s the footnote $\arg{text}$ and a
+% penalty through the register.
+% 
+% \item
+% \!\pcol@fntextbody!\marg{text} refers to the \!\skip! component of the
+% register to cap the height of the footnote $\arg{text}$.
+% \end{itemize}
+% 
+% \item[\rm\Uidx{\!\bx@A!}, \ldots, \Uidx{\!\bx@R!}]
+% have floats created by \!\@xfloat! in the ordinary usage of {\em
+% fundamental\/} \LaTeX{} of 2014 or earlier or that without the extension
+% of e-\TeX{} or its relatives.  On the other hand, in \LaTeX{} of 2015 or
+% later and with e-\TeX{} or its relatives, the set is \!\bx@A!, \ldots,
+% \Uidx{\!\bx@Z!}, \Uidx{\!\bx@AA!}, \ldots, \Uidx{\!\bx@ZZ!}\@.  In addtion
+% to the use in \LaTeX, we use these registers for completed \colpage{}s
+% $s_c(p)$ (\!\pcol@opcol!, \!\pcol@flushcolumn!), main vertical list
+% $\cc_c(\vb)$ (\!\pcol@output@start!, \!\pcol@output@switch!,
+% \!\pcol@flushcolumn!)  and \Mcfnote{}s $\cc_c(\ft)$
+% (\!\pcol@output@switch!) in \ccolpage{}s, \spanning{} including \preenv{}
+% $\pp^i(p)$ (\!\pcol@startpage!, \!\pcol@output@start!) and \Scfnote{}s
+% $\pp^f(p)$ (\!\pcol@makecol!, \!\pcol@output@switch!) in pages,
+% \mvlfloat{}s for main vertical lists in \sync{}ed pages
+% (\!\pcol@synccolumn!), and \pwise{} floats deferred from \env{paracol} to
+% \postenv{} (\!\pcol@output@end!).
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Integer Registers}
+% 
+% \begin{description}
+% \item[\Uidx{\!\deadcycles!}]
+% is \TeX's primitive register to count the number of \!\output! requests
+% made between two \!\shipout! operatios.  It is zero-cleared by
+% \!\pcol@invokeoutput! because it can have a large number in a
+% \env{paracol} environment.
+% 
+% \item[\Uidx{\!\outputpenalty!}]
+% is \TeX's primitive register to have the page-break penalty with which
+% \!\output! routine is invoked.  It is referred to by \!\pcol@output! to
+% know whether it has special code less than $-10000$, and by
+% \!\pcol@specialoutput! in detail for the dispatch according to the code.
+% The register is also used for the communication from the latter, which lets
+% it be $-10000$ for our own special \!\output! routines, to the former to
+% determine \!\vsize! according to if the register has a value greater than
+% $-10004$ or not.
+% 
+% \item[\Uidx{\!\interlinepenalty!}]
+% is \TeX's primitive register to have the page-break penalty inserted
+% between two lines.  The register is referred to in the following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@output@start!  to make \Preenv{} \Mgfnote{}s followed by this
+% \!\penalty! on the \!\insert!ion, and to insert it to start the first
+% \colpage{} allowing page-break before the start unless it is inhibited
+% by $\CSIndex{if@nobreak}=\true$.
+% 
+% \item
+% \!\pcol@restartcolumn! to insert this \!\penalty! to resume a \colpage{}
+% allowing page-break if $\CSIndex{if@nobreak}=\false$.
+% 
+% \item
+% \!\pcol@deferredfootins!  to let the secnod half of split $\df$ have this
+% \!\penalty! as the very first element.
+% 
+% \item
+% \!\pcol@fntexttop!\marg{text} to make the footnote $\arg{text}$ followed
+% by this \!\penalty! on the \!\insert!ion.
+% 
+% \item
+% \!\pcol@fntextother!\marg{text} to make the footnote $\arg{text}$ preceded
+% by this \!\penalty! in $\df$.
+% 
+% \item
+% \!\pcol@fntextbody! to let the register have \!\interfootnotelinepenalty!.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\floatingpenalty!}]
+% is \TeX's primitive register to have the page-break penalty added to
+% \!\insertpenalties! if an \!\insert! is moved to the page next to the page
+% in which the line having the \!\insert! resides.  It is let have 20000 in
+% \!\pcol@fntextbody! for footnote typesetting.
+% 
+% \item[\Uidx{\!\vbadness!}]
+% is \TeX's primitive register to have the threshold of the badness of
+% \!\vbox! construction with underfull messages.  That is, if the badness
+% exceeds the threshold on a \!\vbox! construction, \TeX{} will complain
+% showing an underfull message. In \!\pcol@makenormalcol!  and
+% \!\pcol@deferredfootins!, the register is temporarily let have 10000 to
+% avoid that \!\@makecol! invoked in the former and \!\vsplit! done in the
+% latter causes the message with inevitable underfull.
+% 
+% \item[\Uidx{\!\showboxdepth!}]
+% is \TeX's primitive register to determine the maximum depth of box
+% structure to be shown in logging etc.  The register is let have 10000 in
+% \!\pcol@ShowBox!  for full logging.
+% 
+% \item[\Uidx{\!\showboxbreadth!}]
+% is \TeX's primitive register to determine the maximum breadth of box
+% structure to be shown in logging etc.  The register is let have 10000 in
+% \!\pcol@ShowBox!  for full logging.
+% 
+% \item[\Uidx{\!\interfootnotelinepenalty!}]
+% is an API \!\count! register to have \!\interlinepenalty! for footnotes.
+% It is used in \!\pcol@fntextbody! to let \!\interlinepenalty! have it.
+% 
+% \item[\Uidx{\!\@ne!}]
+% is a \!\chardef! register to have 1.  The register is referred to by the
+% following macros mainly for incrementing another register.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@F@count!,
+% \!\pcol@output!,
+% \!\pcol@opcol!,
+% \!\pcol@setpnoelt!,
+% \!\pcol@nextpage!,
+% \!\pcol@nextpelt!,
+% \!\pcol@startpage!,
+% \!\pcol@checkshipped!,
+% \!\pcol@outputelt!,
+% \!\pcol@ioutputelt!,
+% \!\@outputpage!,
+% \!\pcol@bg@paint@ii!,
+% \!\pcol@output@start!,
+% \!\pcol@makenormalcol!,
+% \!\pcol@output@switch!,
+% \!\pcol@setcurrcol!,
+% \!\pcol@iscancst!,
+% \!\pcol@addmarginpar!,
+% \!\pcol@do@mpbout@i!,
+% \!\pcol@sync!,
+% \!\pcol@flushcolumn!,
+% \!\pcol@measurecolumn!,
+% \!\pcol@synccolumn!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@imakeflushedpage!,
+% \!\pcol@iflushfloats!,
+% \!\pcol@freshpage!,
+% \!\pcol@output@end!,
+% \!\pcol@invokeoutput!,
+% \!\pcol@zparacol!,
+% \!\pcol@setcolwidth@r!,
+% \!\pcol@setcolwidth@s!,
+% \!\pcol@setcw@scan!,
+% \!\pcol@setcw@calcf!,
+% \!\pcol@synccounter!,
+% \!\pcol@com@syncallcounters!,
+% \!\pcol@stepcounter!,
+% \!\pcol@com@switchcolumn!,
+% \!\pcol@sptext!,
+% \!\pcol@visitallcols!,
+% \!\pcol@ifootnote!,
+% \!\pcol@ifootnotemark!.
+% \!\pcol@swapcolumn!,
+% \!\pcol@set@color@push!,
+% \end{quote}
+% 
+% \item[\Uidx{\!\tw@!}]
+% is a \!\chardef! register to have 2.  It is used in \!\pcol@setcurrcol! to
+% let $\cc_c(\sw)=2$ when $\CSIndex{if@nobreak}=\true$ but
+% $\CSIndex{if@afterindent}=\false$, in
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to calculate $x\cdot2^k$, $y/2^k$
+% and $(x/y)\cdot2^k$ with various $k$, and in \!\pcol@swapcolumn! to
+% calculate $\Cto-(c'-\Cfrom)-2=c-1=c^g$ for the \csepgap{} ordinal $c^g$
+% physically following the column $c$ at the position $c'$.
+% 
+% \item[\Uidx{\!\m@ne!}]
+% is a \!\count! register to have $-1$.  It is used in the following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@setpnoelt!, \!\pcol@nextpelt!, \!\pcol@getpelt! and
+% \!\pcol@setmpbelt! to decrement
+% \!\@tempcnta! which initially has $p-\pbase$ for a page $p$.
+% 
+% \item
+% \!\pcol@bg@paint@i! to decrement $\CBto$ by one locally to have the column
+% scanning range $\LBRP\CBfrom{\CBto{-}1}$.
+% 
+% \item
+% \!\pcol@iscancst! to decrement $\npop$ by one.
+% 
+% \item
+% \!\pcol@do@mpbout@i! to let \!\@tempcnta! have it to indicate left margin.
+% 
+% \item
+% \!\pcol@setcolwidth@r! to calculate $\Cto-\Cfrom-1$.
+% 
+% \item
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ in \!\@whilenum! loops to
+% calculate $z'/2^k$ and $z'/2{k-16}$ where $z'/2^k\approx x/y$.
+% 
+% \item
+% \!\pcol@iadjustfnctr! to decrement \!\c@footnote!.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\sixt@@n!}]
+% is a \!\chardef! register to have 16.  It is used in
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to calculate
+% $Z=z\times1\,|pt|=z'\cdot2^{16-k}$ where $z'/2^k\approx x/y$.
+% 
+% \item[\Uidx{\!\@m!}]
+% is a \!\mathchardef! register to have 1000.  It is used in
+% \!\pcol@synccolumn! and \!\pcol@output@end! to let
+% $\!\prevdepth!=1000\,|pt|$ on a \sync{}ation or the closing \env{paracol}
+% environment with an empty main vertical list, and in
+% \!\pcol@setcw@getspec@i! to add 1000\,|pt| to strech and shrink
+% compontents of \!\@tempskipa! having a column\slash gap sepcification to
+% make it sure the skip register has those components.
+% 
+% \item[\Uidx{\!\@M!}]
+% is a \!\mathchardef! register to have 10000.  It is used in the following
+% macros
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@ShowBox! to let \!\showboxdepth! and \!\showboxbreadth!  have
+% 10000 for full logging of a box.
+% 
+% \item
+% \!\pcol@output! to examine if $\!\outputpenalty!<-10000$ to mean a special
+% \!\output! request.
+% 
+% \item
+% \!\pcol@specialoutput! to let $\!\outputpenalty!=-10000$ to tell
+% \!\pcol@output! that the special \!\output! request is our own.
+% 
+% \item
+% \!\pcol@makenormalcol! and \!\pcol@deferredfootins! to let \!\vbadness!
+% have 10000 temporarily to avoid underfull messages.
+% 
+% \item
+% \!\pcol@synccolumn!  to bias \!\pcol@textfloatsep! by 10000\,|pt| to
+% indicate a \colpage{} has an \mvlfloat{} and in \!\pcol@cflt! and
+% \!\pcol@addflhd! to remove the bias.
+% 
+% \item
+% \!\pcol@switchcol! and \!\pcol@flushclear! to put \!\penalty!|-10000| for
+% forced page break.
+% 
+% \item
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to let $Z=z\times1\,|pt|=10000\,|pt|$
+% if $x/y$ is too large.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@Mii!}]
+% is a \!\mathchardef! register to have 10002.  It is used in
+% \!\pcol@end@dblfloat! to examine if $\!\@floatpenalty!=-10002$ to mean the
+% float environment to be closed is given in horizontal mode.
+% 
+% \item[\Uidx{\!\@Miv!}]
+% is a \!\mathchardef! register to have 10004.  It is used in \!\pcol@output!
+% to examine if $\!\outputpenalty!=-10004$ for a dummy \!\output! request
+% made by \LaTeX's float-related macros and our \!\pcol@invokeoutput! to
+% ensure the real request is not eliminated when it is made at the very
+% beginning of a page or a \colpage.  It is also used in
+% \!\pcol@specialoutput! for footnote logging when
+% $\!\outputpenalty!=-10004$.
+% 
+% \item[\Uidx{\!\@MM!}]
+% is a \!\mathchardef! register to have 20000.  It is used in
+% \!\pcol@fntextbody! to let \!\floatingpenalty! have it for footnote
+% typesetting.
+% 
+% \item[\Uidx{\!\@beginparpenalty!}]
+% is a \!\count! register to have the page-break penalty inserted before the
+% first \!\item! of each \env{list}-like environment.  The penalty is
+% determined in class files and is, for example, $-\!\@lowpenalty!=-51$ with
+% \textsf{article.cls}.  It is referred to and inserted by \!\pcol@zparacol!
+% when it finds the \env{paracol} environment to start is at the very
+% beginning of a \env{list}-like environment.
+% 
+% \item[\Uidx{\!\@floatpenalty!}]
+% is a \!\count! register to have the penalty code -10002 or -10003 given by
+% \!\@xfloat! at the beginning of a float environment according to the
+% environment is in horizontal or vertical mode respectively, or by
+% \!\marginpar! for a marginal note in the same meaning.  It is
+% referred to by \!\pcol@end@dblfloat! to insert the penalty, and by
+% \!\pcol@xympar! to confirm \!\marginpar! is error free.
+% 
+% \item[\Uidx{\!\@topnum!}]
+% is a \!\count! register to have the maximum number of top floats which the
+% \ccolpage{} can accept further.  It is used in \!\pcol@setcurrcol!
+% and \!\pcol@iigetcurrcol! to save\slash restore it into\slash from
+% $\cc_c(\tn)$.  The macro \!\pcol@synccolumn! also lets $\!\@topnum!=0$ to
+% inhibit top-float insertions in the \ccolpage{} any more after a
+% \sync{}ation.
+% 
+% \item[\Uidx{\!\@botnum!}]
+% is a \!\count! register to have the maximum number of bottom floats which
+% the \ccolpage{} can accept further.  It is used in \!\pcol@setcurrcol!
+% and \!\pcol@iigetcurrcol! to save\slash restore it into\slash from
+% $\cc_c(\bn)$.
+% 
+% \item[\Uidx{\!\@colnum!}]
+% is a \!\count! register to have the maximum total number of floats which
+% the \ccolpage{} can accept further.  It is used in \!\pcol@setcurrcol!
+% and \!\pcol@iigetcurrcol! to save\slash restore it into\slash from
+% $\cc_c(\cn)$.
+% 
+% \item[\Uidx{\!\col@number!}]
+% is a \!\count! register to have the number of columns.  It is let have 1
+% by \!\pcol@zparacol! and \!\pcol@sptext! regardless the real number of
+% columns $\C$ in order to keep \!\maketitle! from putting the title by
+% \!\twocolumn!.
+% 
+% \item[\Uidx{\!\c@page!}]
+% is \LaTeX's counter \Uidx{\counter{page}} being a \!\count! register to
+% have the page number.  It is referred to by \!\pcol@setpnoelt!, and
+% \!\pcol@output@start! to let $\pp^p(p)=\page(p)$.  The macro
+% \!\pcol@startpage! reload the register from $\pp^p(\ptop{-}1)$ and then
+% increment it by one usually but two in \npaired{} \parapag{}ing, and
+% repeat $\pp^p(\ptop)=\page(\ptop)$ and incrementing $\page(p)$ for each
+% \fpage{}s of \pwise{} floats.  Reloading $\page(p)$ to the register from
+% $\pp^p(p)$ is also done by \!\pcol@getpelt! for macros using
+% \!\pcol@getcurrpage!, and by \!\pcol@outputelt!, \!\pcol@sync! and
+% \!\pcol@makeflushedpage! by \!\pcol@getcurrpinfo!.  Then the register is
+% referred to by the following macros to exmine its parity.
+% 

+% \begin{itemize}
+% \item
+% Our own \!\@outputpage! to give $\page(p)$ or $\page(p)+1$ to
+% \!\pcol@outputpage@l! and \!\pcol@outputpage@r! which finally let the
+% register have the value to be referred to by \!\pcol@@outputpage! being
+% \LaTeX's \!\@outputpage!.
+% 
+% \item
+% \begin{Sloppy}{2800}%
+% \!\pcol@bg@swappage! to determine the values of \!\pcol@bg@leftmargin!
+% and \CSIndex{ifpcol@bg@@swap} with other factors.
+% \end{Sloppy}
+% 
+% \item
+% \!\pcol@shiftspanning! to decide the necessity of shifting \mctext{} left
+% with \cswap{}, examining {\em raw} \!\c@page! at the \!\output! request to
+% close the \mctext{} rather than $\pp^p(\ptop)$ which will have the correct
+% value with respect to possible jump {\em after} the macro completes its
+% work.
+% 
+% \item
+% \!\pcol@addmarginpar! to determine the margin to which a marginal note
+% goes.
+% 
+% \item
+% \!\pcol@do@mpbout@i! to determine which of $\mpb_L^l$ or $\mpb_L^r$ is the
+% target of the operation specified by \!\pcol@do@mpbout@elem!.
+% 
+% \item
+% $\!\pcol@swapcolumn!\<c_1\>\<c_2\>\<\Cfrom\>\<\Cto\>$ to determine $c_2$
+% for $c_1$ if \cswap{} is in effect.
+% \end{itemize}
+% 

+% In addition, to do the parity examination in \!\pcol@bg@swappage! above
+% correctly, the macros \!\pcol@ioutputelt!, \!\pcol@makeflushedpage!,
+% \!\pcol@imakeflushedpage!, \!\pcol@iflushfloats! and \!\pcol@output@end!
+% temporarily increment the register by one when they are working on a right
+% \npaired{} \parapag{}e.
+% 
+% The other users are \!\localcounter!\marg{ctr} to check
+% $\arg{ctr}\neq\counter{page}$, \!\pcol@remctrelt! to let
+% $|\cl@|{\cdot}\theta=\!\pcol@stepcounter!\Arg{\theta}$
+% 

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

+% unless $\theta=\counter{page}$, and \!\pcol@FF! to write it to a log file
+% as a part the logging information of memory leak debugging.
+% 
+% \item[\Uidx{\!\c@footnote!}]
+% is \LaTeX's counter \Uidx{\counter{footnote}} being a \!\count! register
+% to have the footnote number.  It is referred to by \!\pcol@zparacol! to
+% let $\bf=\!\pcol@footnotebase!$ have its value, by \!\pcol@calcfnctr! to
+% calculate the footnote ordinal which the one of its invoker
+% \!\pcol@iadjustfnctr! sets into the register, and by \!\endparacol! to let
+% the register have $\bf+\nf=\!\pcol@footnotebase!+\!\pcol@nfootnotes!$.
+% 
+% \item[$\cs{c@}{\cdot}\theta$]
+% \SpecialArrayUsageIndex{\theta}{\c@}

+% 

+% is a \!\count! register being \LaTeX's counter $\theta$.  It is referred
+% to by \!\pcol@savectrelt! to let $\val_c(\theta)=\Val(\theta)$ for saving
+% it in $\Cc_c$, by \!\pcol@cmpctrelt! to examine if
+% $\val_0(\theta)=\Val(\theta)$ to detect a modification outside
+% \env{paracol} environment, and by \!\pcol@syncctrelt! to let
+% $\val_c(\theta)=\Val(\theta)$ for all $c$ for \csync{}.  It is also
+% referred to by \!\pcol@remctrelt! and \!\localcounter! to examine if
+% $\theta=\counter{page}$.  The macros \!\pcol@setctrelt! and
+% \!\pcol@stpldelt! restore the value of the counter from $\val_c(\theta)$,
+% while \!\pcol@stpclelt! lets $\Val(\theta)=0$ for zero-clearing of
+% descendent counters.
+% 
+% \item[\Uidx{\!\count@!}]
+% is a \!\count! register for temporary use.  It is used in
+% \!\pcol@iscancst! to have $m$ of $\mcelt_{i,m}$,
+% \!\pcol@addmarginpar! to have the physical column position of the current
+% column $c$ in which \!\marginpar! is given, and in
+% $\!\pcol@extract@fil@i!\<s\>\!\@nil!$ to exract the unit of the stretch
+% component $s$ of a glue.
+% 
+% \item[\Uidx{\!\@tempcnta!}]
+% is a \!\count! register for temporary use.  The usages of this register
+% are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@F@count!, it is used to measure the cardinality of
+% \!\@freelist!.
+% 
+% \item
+% In \!\pcol@makecol!, it is used to keep $\page(\ptop)$ gotten by
+% \!\pcol@getcurrpinfo! until we store it back by \!\pcol@defcurrpage!.
+% 
+% \item\begin{Sloppy}{3700}
+% In \!\pcol@setpageno!, \!\pcol@setpnoelt!, \!\pcol@nextpage!,
+% \!\pcol@nextpelt!, \!\pcol@getcurrpage!, \!\pcol@getpelt!,
+% \!\pcol@addmarginpar! and \!\pcol@setmpbelt!, it has $p-q$ when we scan
+% $\pp(q)$ for all $q\in[\pbase,\ptop]$ and the \ccolpage{} is at $p$.
+% \end{Sloppy}
+% 
+% \item
+% In \!\pcol@checkshipped!, it has $c$ when we scan $\S_c$ for all
+% $c\In0\C$ to examine if all of them are not empty and thus we have pages
+% to be shipped out.
+% 
+% \item
+% In \!\pcol@ioutputelt!, it has $c'$ when we scan $\s_c(q)$ for all
+% $c\In0\CL$ or $c\In\CL\C$ to build the shipping out image of a page $q$,
+% where $c=c'$ or $c=\Cto-1-(c'-\Cfrom)$ where
+% $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
+% 
+% \item
+% In \!\@outputpage!, it has $\page(p)$ or $\page(p)+1$ to be given to
+% \!\pcol@outputpage@l! or \!\pcol@outputpage@r! as their argument when they
+% are used to ship out the second (not always right) component of a
+% \parapag{}e pair.
+% 
+% \item
+% In \!\pcol@bg@columnleft!, it has a value in $\LBRP\CBfrom{c}$ to sum up
+% the width of columns and \csepgap{}s in the range.
+% 
+% \item
+% In \!\pcol@output@switch!, it is used to have $\page(p)$ obtained by
+% \!\pcol@getcurrp~info! and simply to store the value in $\pp^p(p)$ by
+% \!\pcol@defcurrpage!  when we use these macros to add an element to
+% $\pp^s(p)$ and/or let $\pp^f(p)=\!\footins!$.
+% 
+% \item
+% In \!\pcol@setcurrcol!, it has the code calculated from
+% \CSIndex{if@nobreak} and |\if@after|\~|indent| to be saved in
+% $\cc_c(\sw)$.
+% 

+% \SpecialIndex{\if@afterindent}

+% 
+% \item
+% In $\!\pcol@scancst!\arg{box}$, it is let have
+% $\arg{box}\in\{\!\pcol@colorins!,|\pcol@color|\~|stack@saved|\}$ and then is
+% referred to in \!\pcol@iscancst!.
+% \SpecialIndex{\pcol@colorstack@saved}

+% 
+% \item
+% In \!\pcol@addmarginpar! besides the page scan shown above, it is used to
+% scan all columns whose physical position is left from the current
+% colum $c$ to measure the distance between the left edges of the leftmost
+% column and $c$.
+% 
+% \item
+% In \!\pcol@do@mpbout@i!, it has $\pm1$ according to the margin ($\rm
+% left=-1$) which marginal notes outside \env{paracol} environments goes
+% to.
+% 
+% \item
+% In \!\pcol@flushcolumn!, it is used to throw $\page(\ptop)$ away when we
+% get it by \!\pcol@getcurrpinfo! because we don't need it.
+% 
+% \item
+% In \!\pcol@setcolwidth@r!, it has $c$ to scan fractions $r_d$ where
+% $d=c-\Cfrom$ in its argument $\arg{ratio}$ specified by \!\columnratio!,
+% and then to distribute the unspecifed portion of \!\textwidth! evenly to
+% $\w_c$ for all $c\In{\Cfrom{+}k{+}1}\Cto$, where $k$ is the number of
+% fractions and $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
+% 
+% \item
+% In $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\Arg{spec}$, it has $c$ for two
+% loops for $c\In\Cfrom\Cto$ to add `|,|' to the tail of $\arg{spec}$ as
+% many as $k=\Cto-\Cfrom$ and then to process first $k$ elements in
+% $\arg{spec}$, and is referred to by \!\pcol@setcw@set! invoked in the
+% second loop.
+% 
+% \item
+% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, it used to calculate and to have
+% $k$ such that $z'/2^k\approx x/y$.
+% 
+% \item
+% In \!\pcol@cmpctrelt!, it has $\Val(\theta)$ of a counter $\theta$ to be
+% compared with $\val_0(\theta)$.
+% 
+% \item
+% In \!\pcol@com@switchcolumn!, it has $(c+1)\bmod\C$ being the target of
+% \cswitch{}.
+% 
+% \item
+% In \!\pcol@sptext!, it temporarily has $d$ being the target of \cswitch{}
+% during we let \!\pcol@nextcol! have 0 to visit the leftmost column
+% to put a \mctext{}.
+% 
+% \item
+% In \!\pcol@visitallcols!, it has $d\In0\C-\{c\}$ being the columns to be
+% visited for \cscan{}ning.
+% 
+% \item
+% In \!\definecolumnpreamble!\marg{c}\marg{pream}, $c$ is assigned to the
+% register to ensure $c$ is a number.
+% 
+% \item
+% In \!\pcol@calcfnctr!, it has the footnote ordinal calculated by the
+% macro to be referred to by the invokers \!\pcol@iadjustfnctr! and
+% \!\pcol@iifootnotetext!.
+% 
+% \item
+% In $\!\marginparthreshold!\Arg{t_l}|[|t_r|]|$ it is let have $t_l$, while
+% in the related macro $\!\pcol@marginparthreshold!|[|t_r|]|$ it is let have
+% $t_r$.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@tempcntb!}]
+% is a \!\count! register for temporary use.  It is used in the following
+% macros.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@ioutputelt! it has $c$, while in \!\pcol@imakeflushedpage! and
+% \!\pcol@iflushfloats! it has $c'$, to have $c=c'$ or $c=\Cto-1-(c'-\Cfrom)$
+% according to \cswap{} for $c'$-th iteration of column scanning loop for
+% $c'\In\Cfrom\Cto$, where $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
+% 
+% \item
+% In \!\pcol@scancst! and \!\pcol@iscancst!, it has $\npop$.
+% 
+% \item
+% In \!\pcol@addmarginpar!, it is let have the column number $d$ whose
+% phisical position is left from the current colum $c$ to measure the
+% distance between the left edges of the leftmost column and $c$.
+% 
+% \item
+% In \!\pcol@sync! and \!\pcol@measurecolumn!, it has the (so-far) tallest
+% column which gives $\VP$.
+% 
+% \item
+% In \!\pcol@setcolwidth@r!, it has $\Cto-\Cfrom-1$ then $\Cto-1$ and
+% finally $\Cto-\min(\Cfrom{+}k,\,\Cto{-}1)$, where $k$ is the number of
+% fractions given in the argument of \!\columnratio! and
+% $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
+% 
+% \item
+% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, at first it is used to calculate
+% $z'/2^k\approx x/y$ and then to calculate
+% $Z=z\times1\,|pt|=z'\cdot2^{16-k}$.
+% 
+% \item
+% In \!\pcol@visitallcols!, it has $c=\!\pcol@currcol!$ to exclude it from
+% the \cscan{} targets.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Dimension Registers}
+% 
+% \begin{description}
+% \item[\Uidx{\!\vsize!}]
+% is \TeX's primitive register to have the height of a page or a \colpage{}
+% being built.  It is let be \!\@colroom! or \!\maxdimen! by
+% \!\pcol@output!.
+% 
+% \item[\Uidx{\!\hsize!}]
+% is \TeX's primitive register to have the width of a page or a \colpage{}
+% being built.  It is let be $\w_c$ by \!\pcol@invokeoutput! to restart (or
+% stay in) the column $c$, be \!\textwidth! by \!\pcol@sptext! for \mctext,
+% and be either of \!\textwidth! or $\w_c$ by \!\pcol@fntextbody! according
+% to the footnote typesetting being \scfnote{} or \mcfnote{} resepectively.
+% 
+% \item[\Uidx{\!\maxdepth!}]
+% is \TeX's primitive register to have the maximum depth of the page being
+% built.  In \LaTeX, it is assumed that its value is fixed at
+% \beginenv{document}, in which the value is saved into \!\@maxdepth!, for
+% the typesetting throughout the document, unless a bottom float is added to
+% a page in which the register is let have 0 until it is shipped out.  This
+% temporary setting for a page with bottom floats has some reasonability but
+% its implementation for \env{paracol} environments having \cswitch{}
+% from/to a \colpage{} with bottom floats to/from another one without
+% them is too costly\footnote{

+% 

+% That is, we would need to incorporate \cs{maxdepth} as a member of
+% \cctext, but we don't because the idea of temporary setting itself is too
+% vague to pay the effort and a precious membership in \cctext.}.
+% 

+% Therefore, we let the register have \!\@maxdepth! in \!\pcol@output! and
+% \!\pcol@combinefloats! to cancel the temporary setting done in
+% \!\@addtobot! for the references by \TeX's page builder and \!\@cflt!
+% respectively.
+% 
+% \item[\Uidx{\!\boxmaxdepth!}]
+% is \TeX's primitive register to have the maximum depth of \!\vbox!es.
+% The macros \!\pcol@cflt!, \!\pcol@opcol!,
+% \!\pcol@ioutputelt!, \!\pcol@combine~floats!, \!\pcol@output@flush! and
+% \!\pcol@output@clear! let it be \!\@maxdepth! for the boxes having a
+% completed \colpage{} or page to cap the depth of the box.  The macro
+% $\!\pcol@@makecol!\<d\>$ also do that when $d=\!\@maxdepth!$ but it can be
+% $d=0$ when it is invoked to build \lpage{}.
+% 
+% \item[\Uidx{\!\splitmaxdepth!}]
+% is \TeX's primitive register to have the maximum depth of the \!\vbox!
+% being the first half of a box being split.  It is used in
+% \!\pcol@deferredfootins! to cap the depth of the first half of deferred
+% footnotes split from $\df$, and in \!\pcol@fntextbody! to let it have the
+% depth of \!\strutbox!.
+% 
+% \item[\Uidx{\!\prevdepth!}]
+% is \TeX's primitive register to have the depth of the box which just has
+% been added to a vertical list, or to be given to \TeX's vertical list
+% builder for the calculation of the vertical skip inserted below the last
+% box.  The macro \!\pcol@invokeoutput! refers to it to save its value in
+% \!\pcol@prevdepth! before putting a dummy \!\vbox! and making a \!\output!
+% request, and then let it have \!\pcol@prevdepth! which is given by
+% \!\output! routine for the column that we resume.  The macro
+% \!\pcol@zparacol!  also refers to it to save it in \!\pcol@firstprevdepth!
+% for the \preenv.
+% 
+% \item[\Uidx{\!\vfuzz!}]
+% is \TeX's primitive register to have the threshold height of overfull
+% messaging.  It is set to 0 in $\!\pcol@ShowBox!\arg{b}$ to ensure overfull
+% for any \!\box! $b$ of non-null height.
+% 
+% \item[\Uidx{\!\maxdimen!}]
+% is a \!\dimen! register to have $16383.99999\,|pt|$ being the largest
+% legal dimensional value.  The usages of this register are as follows.
+% 

+% \begin{itemize}
+% \item
+% For the \!\insert! register set $\!\pcol@colorins!=\cstraw$,
+% \!\dimen!\!\pcol@colorins! is let be \!\maxdimen! for the consistency with
+% our intention that a \colpage{} can have virtually infinite number of
+% \!\insert!ions for text coloring.
+% 
+% \item
+% In \!\pcol@output!, it is set into \!\vsize! when $\!\outputpenalty!=-10004$
+% for the dummy \!\output! request so that no page break should occur
+% between the dummy and real requests.
+% 
+% \item
+% Our own \!\dimen! register \!\pcol@textfloatsep! has \!\maxdimen! if a
+% \colpage{} does not have \sync{}ation points to let top floats are
+% inserted in usual way.  Therefore, \!\pcol@floatplacement! and
+% \!\pcol@zparacol!  let the register have \!\maxdimen! as the initial
+% value.  Then the macros \!\pcol@makecol! and \!\pcol@combinefloats!
+% examine if $\!\pcol@textfloatsep!=\!\maxdimen!$ to determine the operation
+% type of top float insertion, while \!\pcol@synccolumn! does that to know
+% if it is flushing a \colpage{} with a \sync{}ation point or is setting the
+% first \sync{}ation point in the \colpage{}.  The macro \!\pcol@addflhd!
+% also examines it for the measurement of the combined height of top and
+% bottom floats, while \!\pcol@measurecolumn! gives it \!\maxdimen! as its
+% third argument for bottom floats.
+% 
+% \item
+% The \pctext{} $\pp^h(p)$ has $-\!\maxdimen!$ if the page is a \fpage{}.
+% The macro \!\pcol@startpage! makes that when it creates such a page.
+% 
+% \item
+% Our own \!\pcol@prevdepth! and that saved in $\cc_c(\pd)$ have
+% \!\maxdimen! if the main vertical list is empty at a \sync{}ation.  The
+% macro \!\pcol@measurecolumn! makes that when it finds an empty list.
+% 
+% \item
+% The \cctext{} $\cc_c(\tr)$ may have \!\maxdimen! if the column $c$ has a
+% \fcolumn{} in the \lpage{} of a \env{paracol} environment and the floats in
+% it can be put as top floats.  The macro \!\pcol@makefcolumn! makes this
+% special assignment, and \!\pcol@flushcolumn! and \!\pcol@imakeflushedpage!
+% examine it.
+% 
+% \item
+% The macro \!\pcol@makefcolelt! let the room for floats in a \fpage{} be
+% $-\!\maxdimen!$ if it finds no futher floats can be added to the page.
+% 
+% \item
+% At a \sync{}ation, we measure the maximum combined size of top floats and
+% the main vertical list $\VT$, that of footnotes and bottom floats $\VB$,
+% that of four items $\VP$, and $\VPP$ being $\VP$ or $\VP+\!\textfloatsep!$
+% according to the existence of bottom floats.  We also let $\DT$ and $\DP$
+% be the minimum depth of the \colpage{}s which gives $\VT$ and $\VPP$
+% respectively.  For the measurement, the macro \!\pcol@sync! lets
+% $\VT=\VB=\VP=\VPP=-\!\maxdimen!$ and $\DT=\DP=\!\maxdimen!$ as their
+% initial values.  Then the macro \!\pcol@synccolumn! examines if
+% $\DT=\!\maxdimen!$ to mean the \sync{}ation point is set just below the
+% top floats of a column whose main vertical list is empty.  On the other
+% hand, \!\pcol@makeflushedpage! and \!\pcol@output@end! examine if
+% $\VPP=-\!\maxdimen!$ to mean the last \colpage{}s are empty.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\linewidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of a line possibly shorter than \!\columnwidth! in \env{list}-like
+% environments.  It is let have $\w_c-\lrm$ by
+% \!\pcol@invokeoutput! for the outermost paragraphs in \env{paracol}
+% environment, where $\lrm=\!\pcol@lrmargin!=\!\textwidth!-l$ which
+% \!\pcol@zparacol! lets have to represent the left-plus-right margin of the
+% \env{list}-like environment, whose \!\linewidth! is $l$, enclosing
+% \env{paracol} if any.  The macro \!\pcol@sptext! also sets the register
+% temporarily for \mctext{}s but letting it have $\!\textwidth!-\lrm$.
+% 
+% \item[\Uidx{\!\footnotesep!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% vertical space inserted in a footnote when it is split into two or more
+% pages.  It is uesed in \!\pcol@fntextbody! to \!\splittopskip! have it,
+% and to make the first line of the footnote is at least as tall as the
+% amount in the register.
+% 
+% \item[\Uidx{\!\topmargin!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% (height) of the top margin minus 1\,inch.  The register is used as an
+% element of \!\pcol@bg@pagetop! to calculate the distance from the origin
+% at the left-top corner of text area to the top edge of a page.  The
+% other users are \!\pcol@ioutputelt! and \!\pcol@makeflushedpage!
+% temporarily add the height-plus-depth of $\pp^b(p)$ to the register to
+% make the calculation biased shifting the origin to the left-top corner of
+% column area, i.e., below $\pp^b(p)$.  The macro \!\@outputpage! also
+% refers to the register together with \!\headheight! and \!\headsep! to
+% calculate the distance from the page top (ingoring 1\,inch shift) to the
+% text area top.
+% 
+% \item[\Uidx{\!\oddsidemargin!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of the left margin minus 1\,inch for two-sided odd-numbered pages and
+% all single-sided pages.  The register is used together with
+% \!\evensidemargin! in \!\pcol@outputpage@l!, \!\pcol@outputpage@r! and
+% \!\pcol@bg@swappage! to decide the left margin of the page they are
+% working on.
+% 
+% \item[\Uidx{\!\evensidemargin!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of the left margin minus 1\,inch for two-sided even-numbered pages.  The
+% register is used together with \!\oddsidemargin! in \!\pcol@outputpage@l!,
+% \!\pcol@outputpage@r! and \!\pcol@bg@swappage! to decide the left margin
+% of the page they are working on.
+% 
+% \item[\Uidx{\!\headheight!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% height of page headers.  The register is used together with \!\topmargin!
+% and \!\headsep! as an element of \!\pcol@bg@pagetop! and in \!\@outputpage!
+% to calculate the distance from the real and imaginary page top to the text
+% area top respectively.
+% 
+% \item[\Uidx{\!\headsep!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% vertical distance from the bottom of a page header to the text area top.
+% The register is used together with \!\topmargin!  and \!\headheight! as an
+% element of \!\pcol@bg@pagetop! and in \!\@outputpage!  to calculate the
+% distance from the real and imaginary page top to the text area top
+% respectively.
+% 
+% \item[\Uidx{\!\textheight!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% height of text area in a page.  The register is referred to by
+% \!\pcol@output! to examine if a page is very short, by \!\pcol@getpinfo!,
+% \!\pcol@startpage!, \!\pcol@flushfloats! and \!\pcol@output@end! to let
+% \!\@colht! be it for a page without \spanning{} (so far), by
+% \!\pcol@outputelt!, \!\@outputpage!, \!\pcol@output@flush! and
+% \!\pcol@output@clear! to build a page to be shipped out, by
+% \!\pcol@bg@textheight! to calculate $\HT$, and by \!\pcol@fntextbody! to
+% cap the height of a footnote.
+% 
+% \item[\Uidx{\!\textwidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of a page, which we occasionally refer to as $\WT$.  The register is
+% referred to by \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and
+% \!\pcol@iflushfloats! to build a \!\hbox! of \!\textwidth! wide to have
+% all columns (in a left or right \parapag{}e).  It also referred to by
+% following macros; \!\pcol@bg@swappage! to calculate the right margin for
+% \mirror{}ed \bgpaint; \!\pcol@bg@@r!, \!\pcol@bg@@f!, \!\pcol@bg@@n!,
+% \!\pcol@bg@@p!  and \!\pcol@bg@@s! to specify the width of \bground{} of
+% \pwstuff{} to be painted; \!\pcol@shiftspanning! to calculate the
+% left-shift amount of a \mctext{} in \cswap; \!\pcol@addmarginpar! to
+% measure the distance between the right edges of the rightmost and current
+% columns; \!\pcol@zparacol! for the calculation of
+% $\lrm=\!\pcol@lrmargin!$; \!\pcol@setcolwidth@r! for the calculation of
+% $\w_c$ for all $c\In0\CL$ or $c\In\CL\C$; \!\pcol@setcw@calcfactors! for
+% the calculation of $\WT/W$ and $(\WT-W)/F$; \!\pcol@sptext!,
+% \!\footnoterule!  of \env{paracol}'s local and \!\endparacol!  to set it
+% in \!\columnwidth!; and \!\pcol@fntextbody!  to set it in \!\hsize! if
+% \Scfnote{} typesetting is in effect.
+% 
+% \item[\Uidx{\!\columnwidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of a column.  The register is let have $\w_c$ by \!\pcol@getcurrcol! for
+% the column $c$, then is referred to by the following macros;
+% \!\pcol@shiftspanning! to calculate the left-shift amount of a \mctext{} in
+% \cswap; \!\pcol@addmarginpar! to measure the distance between the right
+% edges of the rightmost and current columns; \!\pcol@imakeflushedpage! and
+% \!\pcol@iflushfloats! to put each \colpage{} into a \!\hbox! of $\w_c$ wide
+% for shipping a page out; \!\pcol@invokeoutput! to let \!\linewidth! and
+% \!\hsize!  have the value of or based on it; and \!\pcol@fntextbody! to
+% let \!\hsize! have it for \Mcfnote{} typesetting.  The register is also
+% let have \!\textwidth! by \!\footnoterule! of \env{paracol}'s local
+% defined in \!\pcol@zparacol! if \Scfnote{} typesetting is in effect, by
+% \!\pcol@sptext!  for \mctext{}s, and by \!\endparacol! for \postenv.
+% 
+% \item[\Uidx{\!\columnsep!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of \csepgap{}s.  It is referred to by \!\pcol@setcolwidth@r! to
+% calculate $\w_c$ for all $c\In0\CL$ or $c\In\CL\C$, and by
+% \!\pcol@setcw@getspec! as the default width of \csepgap{}s.
+% 
+% \item[\Uidx{\!\columnseprule!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of the rules to be drawn in \csepgap{}s. It is referred to by
+% \!\pcol@buildcolseprule! and \!\pcol@buildcselt! to draw the rule, and by
+% \!\pcol@hfil! to examine if it is positive to mean the rule is really
+% drawn and if so to add skips of $-\!\columnseprule!/2$ to surround the
+% rule to nullify the width of the rule.
+% 
+% \item[\Uidx{\!\marginparwidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of a marginal note.  It is temporarily modified by \!\pcol@addmarginpar!
+% so that a left marginal note is placed appropriately.
+% 
+% \item[\Uidx{\!\marginparsep!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% distance between a marginal note and text area.  It is temporarily
+% modified by \!\pcol@addmarginpar!  so that a right marginal note is placed
+% appropriately.
+% 
+% \item[\Uidx{\!\marginparpush!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% minimum vertical distance between two marginal notes.  It is referred to
+% by \!\pcol@addmarginpar! to find a place for a marginal note and remember
+% the place in $\pp^m(p)$.
+% 
+% \item[\Uidx{\!\paperheight!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the height
+% of physical pages $\HP$.  It is referred to by \!\pcol@bg@paperheight!
+% to calculate $\HP-2\WR$.
+% 
+% \item[\Uidx{\!\paperwidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of physical pages $\WP$.  It is referred to by \!\pcol@bg@swappage! to
+% calculate the right margin for \mirror{}ed \bgpaint, and by
+% \!\pcol@bg@paperwidth!  to calculate $\WP-2\WR$.
+% 
+% \item[\Uidx{\!\z@!}]
+% is a \!\dimen! register to have 0\,|pt| to initialize \!\pagerim!,
+% \!\belowfootnoteskip! and \!\skip!\!\pcol@colorins! at their declarations,
+% and is used in the following macros.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@ShowBox!,
+% \!\pcol@makecol!,
+% \!\pcol@combinefloats!,
+% \!\pcol@nextpelt!,
+% \!\pcol@floatplacement!,
+% \!\pcol@startpage!,
+% \!\pcol@restartcolumn!,
+% \!\pcol@outputelt!,
+% \!\pcol@ioutputelt!,
+% \!\pcol@buildcolseprule!,
+% \!\pcol@buildcselt@S!,
+% \!\pcol@buildcselt!,
+% \!\@outputpage!,
+% \!\pcol@startcolumn!,
+% \!\pcol@bg@paint@i!,
+% \!\pcol@bg@paintregion!,
+% \!\pcol@output@start!,
+% \!\pcol@putbackmvl!,
+% \!\pcol@iscancst!,
+% \!\pcol@deferredfootins!,
+% \!\pcol@combinefootins!,
+% \!\pcol@addmarginpar!,
+% \!\pcol@getmparbottom!,
+% \!\pcol@sync!,
+% \!\pcol@measurecolumn!,
+% \!\pcol@synccolumn!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@imakeflushedpage!,
+% \!\pcol@output@end!,
+% \!\pcol@invokeoutput!,
+% \!\pcol@setcolwidth@s!,
+% \!\pcol@setcw@calcfactors!,
+% \!\pcol@setcw@calcf!,
+% \!\pcol@extract@fil@ii!,
+% \!\pcol@sptext!,
+% \!\pcol@fntextbody!.
+% \!\pcol@marginpar!,
+% \!\pcol@icolumncolor!,
+% \!\pcol@set@color@push!,
+% \!\pcol@reset@color@pop!,
+% \!\pcol@reset@color@mpop!,
+% \!\pcol@backgroundcolor@iii!.
+% \end{quote}
+% 

+% It is also used to give the number 0 for the initializations of
+% \!\pcol@currcol!, \!\pcol@ncol!, \!\pcol@ncolleft! and
+% \!\count!\!\pcol@colorins! at their declarations, and in the following
+% macros.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@ShowBox!,
+% \!\pcol@F@count!,
+% \!\pcol@makecol!,
+% \!\pcol@opcol!,
+% \!\pcol@setpnoelt!,
+% \!\pcol@nextpelt!,
+% \!\pcol@checkshipped!,
+% \!\pcol@getpelt!,
+% \!\pcol@outputelt!,
+% \!\pcol@ioutputelt!,
+% \!\@outputpage!,
+% \!\pcol@startcolumn!,
+% \!\pcol@output@start!,
+% \!\pcol@output@switch!,
+% \!\pcol@setcurrcol!,
+% \!\pcol@iscancst!,
+% \!\pcol@addmarginpar!,
+% \!\pcol@setmpbelt!,
+% \!\pcol@do@mpbout@i!,
+% \!\pcol@sync!,
+% \!\pcol@synccolumn!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@imakeflushedpage!,
+% \!\pcol@flushfloats!,
+% \!\pcol@iflushfloats!,
+% \!\pcol@freshpage!,
+% \!\pcol@output@end!,
+% \!\pcol@zparacol!,
+% \!\pcol@setcolwidth@r!,
+% \!\pcol@setcw@calcf!,
+% \!\pcol@synccounter!,
+% \!\pcol@com@syncallcounters!,
+% \!\pcol@stepcounter!,
+% \!\pcol@stpclelt!,
+% \!\pcol@com@switchcolumn!,
+% \!\pcol@switchcolumn!,
+% \!\pcol@sptext!,
+% \!\pcol@switchcol!,
+% \!\pcol@visitallcols!,
+% \!\pcol@xympar!,
+% \!\endparacol!.
+% \end{quote}
+% 
+% \item[\Uidx{\!\p@!}]
+% \begin{Sloppy}{3950}%
+% is a \!\dimen! register to have 1\,|pt|.  It is used in \!\pcol@ShowBox!,
+% \!\pcol@cflt!, \!\pcol@addflhd!, \!\pcol@synccolumn!, \!\pcol@output@end!,
+% \!\pcol@setcolwidth@s!, \!\pcol@setcw@getspec@i!, \!\pcol@setcw@fill! and
+% \!\pcol@setcw@calcf!, and the top level assignment to \!\@tempskipa! for
+% the invocation of \!\pcol@defkw!, as the shorthand of |pt|.
+% \end{Sloppy}
+% 
+% \item[\Uidx{\!\@totalleftmargin!}]
+% is a \!\dimen! register to have the total size of the left margins of a
+% \env{list}-like environment and those surrounding it.  It is given to
+% \!\parshape! by \!\pcol@invokeoutput! and \!\pcol@sptext! if \env{paracol}
+% is enclosed in a \env{list}-like environment.
+% 
+% \item[\Uidx{\!\@themargin!}]
+% is a control sequence \!\let!-equal to \!\evensidemargin! for two-sided
+% even numbered pages or \!\oddsidemargin! for others.  In
+% \!\pcol@outputpage@l! and \!\pcol@outputpage@r! it is bound to one of
+% \!\dimen! registers for the references in \!\pcol@outputpage@ev!\footnote{

+% 

+% The reference in \CSIndex{pcol@@outputpage} being \LaTeX's
+% \CSIndex{@outputpage} is done after the macro itself makes the assignment,
+% which is of course consistent with those in our macros.}.
+% 
+% \item[\Uidx{\!\@maxdepth!}]
+% is a \!\dimen! register to have \!\maxdepth! at \beginenv{document} to
+% recover the temporary update of \!\maxdepth! with 0 by \!\@addtobot! for
+% bottom float incorporation in a page.  As discussed in the explanation of
+% \!\maxdepth!, in \env{paracol} environments \!\maxdepth! is let have
+% \!\@maxdepth! always by the assignments in \!\pcol@output! and
+% \!\pcol@combinefloats!.  Other users, \!\pcol@cflt!, \!\pcol@opcol!,
+% \!\pcol@ioutputelt!, \!\pcol@combinefootins!, \!\pcol@output@flush! and
+% \!\pcol@output@clear!, let \!\boxmaxdepth! have \!\@maxdepth! so as to
+% limit the depth of boxes for a completed \colpage{} or page to the value
+% for page typesetting, while \!\pcol@flushcolumn! and
+% \!\pcol@imakeflushedpage! do that by \!\pcol@@makecol! giving the register
+% to it.  The other usage of the register is to calculate \bgpaint{}
+% parameter $\HT$ by \!\pcol@bg@textheight!, and to determine the bottom
+% edge of the \bground{}s of columns and \csepgap{}s through the argument of
+% \!\pcol@buildcolseprule! given by \!\pcol@ioutputelt!,
+% \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats!.  The register is also
+% referred to by \!\pcol@unvbox@cclv! to go back the last baseline of the
+% main vertical list in \!\box!|255|, and by \!\pcol@deferredfootins! to let
+% \!\splitmaxdepth! have its value to cap the depth of the first half of
+% footnotes split from $\df$.
+% 
+% \item[\Uidx{\!\@colht!}]
+% is a \!\dimen! register to have the height of columns in a page possibly
+% shrunk from \!\textheight! by \spanning.  The usages of the register
+% are as folllows.
+% 

+% \begin{itemize}
+% \item\begin{Sloppy}{1600}
+% In \!\pcol@startpage!, \!\pcol@output@start!, \!\pcol@flushfloats!  and
+% \!\pcol@output@end!, it is initialized to \!\textheight!.  In first two,
+% the value of the register is reduced to reflect \spanning{} if exists and
+% then set into $\pp^h(p)$, while the setting by the third is referred to by
+% its callee \!\pcol@iflushfloats!.
+% \end{Sloppy}
+% 
+% \item
+% In \!\pcol@getpelt!, \!\pcol@sync!, \!\pcol@flushcolumn!,
+% \!\pcol@makeflushedpage! and \!\pcol@imakeflushedpage!, it is let have
+% $\pp^h(p)$.  In addition \!\pcol@sync! examines if
+% $\!\@colht!<\VT+\VB+v(f)$, and \!\pcol@makefcolumn! uses it to initialize
+% the room of a \fcolumn{} as well as the height of $\cc_c(\vb)$ for it.
+% 
+% \item
+% In \!\pcol@opcol!, it is used to add \!\pcol@clearcolorstack! to the
+% bottom of $\cc_c(\vb)$ whose height is \!\@colht!.
+% 
+% \item
+% In \!\pcol@startcolumn!(*), \!\pcol@flushcolumn!(*) and
+% \!\pcol@freshpage!, it is used to let \!\@colroom! have it.
+% 
+% \item
+% In \!\pcol@restartcolumn!(*), it is saved and restored for the use as the
+% height cap of deferred footnote \!\insert!ion in \!\pcol@deferredfootins!
+% because it can be shrunk by the non-deferred \Scfnote{}s.
+% 
+% \item
+% In \!\pcol@output@flush! and \!\pcol@output@clear!, it is given to
+% \!\pcol@make~flushedpage! as its argument.  The macro
+% \!\pcol@makeflushedpage!(*) lets \!\@colht! be the argument if it is less
+% than \!\@colht! and thus is given by \!\pcol@output@end!.
+% \end{itemize}
+% 

+% In addition, in the macros with `(*)' above and \!\pcol@makecol!, the
+% register is passed to \!\pcol@shrinkcolbyfn! to shrink the height in it
+% temporarily to keep the space required to put \Scfnote{}s in the page they
+% are working on, for the reference by starred macros themselves or
+% \!\@makecol! invoked in \!\pcol@makecol!.
+% 
+% \item[\Uidx{\!\@colroom!}]
+% is a \!\dimen! register to have the height of a column possibly shrunk
+% from \!\@colht! by top and bottom floats.  The register is initialized to
+% have \!\@colht! by \!\pcol@startcolumn!, \!\pcol@output@start!,
+% \!\pcol@flushcolumn! and \!\pcol@freshpage!, the last three of which also
+% save it into $\cc_c(\vb^r)$.  This save operation is also done by
+% \!\pcol@output@switch! while restoring from it done by
+% \!\pcol@restartcolumn!, but the latter macro may shrink the amount in its
+% callee \!\pcol@putbackmvl! to capture a \mctext{} while the former cancel
+% this shrinkage.  The macros \!\pcol@output! and \!\pcol@output@start! also
+% refer to this register to let \!\vsize! have it in the former and to
+% calculate the room for each \colpage{} in the \spage{} in the latter.  The
+% macro \!\pcol@output@end!  lets the register have \!\textheight! for the
+% \postenv{} because the \colpage{}s above it simply precedes the stuff in
+% the main vertical list.  The other users \!\pcol@makefcolumn! and
+% \!\pcol@makefcolelt! use this register to accumulate the total size of
+% floats to be put in a \fcolumn{} temporarily.
+% 
+% \item[\Uidx{\!\@pageht!}]
+% is a \!\dimen! register to be used in \LaTeX's \!\@specialoutput! to have
+% the height of \!\@holdpg!.  It is referred to by \!\pcol@addmarginpar! to
+% deteremine the position at which a marginal note is placed.
+% We also use it as a scratchpad to have $\VP$ in \!\pcol@sync! and
+% \!\pcol@measurecolumn!, and to save $\pp^h(\ptop)$ in \!\pcol@flushcolumn!
+% for the reference in itself, and to do so in \!\pcol@makeflushedpage! for
+% \!\pcol@imakeflushedpage!.
+% 
+% \item[\Uidx{\!\@pagedp!}]
+% is a \!\dimen! register to be used in \LaTeX's \!\@specialoutput! to have
+% the depth of \!\@holdpg!.  However, we use it as a scratchpad in
+% \!\pcol@sync! and \!\pcol@measurecolumn! to have $\DP$, and in
+% \!\pcol@output@end! to have the value to be set in \!\pcol@prevdepth!.
+% 
+% \item[\Uidx{\!\@toproom!}]
+% is a \!\dimen! register to have the room for top floats.  The register is
+% saved in $\cc_c(\tr)$ by \!\pcol@setcurrcol! and restored from it by
+% \!\pcol@iigetcurrcol!.  The macro \!\pcol@makefcolumn! uses this register
+% as a flag to indicate that $\cc_c(\tl)$ of the column $c$ having
+% $\cc_c(\tr)=\infty$ contains floats to be put in its last \fcolumn{}
+% possibly as top floats so that it is examined by \!\pcol@flushcolumn! and
+% \!\pcol@imakeflushedpage!, the former of which then lets $\cc_c(\tr)=0$ to
+% mean the floats are put in a \fcolumn{} in a non-\lpage{} by the macro.
+% 
+% \item[\Uidx{\!\@botroom!}]
+% is a \!\dimen! register to have the room for bottom floats.  The register
+% is saved in $\cc_c(\br)$ by \!\pcol@setcurrcol! and restored from it by
+% \!\pcol@iigetcurrcol!.
+% 
+% \item[\Uidx{\!\@fpmin!}]
+% is a \!\dimen! register to have $\!\floatpagefraction!\times\!\@colht!$
+% being the minimum total size of floats for which an ordinary (not flushed)
+% \fcolumn{} can be build.  It is referred to by \!\pcol@makefcolumn! as the
+% threshhold below which floats in the last \fcolumn{} can be put as top
+% floats.
+% 
+% \item[\Uidx{\!\@mparbottom!}]
+% is a \!\dimen! register to have the bottom position of the last
+% \!\marginpar! stuff.  Its value at \beginparacol{} is referred to by
+% \!\pcol@output@start! to let $\mpb_L^l$ or $\mpb_L^r$ of $\pp^m(0)$ has an
+% element based on it, while the tail of one of the lists in $\pp^m(\ptop)$
+% defines the value at \Endparacol{} which \!\pcol@output@end! lets the
+% register have.  The register is also updated by \!\pcol@getmparbottom! and
+% \!\pcol@getmpbelt! to let \!\pcol@@addmarginpar! being \LaTeX's original
+% \!\@addmarginpar! know the uppermost available position for the marginal
+% note to be added.  This update is, however, just for communicatoin betwee
+% these macros and thus is ineffective for typesetting posterior to that, as
+% well as the update in \!\pcol@@addmarginpar!, because whole information
+% for marginal note placement is kept in $\pp^m(p)$ in $\PPP$.
+% 
+% \item[\Uidx{\!\@textfloatsheight!}]
+% is a \!\dimen! register to have the combined height of mid floats and
+% their separators.  It is initialize to be 0 by \!\pcol@floatplacement!,
+% saved in $\cc_c(\fh)$ by \!\pcol@setcurrcol!, and restored from it by
+% \!\pcol@iigetcurrcol!.
+% 
+% \item[\Uidx{\!\dimen@!}]
+% is a \!\dimen! register for temporary use.  It is used in the following
+% macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@buildcolseprule!, \!\pcol@buildcselt@S! and \!\pcol@buildcselt! to
+% have the argument $d\in\{\!\@maxdepth!,0\}$ of the first macro.
+% 
+% \item
+% \!\pcol@bg@paintregion@i! to have $y_1$ of $\bgr_a^{[c]}$.
+% 
+% \item
+% $\!\pcol@bias@mpbout@i!\Arg{y}\Arg{t}\Arg{b}$ to have $t$ and then $t+y$.
+% 
+% \item
+% \!\pcol@output@switch! to have the height of \prespan{} in
+% \!\pcol@prespan!, or 0 if it is $\bot$.
+% 
+% \item
+% \!\pcol@sync! to have $V$ or $V-\DT+\VE$.
+% 
+% \item
+% \!\pcol@addflhd! and \!\pcol@hdflelt! to measure the height of top and
+% bottom floats, \!\pcol@makecol! and \!\pcol@output@switch! to measure
+% the height of \prespan{} including the top floats, and
+% \!\pcol@measurecolumn! for top and bottom floats and $\VT$, $\VB$ and
+% $\VP$.
+% 
+% \item
+% \!\pcol@setcolwidth@s! and \!\pcol@setcw@accumwd! to accumulate $W$ being
+% the sum of natural widths of column\slash gap specifications, and then
+% used by \!\pcol@setcw@calcfactors! to calculate $W/\WT$ and $W-\WT$.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\dimen@ii!}]
+% is a \!\dimen! register for temporary use.  It is used in the following
+% macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! to measure the total height of top floats by
+% \!\pcol@addflhd!.
+% 
+% \item
+% \!\pcol@bg@addext! to have
+% $e=|pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}\{a{\cdot}|@|{\cdot}c,a\}$
+% 

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}

+%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% 

+% and then $10000\PT-e$ to calculate an \bgext{} of \bgpaint.
+% 
+% \item
+% $\!\pcol@bias@mpbout@i!\Arg{y}\Arg{t}\Arg{b}$ to have $b$ and then $b+y$.
+% 
+% \item
+% \!\pcol@measurecolumn! to measure $\VT$, $\VP$ and $\DP$.
+% 
+% \item
+% \!\pcol@setcolwidth@s! and \!\pcol@setcw@accumwd! to accumulate $F$ being
+% the sum of infinite stretch factors in column\slash gap specifications with
+% the unit of pt, and then used by \!\pcol@setcw@calcfactors! to calculate
+% $(W-\WT)/F$, where $W$ is the sum of natural widths.
+% 
+% \item
+% \!\pcol@setcw@calcfactors! to have $(W-\WT)/F$ above or 0 to be used in
+% \!\pcol@def@extract@fil@iii!  through \!\pcol@setcw@filunit!  made
+% \!\let!-equal to the register by \!\pcol@setcolwidth@s!.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@tempdima!}]
+% is a \!\dimen! register for temporary use.  The usages of this register
+% are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@makecol! and \!\pcol@startpage!, it is used to throw
+% $\pp^h(\ptop)$ away when we get it by \!\pcol@getcurrpinfo! because we
+% don't need it.
+% 
+% \item
+% In \!\pcol@outputelt!, it has $\pp^h(p)$ to examine if $p$ is a \fpage.
+% 
+% \item
+% In \!\pcol@ioutputelt!, it has $\pp^h(p)$ possibly shrunk by \Scfnote{}s
+% to know the \bground{}s to be painted for columns etc.  After that it has
+% $\w_c$ being the width of each \!\hbox! into which the \colpage{} of each
+% column $c$ is put.
+% 
+% \item
+% In \!\pcol@buildcolseprule! and its callees \!\pcol@buildcselt@S! and
+% \!\pcol@buildcselt!, the register has the first argment $H=\pp^h(p)$ of
+% the caller macro.
+% 
+% \item
+% In \!\pcol@hfil!$\<c\>$, it has $\gap_c=|\pcol@columnsep|{\cdot}c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 
+% \item
+% In \!\@outputpage!, it has the sum of \!\topmargin!, \!\headheight! and
+% \!\headsep! being the distance between tops of imaginary page and its text
+% area.
+% 
+% \item
+% In \!\pcol@startcolumn!, it is used to save \!\@colht! which can be shrunk
+% temporarily by \Scfnote{}s.
+% 
+% \item
+% In \!\pcol@bg@paintregion@i!, it is let have $x_0$ of $\bgr_a^{[c]}$.
+% 
+% \item
+% In \!\pcol@output@start!, it is used to have the room for each \colpage{}
+% in the \spage, and then the height-plus-depth of the \preenv.
+% 
+% \item
+% In \!\pcol@output@switch!, it is used to throw $\pp^h(p)$ away when
+% we get it by \!\pcol@getcurrpinfo! because we don't need it.
+% 
+% \item
+% In \!\pcol@shiftspanning!, it is let have the left-shift amount of a
+% \mctext{} in \cswap.
+% 
+% \item
+% In \!\pcol@restartcolumn!, it is used to save \!\@colht! which can be
+% shrunk temporarily by \Scfnote{}s.
+% 
+% \item
+% In \!\pcol@unvbox@cclv!$\arg{ins}$, it has the depth of \!\box!|255| for
+% going back to the baseline of the box, and then has the natural component
+% of $\!\skip!\arg{ins}$ to add its stretch and shrink components only.
+% 
+% \item
+% In \!\pcol@addmarginpar!, at first it has the distance between left edges
+% of the leftmost and current columns.  Then it is let have the distance
+% between top edges of the column and the marginal text to be put.
+% 
+% \item
+% In $\!\pcol@getmparbottom!\<t\>\<h\>$ and
+% $\!\pcol@getmpbelt!\<t_i\>\<b_i\>$, it at first has $t$ and then is
+% let have $b_i$ when the marginal note cannot be put at $t$.
+% 
+% \item
+% In \!\pcol@sync!, \!\pcol@measurecolumn! and \!\pcol@synccolumn!, it has
+% $\VT$ being the maximum combined height of top floats and the main
+% vertical list.
+% 
+% \item
+% In \!\pcol@makefcolumn! and \!\pcol@makefcolelt!, it has the room for
+% floats to be put in a \fcolumn{}.
+% 
+% \item
+% In \!\pcol@makeflushedpage!, it has the height-plus-depth of \spanning in
+% $\pp^i(\ptop)$.
+% 
+% \item
+% In \!\pcol@output@end!, at first it is let have $\VPP-H$, where $H$ is the
+% height(-plus-depth) of \!\@outputbox! having the ship-out image of the
+% \lpage, being the negative counterpart of the height-plus-depth of
+% \spanning{} in the \lpage{} for setting $\mpbout$, and then have $H$ to be
+% set in \!\pcol@bg@preposttop! for the \bgpaint{} of \postenv.
+% 
+% \item
+% In \!\pcol@setcolwidth@r!, it has
+% $\!\textwidth!-(\Cto-\Cfrom-1)\!\columnsep!$ being the base of $\w_c$.
+% 
+% \item
+% In \!\pcol@setcw@getspec@i!, it is let have the natural width of a
+% column\slash gap specification, to be used in \!\pcol@setcolwidth@s!,
+% \!\pcol@setcw@accumwd! and \!\pcol@setcw@set!, while in the last of them
+% it finally has $\w_c$ or $\gap_c$.
+% 
+% \item
+% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, at first it has $y$, then
+% $y/2^{k_2}$, and then $\lceil y/2^{k_2+k_3}\rceil$, where $k_2$ and $k_3$
+% are scaling parameters for good approximation.
+% 
+% \item
+% In \!\pcol@switchcol!, it is let have what \!\pcol@ensurevspace! has so
+% that the dimensional expression in it is evaluated in the macro and the
+% evaluateion result is assigned to $\VE=\!\pcol@@ensurevspace!$.
+% 
+% \item
+% In $\!\ensurevspace!\ARg{space}$, it is let have $\arg{space}$ to ensure
+% the argument is a dimension including forced one.
+% 
+% \item
+% In \!\pcol@fntextbody!, it has the height-plus-depth of the \!\vbox! in
+% which the footnote is encapsulated.
+% 
+% \item
+% In \!\pcol@set@color@push!, it has the width of the \!\vbox! to be
+% \!\insert!ed, which is $m$\,|sp| for a math-mode push of $\mcelt_{i,m}$ or
+% 0 for a non-math one $\celt_i$.
+% 
+% \item
+% In $\!\pcol@bg@defext!\Arg{d}\Arg{e}$, it is let have $e$ to confirm $e$
+% is a proper dimension.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@tempdimb!}]
+% is a \!\dimen! register for temporary use.  The usages of this register
+% are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@makecol!, it is used to measure the height-plus-depth $h_i$ of
+% decapsulated \!\box!|255| and its original form to add an element
+% $\spt(H_i,h_i)$ to $\pp^s(\ptop)$ for a \mctext{} captured in the box.
+% 
+% \item
+% In \!\pcol@ioutputelt!, if has the height-plus-depth of \spanning{}
+% $\pp^b(q)$ to be temporarily added to \!\topmargin!.
+% 
+% \item
+% In \!\pcol@buildcolseprule! it has $H_0+h_0$, while in its callee
+% $\!\pcol@buildcselt!\<H_i\>\~\<h_i\>$ it has $H_{i-1}+h_{i-1}$ and then
+% $H_i+h_i$ where $\spt(H_i,h_i)\in\pp^s(p)$.
+% 
+% \item
+% In \!\pcol@bg@paintregion@i!, it is let have $y_0$ of $\bgr_a^{[c]}$.
+% 
+% \item
+% In \!\pcol@output@switch!, it is let have the height-plus-depth $h_i$ of
+% \!\@holdpg! having a \mctext{} to add an element $\spt(H_i,h_i)$ to
+% $\pp^s(\ptop)$.
+% 
+% \item
+% In \!\pcol@shrinkcolbyfn!, it is let have the inverse of the \!\skip!
+% component of the argument \!\insert! register of the macro, so that in
+% \!\pcol@startcolumn! and \!\pcol@restartcolumn! it has that of $\pp^f(p)$
+% if $p$ has \Scfnote{}s, or 0 otherwise, and then is referred to by
+% \!\pcol@deferredfootins! which then lets the register have the height cap
+% of $\df$ splitting.
+% 
+% \item
+% In \!\pcol@addmarginpar!, \!\pcol@getmparbottom! and \!\pcol@getmpbelt!,
+% it is let have the vertical space to be occupied
+% by the marginal text to be put, being the second argument of
+% \!\pcol@getmparbottom!.
+% 
+% \item
+% In \!\pcol@sync! and \!\pcol@measurecolumn!, it has $\VB$ and then, in the
+% former, it has $\VP+v(f)$, $\VT$ or $\VT+\VB+v(f)$ according to the
+% contents of the page to be \sync{}ed.
+% 
+% \item
+% In \!\pcol@makefcolelt!, it has the size of vertical space consumed by a
+% float.
+% 
+% \item
+% In \!\pcol@synccolumn!, it has $\VT-\vc(t)$ being the vertical space from
+% the bottom of $\cc_c(\vb^b)$ to the \sync{}ation point.  If the
+% \sync{}ation point is defined by a column without main vertical list but
+% with top floats, then the register is let have
+% $\VT-\vc(t)+\!\textfloatsep!-\!\floatsep!+10000\,|pt|$ to be set in
+% $\cc_c(\tf)=\!\pcol@textfloatsep!$ as the space below the \mvlfloat{}
+% biased by 10000\,|pt| to indicate the last float is the \mvlfloat{}.
+% 
+% \item
+% In \!\pcol@setcolwidth@r!, it has
+% $\!\textwidth!-(\Cto-\Cfrom-1)\!\columnsep!-\sum_{d=0}^{k-1}w_d$ being the
+% base of $\w_c$ for $c\In{\Cfrom{+}k}{\,\Cto}$ where $k$ is the number of
+% fractions given in the argument of \!\columnratio!.
+% 
+% \item
+% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, at first it is let have $x$,
+% then $x\cdot2^{k_1}$, then
+% $z'=\break\lfloor(x\cdot2^{k_1})/\lceil{}y/2^{k_2+k_3}\rceil\rfloor$, and
+% finally
+% $Z=z\times1\,|pt|=z'\cdot2^{16-k}$ referred to by
+% \!\pcol@setcw@calcfactors! as $\phi_f=(\WT-W)/F$, where $k_1$, $k_2$ and
+% $k_3$ are scaling parameters for good approximation and $k=k_1+k_2+k_3$.
+% 
+% \item
+% In \!\pcol@extract@fil@ii! and \!\pcol@extract@fil@iii!, it is let have
+% the infinite stretch factor of a column\slash gap specification
+% represented with the unit \!\pcol@setcw@filunit!, to be used in
+% \!\pcol@setcolwidth@s!, \!\pcol@setcw@accumwd!, and \!\pcol@setcw@set!.
+% 
+% \item
+% In \!\pcol@fntextbody!, it has $\!\textheight!-\!\skip!\!\footins!$ as the
+% cap of the footnote.
+% \end{itemize}
+% 
+% 
+% \item[\Uidx{\!\@tempdimc!}]
+% is a \!\dimen! register for temporary use.  It is let have values as
+% follows.
+% 

+% \begin{itemize}
+% \item
+% $H_i-(H_{i-1}+h_{i-1})$ in $\!\pcol@buildcselt!\<H_i\>\<h_i\>$.
+% 
+% \item
+% $x_1$ of $\bgr_a^{[c]}$ in \!\pcol@bg@paintregion@i!.
+% 
+% \item
+% $t+h$ in $\!\pcol@getmparbottom!\<t\>\<h\>$.
+% 
+% \item
+% $\max(t,b_{i-1})+h$ in $\!\pcol@getmpbelt!\<t_i\>\<b_i\>$ invoked from
+% $\!\pcol@getmparbottom!\<t\>\~\<h\>$.
+% 
+% \item
+% $\DT$ in \!\pcol@sync!, \!\pcol@measurecolumn! and \!\pcol@synccolumn!.
+% 
+% \item
+% \!\floatsep! or \!\@fpsep! in \!\pcol@makefcolumn! and
+% \!\pcol@makefcolelt!.
+% 
+% \item
+% $\w_c$ being the width of column $c$ in \!\pcol@setcolwidth@r!.
+% 
+% \item
+% $\WT-W$ in \!\pcol@setcw@calcfactors!.
+% 
+% \item
+% At first for calculation of $y/2^{k_2}$ and then $z'/2^k\approx x/y$
+% in $\!\pcol@setcw@calcf!\<x\>\<y\>\~\<z\>$ where $k_2$ and $k$ are scaling
+% parameters for good approximation.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Skip Registers}
+% 
+% \begin{description}
+% \item[\Uidx{\!\baselineskip!}]
+% is \TeX's primitive register to have the vertical skip to separate
+% adjacent baselines.  It is referred to by \!\pcol@output! and
+% \!\pcol@output@start! to examine if \!\@colroom! is unexpectedly small,
+% and by \!\pcol@switchcol! to give it to \!\ensurevspace! to let
+% \!\pcol@ensurevspace! have the default value.
+% 
+% \item[\Uidx{\!\topskip!}]
+% is \TeX's primitive register to have the vertical skip from the top edge
+% of a page to the baseline of its first vertical item.  It is let be 0 by
+% \!\pcol@output@start! if we have \preenv{} and is saved in $\pp^t(0)$,
+% while \!\pcol@startpage! lets it be \!\pcol@topskip!, into which
+% \!\pcol@zparacol! saves the value outside \env{paracol} environment,
+% saving the value in $\pp^t(p)$.  Then the register is restored from
+% $\pp^t(p)$ by \!\pcol@getpelt! and \!\pcol@sync!, while
+% \!\pcol@synccolumn! refers to the value restored by the latter to adjust a
+% \sync{}ation point.  The macro \!\pcol@putbackmvl! lets the register have
+% 0 when it starts a \mctext{} because it originally follows \prespan{} in
+% the \colpage{} to be restarted rather than at the page top.  The macro
+% \!\pcol@output@end!  temporarily lets the register have 0 if we have
+% non-empty columns in the last page, while \!\endparacol! restores it from
+% \!\pcol@topskip! for the pages outside \env{paracol} environmnet.
+% 
+% \item[\Uidx{\!\splittopskip!}]
+% is \TeX's primitive register to have the vertical skip inserted at the
+% beginning of the second half of the box split by \!\vsplit! or \TeX's
+% internal operation for splitting an \!\insert! at a page break.  The
+% register is temporarily let have 0 by \!\pcol@deferredfootins! when it
+% splits $\df$ so that the second half does not have any skip at the top.
+% The register is also let have \!\footnotesep! in \!\pcol@fntextbody! for
+% footnote typesetting.
+% 
+% \item[\Uidx{\!\parskip!}]
+% is \TeX's primitive register to have the vertical skip inserted above each
+% paragraph.  It is referred to by \!\pcol@zparacol! to nullify the
+% insertion going to be made by the first \!\item! of a \env{list}-like
+% environment, when the macro finds the \env{paracol} environment to start
+% is at the very beginning of a \env{list}-like environment.
+% 
+% \item[\Uidx{\!\fill!}]
+% is an API \!\skip! register to have a skip 0\,|pt| |plus| 1\,|fill|.  In
+% our macros, however, it is used as a keyword in \!\pcol@setcw@getspec!,
+% \!\pcol@setcw@getspec@i! and \!\pcol@setcw@fill! to extract the infinite
+% stretch factor $f$ given as $f\!\fill!$ in the specification.
+% 
+% \item[\Uidx{\!\itemsep!}]
+% is an API \!\skip! register to have the vertical skip inserted above each
+% non-first \!\item! in \env{list}-like environments.  It is referred to by
+% \!\pcol@zparacol! to nullify the insertion going to be made by the first
+% \!\item! of a \env{list}-like environment, when the macro finds the
+% \env{paracol} environment to start is at the very beginning of a
+% \env{list}-like environment.
+% 
+% \item[\Uidx{\!\floatsep!}]
+% is an API \!\skip! register to have the vertical skip between adjacent floats.
+% It is referred to by \!\pcol@cflt! to cancel the skip following the last
+% float, by \!\pcol@makefcolumn! to let \!\pcol@makefcolelt! examine the
+% capacity of a \fcolumn{} in the \lpage, by \!\pcol@addflhd! and
+% \!\pcol@hdflelt!  to measure the total height of top and bottom floats,
+% and by \!\pcol@sync! to calculate the space below the \mvlfloat.
+% 
+% \item[\Uidx{\!\textfloatsep!}]
+% is an API \!\skip! register to have the vertical skip between the main
+% vertical list and top\slash bottom floats.  It is referred to by
+% \!\pcol@output@start! to calculate the room for each \colpage{} in the
+% \spage{} with bottom floats in the \preenv{}, by \!\pcol@combinefloats! to
+% insert a skip below the bottom floats in the \preenv{} and \lpage{},
+% by \!\pcol@measurecolumn! to take this skip into account in the
+% calculation of $\VPP$, by \!\pcol@addflhd!  to measure the vertical space
+% for top and bottom floats, and by \!\pcol@synccolumn! to calculate the
+% \sync{}ation point for columns with top floats.
+% 
+% \item[\Uidx{\!\dblfloatsep!}]
+% is an API \!\skip! register to have the vertical skip between adjacent
+% \pwise{} floats, and is used in \!\pcol@startpage! to cancel the skip
+% below the last float.
+% 
+% \item[\Uidx{\!\dbltextfloatsep!}]
+% is an API \!\skip! register to have the vertical skip between the last
+% \pwise{} float and the top of columns, and is used in
+% \!\pcol@startpage! to put the skip.
+% 
+% \item[\Uidx{\!\@topsep!}]
+% is a \!\skip! register to have the vertical skip inserted above the first
+% \!\item! of a \env{list}-like environment.  The actual value is determined
+% by \!\@trivlist! from API parameters \!\topsep!, \!\partopsep! and
+% \!\parskip! depending on how the environment appears.  The skip in the
+% register is inserted by \!\pcol@zparacol! when it finds the \env{paracol}
+% environment to start is at the very beginning of a \env{list}-like
+% environment.
+% 
+% \item[\Uidx{\!\@fptop!}]
+% is a \!\skip! register to have the vertical skip inserted at the top of
+% a \fcolumn, and is used in \!\pcol@makefcolpage!.
+% 
+% \item[\Uidx{\!\@fpsep!}]
+% is a \!\skip! register to have the vertical skip between adjacent floats
+% in a \fcolumn, and is used in \!\pcol@makefcolpage!.
+% 
+% \item[\Uidx{\!\@fpbot!}]
+% is a \!\skip! register to have the vertical skip inserted at the bottom of
+% a \fcolumn, and is used in \!\pcol@makefcolpage!.
+% 
+% \item[\Uidx{\!\@tempskipa!}]
+% is a \!\skip! register for temporary use.  It is used in the following
+% macros.
+% 

+% \begin{itemize}
+% \item
+% \begin{Sloppy}{2400}%
+% \!\pcol@makecol!, \!\pcol@startpage!, \!\pcol@outputelt!,
+% \!\pcol@output@switch!, \!\pcol@flushcolumn! and \!\pcol@makeflushedpage!
+% to throw $\pp^t(p)$ away because we don't need it.
+% \end{Sloppy}
+% 
+% \item
+% \!\pcol@output@start! to determine \!\topskip! for the \spage.
+% 
+% \item
+% \!\pcol@setcw@getspec@i! and \!\pcol@setcw@fill! to have the width
+% specification of a column or gap.
+% \end{itemize}
+% It is also used in the top level invocation of \!\pcol@defkw! with a glue
+% of $0\,|pt|\ |plus|\ 1\,|fil|\~\ |minus|\ 1\,|fil|$.
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Box Registers}
+% 
+% \begin{description}
+% \item[\Uidx{\!\strutbox!}]
+% is an API \!\box! register to have the strut for the current font size.
+% It is used in \!\pcol@fntextbody!\marg{text} to let \!\splitmaxdepth! have
+% its depth, and to let the last line of the footnote $\arg{text}$ have its
+% depth at shallowest.
+% 
+% \item[\Uidx{\!\@cclv!}] 
+% is a \!\box! register but \TeX{} defines that it has the main vertical
+% list when \!\output! routine is invoked.  It is referred to by
+% \!\pcol@makecol! when it has a broken \mctext{} to measure its
+% height-plus-depth for the element to be added to $\pp^s(\ptop)$ and to
+% update it combining its contents with \prespan{} optionally shifting it
+% left by passing the register to \!\pcol@shiftspanning!.  The macro also
+% uses the register together with its callee \!\pcol@unvbox@cclv! to add
+% stretch\slash shrink factor of \!\skip!\!\footins! at its bottom for a
+% \colpage{} in a page having \Scfnote{}s.  The macro \!\pcol@specialoutput!
+% examines the register to discard the dummy \!\vbox! inserted in it by
+% \!\pcol@invokeoutput!.  The other users \!\pcol@output@start!,
+% \!\pcol@makenormalcol!, \!\pcol@flushcolumn! and \!\pcol@imakeflushedpage!
+% let the register have the main vertical list of \preenv{} or a column to
+% be passed to \!\@makecol!, and \!\pcol@flushcolumn! also takes care the
+% skip above \Scfnote{}s.
+% 
+% \item[\Uidx{\!\voidb@x!}]
+% is a \!\box! register to be void ($\bot$) always.  It is used to
+% initialize \!\pcol@prespan! and \!\pcol@rightpage! at their declaration,
+% and is referred to by the following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! to make \!\pcol@currfoot! void unless \Scfnote{}s in
+% \!\foot~ins! is saved into $\pp^f(p)$.
+% 
+% \item
+% \!\pcol@startpage! to let
+% $\pp^i(\ptop)=\bot$ if the new \tpage{} does not have \spanning{} and
+% $\pp^f(\ptop)=\bot$ for all \fpage{}s and the new \tpage.
+% 
+% \item
+% \!\pcol@outputelt! to initialize \!\@outputbox!.
+% 
+% \item
+% \!\pcol@ioutputelt! to examine if $\S_c$ is empty.
+% 
+% \item
+% \!\pcol@output@start! to let $\pp^f(0)=\bot$, and $\Celt^c=\bot$ if
+% $\Celtshadow^c$ is undefined.
+% 
+% \item
+% \!\pcol@output@switch! to let $\cc_c(\ft^b)=\bot$ if the column does
+% not have \Mcfnote{}s.
+% 
+% \item
+% \!\pcol@getcurrfoot! to let \!\footins! be void if so.
+% 
+% \item
+% \!\pcol@setcurrcolnf! to let $\cc_c(\ft^b)=\bot$ because the column $c$
+% does not have \Mcfnote{}s.
+% 
+% \item
+% \!\pcol@putbackmvl! to let $\!\pcol@prespan!=\bot$ if a \mctext{} really
+% starts from the top of a \colpage, and $\csts=\bot$ if the \colpage{}
+% $\cc_c(\vb)$ to be restarted is non-empty.
+% 
+% \item
+% \!\pcol@savecolorstack! to let $\csts=\bot$ or its first item be $\bot$ if
+% $\CST^c$ or $\Celt^c$ is $\bot$, resepectively.
+% 
+% \item
+% \!\pcol@savefootins! to let its argument macro have a void box if
+% \!\@freelist! is exhausted.
+% 
+% \item
+% \!\pcol@makeflushedpage! to initialize \!\@outputbox! and
+% \!\pcol@rightpage! to be $\bot$ if the flushed page does not have
+% \spanning{}, and to let $\pp^f(\ptop)=\bot$ after putting it in the
+% \lpage{} so that \!\pcol@output@end! will be unaware of the \scfnote{} and
+% non-\Mgfnote{}s.
+% 
+% \item
+% \!\pcol@flushfloats! to let $\!\pcol@rightpage!=\bot$ if \parapag{}ing is
+% not in effect.
+% 
+% \item
+% \!\pcol@output@end! to let $\!\pcol@rightpage!=\bot$ if
+% the last page has nothing other than \spanning{} being \pwise{} floats
+% and thus we don't have the right \parapag{}e.  The macro also lets
+% $\Celt^c=\bot$ for all $c$ and $\cst=\bot$.
+%
+% \item
+% \!\pcol@com@flushpage! and \!\pcol@com@clearpage! gives the void box to
+% \!\pcol@flushclear! as its argument to mean these macros are only aware
+% of \CSIndex{ifpcol@flush} as the result of \pfcheck.  The macro
+% \!\endparacol! also does that if the footnote typesetting is \mgfnote.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@holdpg!}]
+% is a \!\box! register to have the main vertical list when \!\output! is
+% invoked with a special \!\penalty! code.  It is let have that by
+% \!\pcol@specialoutput!, and is referred to by \!\pcol@output@start!  and
+% \!\pcol@makenormalcol! for \preenv{}, and by \!\pcol@output@switch! for the
+% column from which we are leaving.
+% 
+% \item[\Uidx{\!\@outputbox!}]
+% is a \!\box! register to have a partial or the complete ship-out image
+% of a column or a page.  The usages of the register are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@@makecol!, it has a \colpage{} made by \!\@makecol! for
+% \!\pcol@flush~column! and \!\pcol@imakeflushedpage!.
+% 
+% \item
+% In \!\pcol@combinefloats!, it has a \colpage{} to which top and bottom
+% floats are combined.
+% 
+% \item
+% In \!\pcol@cflt!, it has a \colpage{} to which top floats are combined.
+% 
+% \item
+% In \!\pcol@opcol!, it has the complete \colpage{} built by \!\@makecol!.
+% 
+% \item
+% In \!\pcol@startpage!, it has the complete \fpage{} built by \!\@tryfcolumn!.
+% 
+% \item
+% In \!\pcol@outputelt!, it has the complete (left parallel-) page to be
+% shipped out by \!\@outputpage!.
+% \Index{parallel-paging}
+% 
+% \item
+% In \!\pcol@outputpage@r!, it is temporarily made \!\let!-equal to
+% \!\pcol@rightpage! so that the box is shipped out by \!\pcol@@outputpage!
+% being \LaTeX's \!\@outputpage! instead of the real \!\@outputbox!.
+% 
+% \item\begin{Sloppy}{1700}
+% In \!\pcol@output@start!, it has the \preenv{} built by
+% \!\pcol@makenormalcol!.
+% \end{Sloppy}
+% 
+% \item
+% In \!\pcol@combinefootins!, it is let have the \preenv{} with footnotes.
+% 
+% \item
+% In \!\pcol@flushcolumn!, it has a flushed \colpage{} built by \!\@makecol!
+% or a \fcolumn{} built by \!\@makefcolumn!.
+% 
+% \item
+% In \!\pcol@output@flush! and \!\pcol@output@clear!, it has a flushed page
+% built by \!\pcol@makeflushedpage! and \!\pcol@imakeflushedpage! in which
+% it has each of flushed \colpage{} built by \!\@makecol!.
+% 
+% \item
+% In \!\pcol@flushfloats!, it has the complete (left parallel) page for
+% flushed \fcolumn{}s.
+% 

+% \Index{parallel-paging}

+% 
+% \item
+% In \!\pcol@iflushfloats!, it has a \fcolumn{} built by
+% \!\pcol@makefcolumn!.
+% 
+% \item
+% In \!\pcol@output@end!, it has the ship-out image of the \lpage{} of a
+% \env{paracol} environment built by \!\pcol@makeflushedpage! and
+% \!\pcol@imakeflushedpage!.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@tempboxa!}]
+% is a \!\box! register for temporary use.  The usages of the register are
+% as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@makecol!, it is used to decapsulate \!\box!|255| containing a
+% broken \mctext{}.  In the macro and \!\pcol@output@switch!, it is also
+% used as a waste bascket to make \!\footins! void when it contains
+% \Scfnote{}s in a non-\tpage.
+% 
+% \item\begin{Sloppy}{2100}
+% In \!\pcol@cflt! and \!\pcol@startpage!, it has top column-\slash
+% \pwise{} floats combined by the application of
+% \!\@comflelt!\slash\!\@comdblflelt! to \!\@toplist!\slash\!\@dbltoplist!
+% respectively.
+% \end{Sloppy}
+% 
+% \item
+% In \!\pcol@phantom!$\<b\>$, it has an empty box whose height and depth are
+% equal to those of the argument box $b$.
+% 
+% \item
+% By \!\pcol@buildcolseprule! and its callees \!\pcol@buildcselt@S! and
+% \!\pcol@buildcselt!, it is let have the painted \bground{}s for columns,
+% \csepgap{}s and \mctext{}s in a page, and then is put into the ship-out
+% image of the page by \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! or
+% \!\pcol@iflushfloats!.
+% 
+% \item
+% In \!\@outputpage!, it is let have the painted \bground{} of the right
+% page referred to by its callee \!\pcol@outputpage@r!.
+% 
+% \item
+% In $\!\pcol@bg@paint@i!\Arg{body}$, it is let have painted \bground{}s
+% built by $\arg{body}$.
+% 
+% \item
+% In $\!\pcol@bg@paintregion!\arg{a}\arg{c}$, it is let have painted
+% \bground{} of the region $\bgr_a^{[c]}$.
+% 
+% \item
+% In \!\pcol@specialoutput!, it is used to discard the dummy \!\vbox! put by
+% \!\pcol@invokeoutput!.
+% 
+% \item
+% In \!\pcol@makenormalcol!, it is used to save \!\footins! into it and make
+% it $\bot$ temporarily to exclude \mgfnote{} footnotes from \spanning{} for
+% \preenv.
+% 
+% \item
+% In \!\pcol@ifempty!$\arg{box}\arg{then}\arg{else}$, it is used to examine
+% if $\arg{box}$ is empty.
+% 
+% \item
+% In $\!\pcol@scancst!\arg{box}$ and \!\pcol@iscancst!, it is used to have
+% what $\cst$ or $\csts$ has after the scan of $\arg{box}\in\{\cst,\csts\}$.
+% 
+% \item
+% In \!\pcol@savecolorstack!, it is used to have the \!\vbox! for $\Celt^c$
+% to be placed at the top of $\csts$.
+% 
+% \item
+% In \!\pcol@deferredfootins!, it is used to have the first half split from
+% $\df$ being the deferred footnotes to be \!\insert!ed.
+% 
+% \item
+% In \!\pcol@fntextbody!\marg{text}, it is used to encapsulate $\arg{text}$
+% in it.
+% 
+% \item
+% In \!\pcol@icolumncolor!, it is used to have a \!\vbox! to be \!\insert!ed
+% for the update of $\Celt^c$.
+% 
+% \item
+% In \!\pcol@set@color@push!, it is used to have a \!\vbox! to be \!\insert!ed
+% to push $\celt_i$ or $\mcelt_{i,m}$ to $\cstraw$.
+% 
+% \item
+% In \!\pcol@reset@color@pop! and \!\pcol@reset@color@mpop!, it is used to
+% have a \!\vbox! to be \!\insert!ed to add $\celtpop_i$ or
+% $\mceltpop_{i,m}$ to $\cstraw$.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Token Registers}
+% 
+% \begin{description}
+% \item[\Uidx{\!\output!}]
+% is \TeX's primitive to have \!\output! routine.  It is let have
+% \!\pcol@output! as its sole token by \!\pcol@zparacol!.
+% 
+% \item[\Uidx{\!\everypar!}]
+% is \TeX's primitive to have tokens inserted at the beginning of each
+% paragarph.  In \!\pcol@sptext! and \!\pcol@com@endcolumn!, it is
+% \!\global!ized to keep its contents after the end of a group.  In
+% \!\pcol@output@switch!, its contents are broadcasted to $\cc_c(\ep)$ for
+% all $c\In0\C$ if columns are \sync{}ed with a \mctext.  Then these values
+% or that simply given in a column are saved into $\cc_c(\ep)$ by
+% \!\pcol@setcurrcol!, and then restored from it by \!\pcol@iigetcurrcol!.
+% 
+% \item[\Uidx{\!\everyvbox!}]
+% is \TeX's primitive to have tokens inserted at the beginning of each
+% \!\vbox!.  In \!\pcol@zparacol!, after tokens in it are saved into
+% \!\pcol@everyvbox!, it is let have a \!\the!-reference to
+% \!\pcol@everyvbox! and |\pcol@innertrue| to turn
+% $\CSIndex{ifpcol@inner}=\true$, and then the register itself is made
+% \!\let!-equal to \!\pcol@everyvbox!.  In addition, it is let have tokens
+% in \!\pcol@everyvbox! if a \!\global! assignment to the register is made
+% in the \env{paracol} just having been closed.  Another usage of this
+% register is to insert a painted page \bground{} to the \!\vbox! to be
+% \!\shipout! by \!\pcol@@outputpage! being \LaTeX's \!\@outputpage!, and is
+% used for this purpose by \!\pcol@outputpage@l! and \!\pcol@outputpage@r!,
+% and by \!\pcol@outputpage@ev! to nullify this special function for other
+% inside \!\vbox!es.
+% 
+% \item[\Uidx{\!\@temptokena!}]
+% is a \!\toks! register for temporary use.  It is used in
+% \!\pcol@output@switch! to broadcast \!\everypar! to $\cc_c(\ep)$ for all
+% $c\In0\C$.
+% 
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Switches}
+% 
+% \begin{description}
+% \item[\Uidx{\CSIndex{if@twocolumn}}]
+% is a switch to be $\true$ iff multi-column pages are being typeset.  It is
+% turned $\true$ by \!\pcol@zparacol!, and then turned $\false$ by
+% \!\endparacol!.  In addition, it is turned $\false$ when \!\pcol@output!
+% finds that the \!\output! request for a page break outside \env{paracol}
+% is sneaked into our own \!\output! routine, in order to avoid that
+% \LaTeX's original \!\output! routine misunderstands it is working on a
+% two-columned document.  The switch is examined by \LaTeX's own macros
+% including old \!\end@dblfloat! kept in our own \!\pcol@end@dblfloat!.  It
+% is also examined by \!\pcol@zparacol! before being turned $\true$ to
+% ensure it is $\false$ or to complain about the inappropriateness otherwise.
+% 
+% \item[\Uidx{\CSIndex{if@firstcolumn}}]
+% is a switch to be $\true$ iff the first column is being typeset.  Its
+% truth value is determined by \!\pcol@addmarginpar! to tell
+% \!\pcol@@addmarginpar!, \!\pcol@getmparbottom@i! and \!\pcol@setmpbelt@i!
+% the margin which a marginal note goes to.
+% 
+% \item[\Uidx{\CSIndex{if@twoside}}]
+% is a switch to be $\true$ iff two-sided page typesetting is in effect and
+% thus even numbered page may have their own left margins, headers and
+% footers different from those for odd numbered pages.  Besides the
+% initialization by the main class file such as \textsf{article.cls}
+% according to the class option |twoside|, the switch is \!\global!ly turned
+% $\false$ by \!\pcol@twosided! for the case in which API macro \!\twosided!
+% does not have `|p|' in its optional argument, and then \!\global!ly turned
+% $\true$ by \!\pcol@twosided@p! which is invoked when the argument contains
+% `|p|', or the API macro does not have the argument at all.  Then the
+% switch is referred to by \!\pcol@outputpage@l!, \!\pcol@outputpage@r! and
+% \!\pcol@bg@swappage! to decide the left margin of even numbered pages,
+% i.e., \!\evensidemargin! if the switch is $\true$ or \!\oddsidemargin!
+% otherwise.  The switch is also referred to by \!\pcol@com@cleardoublepage!
+% to have a blank page if the switch is $\true$ and the command
+% \!\cleardoublepage! is used in an odd-numbered page.
+% 
+% \item[\Uidx{\CSIndex{if@reversemargin}}]
+% is a switch to be $\true$ iff \!\reversemarginpar! is specified to reverse
+% the side which marginal notes go to.  It is examined by
+% \!\pcol@addmarginpar! as a factor to decide the margin which a marginal
+% note goes to, and by \!\pcol@do@mpbout@i! for the same purpose but for
+% marginal notes in pre-environment or \postenv.
+% 

+% \Index{pre-environment stuff}

+% 
+% \item[\Uidx{\CSIndex{if@mparswitch}}]
+% is a switch to be $\true$ iff it is specified by, for example,
+% \texttt{twoside} option of a class such as \textsf{article}, that marginal
+% notes in even numbered pages go to thier left margin.  It is examined by
+% \!\pcol@do@mpbout@i! as a factor to decide the margin which a maginal note
+% goes to in pre-environment or \postenv{}.
+% 

+% \Index{pre-environment stuff}

+% 
+% \item[\Uidx{\CSIndex{if@nobreak}}]
+% is a switch to be $\true$ iff the last paragraph is for a sectioning
+% command.  The switch is saved into $\cc_c(\sw)$ together with
+% \CSIndex{if@afterindent} by \!\pcol@setcurrcol!, and then restored from
+% it by \!\pcol@iigetcurrcol!.  The macro \!\pcol@output@switch! refers to
+% it to broadcast its value set by a \mctext{} to $\cc_c(\sw)$ for all
+% $c\In0\C$, while \!\pcol@output@start! and \!\pcol@restartcolumn! insert
+% $\!\penalty!=10000$ by \!\nobreak! if the switch is $\true$.  This
+% conditional \!\nobreak!  is also done by \!\pcol@icolumncolor!,
+% \!\pcol@set@color@push!, \!\pcol@reset@color@pop! and
+% \!\pcol@reset@color@mpop! to avoid a break after an \!\insert!.  The macro
+% \!\pcol@zparacol! also exmaines the switch, but with the truth value in it
+% given outside \env{paracol} environment, to invoke \!\@nbitem! if $\true$
+% when the macro finds the \env{paracol} environment to start is at the very
+% beginning of a \env{list}-like environment.
+% 
+% \item[\Uidx{\CSIndex{if@newlist}}]
+% is a switch to be $\true$ in the duration after a \env{list}-like
+% environment starts and until its first \!\item! appears.  The switch is
+% examined by \!\pcol@zparacol! to know if the \env{paracol} environment to
+% start is at the very beginning of a \env{list}-like environment and, if
+% so, is turned $\false$ by the macro after it inserts vertical skips
+% pretending the first \!\item! is given.
+% 
+% \item[\Uidx{\CSIndex{if@inlabel}}]
+% is a switch to be $\true$ in the duration after an \!\item! appears and
+% until its first paragraph is given.  The switch is examined by
+% \!\pcol@zparacol! together with \CSIndex{if@newlist} to know if the
+% \env{paracol} environment to start is at the very beginning of a
+% \env{list}-like environment ($\false$) and not \env{trivlist}-like one
+% ($\true$).
+% 
+% \item[\Uidx{\CSIndex{if@afterindent}}]
+% is a switch to be $\true$ iff a sectioning commmand tells that the fisrt
+% paragraph following it is to be indented.  The switch is saved into
+% $\cc_c(\sw)$ together with \CSIndex{if@nobreak} by \!\pcol@setcurrcol!,
+% and then restored from it by \!\pcol@iigetcurrcol!.  The macro
+% \!\pcol@output@switch! refers to it to broadcast its value set by a
+% \mctext{} to $\cc_c(\sw)$ for all $c\In0\C$.
+% 
+% \item[\Uidx{\CSIndex{if@fcolmade}}]
+% is a switch to be $\true$ iff a \fcolumn{} or \fpage{} is built by
+% \!\@tryfcolumn! or \!\@makefcolumn!.  The value is set by \!\@tryfcolumn!
+% for $\cc_c(\dl)$ is referred to by \!\pcol@output!, \!\pcol@startcolumn!
+% and \!\pcol@freshpage!, while that for \!\@dbldeferlist! is referred to by
+% \!\pcol@startpage!.  The value set by \!\@makefcolumn! for $\cc_c(\dl)$ is
+% referred to by \!\pcol@flushcolumn!, while that for \!\@dbldeferlist! is
+% referred to by \!\pcol@output@clear!.  The macros \!\pcol@flushfloats! and
+% \!\pcol@iflushfloats! also refer to the switch to build pages having only
+% \fcolumn{}s and turn the switch $\true$ or $\false$ by themselves to know
+% such paegs are still to be built or not.  The macro \!\pcol@output@end!
+% also turns the switch $\true$ if a \lpage{} will be followed by page(s)
+% having \fcolumn{}s to tell that to \!\pcol@flushfloats!.
+% 
+% \item[\Uidx{\CSIndex{if@tempswa}}]
+% is a switch for temporary use.  The usages of the switch are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@checkshipped!, it is turned $\true$ iff $\S_c$ for all
+% $c\In0\C$ have \colpage{}s to be shipped out, and then it is examined by 
+% \!\pcol@opcol!.
+% 
+% \item
+% In \!\pcol@nextpage! and \!\pcol@nextpelt!, it is $\true$ until
+% \!\pcol@nextpelt! finds the first $q$ such that $q>p$ and
+% $\pp^h(q)\geq0$ to mean $q$ is not for a \fpage{}, so that we let $p=q$
+% to skip \fpage{}s following to the old $p$ if any.
+% 
+% \item
+% In \!\pcol@outputcolumns! and \!\pcol@outputelt!, it is $\true$ until
+% \!\pcol@outputelt! finds the first $q$ such that $q\geq\pbase$ and
+% $\pp^h(q)\geq0$ to mean $q$ is not for a \fpage{}, and the arguemnt of
+% \!\pcol@outputcolumns! is 0 to mean that it is not for page flushing, so that
+% we ship out $q$ and all \fpage{}s following it if any.
+% 
+% \item
+% In \!\@outputpage! it is let have the value of \CSIndex{ifpcol@bg@painted}
+% indicating if \bgpaint{} for the left page is done, and then it is
+% examined by \!\pcol@outputpage@l! to determine whether the \bground{} is
+% put into the final ship-out image.
+% 
+% \item
+% In \!\pcol@makenormalcol!, it is $\true$ iff the footnotes in \preenv{} is
+% included in \!\@outputbox! which the macro builds.
+% 
+% \item
+% In \!\pcol@output@switch!, at first it holds \CSIndex{if@nobreak} of the
+% \mctext{} if columns are \sync{}ed with it to broadcast
+% \CSIndex{if@nobreak} to all $\cc_c(\sw)$.  Then it is turned $\true$ iff
+% $\CSIndex{ifpcol@sync}=\true$ for \sync{}ation or
+% $\CSIndex{ifpcol@clear}={\true}$ for flushing, so as to invoke
+% \!\pcol@sync!.  And finally, it is turned $\true$ iff
+% $\CSIndex{ifpcol@clear}={\false}$ or $\CSIndex{ifpcol@sync}=\true$, so as
+% to invoke \!\pcol@restartcolumn!.
+% 
+% \item
+% In \!\pcol@restartcolumn!, it is turned $\true$ iff footnote typesetting
+% is \scfnote{} and $p<\ptop$.
+% 
+% \item
+% In \!\pcol@scancst!, it is initialized to be $\true$.  Then it is referred
+% to by \!\pcol@iscancst! for each $\celt\in\cstraw$ to update $\Celt^c$ and
+% then turned $\false$ when the first one is found.
+% 
+% \item
+% In \!\pcol@savecolorstack!, it is $\true$ iff either $\cst\neq\bot$ or
+% $\Celt^c\neq\bot$, i.e., $\CST^c$ to be saved is not $\bot$.
+% 
+% \item
+% In \!\pcol@getmparbottom!, it is intialized to be $\false$ and then may be
+% turned $\true$ by \!\pcol@getmpbelt! if it finds a gap between two marginal
+% notes to accommodate that to be added, and then examined by
+% \!\pcol@getmparbottom! to know the fact.
+% 
+% \item
+% In \!\pcol@sync!, it is turned $\true$ iff the \sync{}ed or flushed page
+% can be built by \!\pcol@synccolumn!.
+% 
+% \item
+% In \!\pcol@makefcolumn! having non-empty $\cc_c(\tl)$, it is turned
+% $\false$ iff the macro is acting on a column in the \lpage{}, $\cc_c(\dl)$
+% is emptied by the macro itself, and the total size of the floats to be put
+% in the \fcolumn{} being built by the macro is less than \!\@fpmin!, to
+% mean it is possible that the floats in $\cc_c(\tl)$ is put in the
+% \fcolumn{} as top floats.
+% 
+% \item
+% In \!\pcol@measurecolumn! and \!\pcol@addflhd!, it is set to be $\false$
+% iff both top floats and the main vertical list are empty, so that
+% \!\pcol@measureupdate! examines it for the update of $\VT$ and $\DT$.
+% Then it is kept $\false$ iff both of footnotes and bottom floats are
+% empty, so that \!\pcol@measurecolumn! examines it for the update of $\VP$
+% and \!\pcol@measureupdate! does for $\VPP$ and $\DP$.
+% 
+% \item
+% In \!\pcol@makeflushedpage!, it is made $\false$ iff $\ptop$ is the
+% \lpage{}, $\VPP=-\infty$ to mean all columns are empty and
+% $\pp^f(\ptop)=\bot$, so as to make the \spanning{} in $\pp^i(\ptop)$ a
+% float in \postenv{} if \CSIndex{ifpcol@dfloats} also $\false$.  Then it is
+% kept $\false$ if $\CSIndex{ifpcol@dfloats}=\false$ or $\pp^i(\ptop)=\bot$
+% to mean nothing is shipped out for \lpage{}.  Then it is made $\false$ iff
+% $\ptop$ is the \lpage{} without deferred floats and \Mgfnote{}
+% typesetting is in effect, i.e., the switch is $\true$ iff \Scfnote{}s are
+% put in the page to be flushed.
+% 
+% \item
+% In \!\pcol@imakeflushedpage!, it is turned $\true$ iff $\cc_c(\tr)=\infty$
+% and $\VPP=\pp^h(\ptop)$ to mean the floats in $\cc_c(\tl)$ should be put in
+% a \fcolumn{} in the \lpage{} as usual.
+% 
+% \item
+% In \!\pcol@iflushfloats!, it is turned $\true$ iff one or more columns have
+% non-empty $\cc_c(\dl)$ after shipping a page for \fcolumn{}s out, so that
+% \CSIndex{if@fcolmade} is let have its value after scanning all columns.
+% 
+% \item
+% In \!\pcol@output@end!, it is turned $\true$ iff we built \fcolumn{}s, or
+% the main vertical list in the \lpage{} is empty and the page is not the
+% \spage, so that we create a new page for the \postenv.
+% 
+% \item
+% In \!\globalcounter!\marg{ctr}, it is turned $\true$ iff $\arg{ctr}\in\CG$
+% already.
+% 
+% \item
+% In $\!\pcol@cmpctrelt!\arg{\theta}$, it is turned $\true$ iff $\theta$ is
+% not in $\Cc_0$ or $\Val(\theta)\neq\val_0(\theta)$, so that $\theta$ is
+% added to \!\@gtempa! being the list of \lcounter{}s to be synchronized.
+% 
+% \item
+% In \!\pcol@switchcolumn!$|[|d|]|$, it is turned $\false$ iff $0\leq d<\C$
+% so that we complain $c$ is invalid if the switch is $\true$.
+% 
+% \item
+% In $\!\pcol@ac@caption@def!\arg{s}\arg{t}$, \CSIndex{@tempswatrue} or
+% \CSIndex{@tempswafalse} is given as its first argument $s$ by
+% $\!\pcol@ac@caption@enable!$ or $\!\pcol@ac@caption@disable!$ respectively,
+% so that $|\if@ac@caption@if@|{\cdot}t$ is made \!\let!-equal to $s$ and
+% \!\pcol@ac@caption! examines it for enabling\slash disabling
+% \!\addcontentsline! respectively.  The macros \!\pcol@ac@caption@if@lof!
+% and \!\pcol@ac@caption@if@lot! are initialized to be \!\let!-equal to
+% \!\@tempswatrue! as the default.
+% 
+% \item
+% In \!\pcol@icolumncolor!, it is turned $\true$ iff we are in a \!\vbox! or
+% in restricted horizontal or math mode.
+% 
+% \item
+% In \!\pcol@backgroundcolor@i!, it is exmained if the root of the
+% invocation chain is \!\backgroundcolor! which turns the switch $\true$, or
+% \!\nobackgroundcolor! which turns it $\false$, to determine whether the
+% \bground{} of a region is painted or not.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Macros}
+% \label{sec:imp-tex-macro}
+% 
+% \subsubsection{Procedural Macros}
+% 
+% \begin{description}
+% \item[\Uidx{\CSIndex{par}}]
+% is \TeX's primitive to end\slash start paragraphs, but may be modified by
+% \LaTeX{} to have some special functionality occasionally.  The macro
+% \!\pcol@output! makes it \!\let!-equal to \hbox{\!\@@par!} in which the
+% \TeX's orinigal definition is kept, while \!\pcol@zparacol! and
+% \!\pcol@par! use it as is.
+% 
+% \item[\Uidx{\!\space!}]
+% is an API macro to have a space token.  It is used in \!\pcol@output!,
+% \!\pcol@icolumncolor!, \!\pcol@defcseprulecolor@i! and
+% \!\pcol@backgroundcolor@ii! for warning messages, and in
+% \!\pcol@def@extract@fil! to \!\def!ine the macro \!\pcol@extract@fil!
+% having spaces in its argument specification.
+% 
+% \item[\Uidx{\!\nointerlineskip!}]
+% is an API macro to let $\!\prevdepth!=-1000$\,pt to inhibit \TeX's
+% baseline progress mechanism.  It is used in \!\pcol@ioutputelt!,
+% \!\pcol@makeflushedpage! and \!\pcol@imakeflushedpage! to joint boxes
+% without \!\baselineskip! between them, in \!\pcol@outputpage@ev! to
+% suppress the \!\baselineskip! insertion after the first box of painted
+% \bground{} in the final ship-out image, and in \!\pcol@bg@paint@i!
+% for the same purpose for the box having painted \bground{}s.
+% 
+% \item[\Uidx{\!\offinterlineskip!}]
+% is an API macro to let $\!\baselineskip!=-1000$\,pt, $\!\lineskip!=0$ and
+% $\!\lineskiplimit!=\!\maxdimen!$ to supress \!\baselineskip! insertion for
+% all boxes following this macro.  It is used in \!\pcol@bg@paint@i! to do
+% that in the box in which painted \bground{}s are built.
+% 
+% \item[\Uidx{\!\thepage!}]
+% is an API macro to have the representation of the counter \counter{page}.
+% It is used in \!\pcol@output! for a warning message.
+% 
+% \item[\Uidx{$\cs{the}{\cdot}\theta$}]
+% \SpecialArrayIndex{\theta}{\the}

+% 

+% is an API macro to have the representation of the counter $\theta$.  The
+% macro is kept in $|\pcol@thectr@|{\cdot}\theta$
+% 

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

+% 

+% by \!\pcol@thectrelt! which also makes the macro \!\let!-equal to
+% $|\pcol@thectr@|{\cdot}\theta{\cdot}0$
+% 

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

+% 

+% if the \lrep{} of $\theta$ in the column 0 is defined by
+% \!\definethecounter!.  The macro \!\pcol@setctrelt! also makes this
+% overriding for the column $c$ to which the macro belongs if
+% $|\pcol@thectr@|{\cdot}\theta{\cdot}c$
+% 

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

+% 

+% being the \lrep{} for $c$ is defined, while it makes $|\the|{\cdot}\theta$
+% 

+% \SpecialArrayIndex{\theta}{\the}

+% 

+% \!\let!-equal to $|\pcol@thectr@|{\cdot}\theta$
+% 

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

+% 

+% otherwise to give it its original definition.
+% 
+% \item[\Uidx{$\!\stepcounter!\<\theta\>$}]
+% is an API macro to increment the counter $\theta$ and zero-clear its
+% descendant counters.  It is used in \!\pcol@startpage! for the counter
+% \counter{page}, and in \!\pcol@iifootnotetext! for \counter{footnote}.
+% 
+% \item[\Uidx{\!\nobreak!}]
+% is an API macro to insert $\!\penalty!=10000$ to inhibit line or page
+% breaks.  It is used in \!\pcol@output@start!, \!\pcol@restartcolumn!,
+% \!\pcol@icolumncolor!, \!\pcol@set@color@push!, \!\pcol@reset@color@pop!
+% and \!\pcol@reset@color@mpop!  to meet the page-break inhibition request
+% made by $\CSIndex{if@nobreak}=\true$.
+% 
+% \item[\Uidx{$\!\addvspace!$\marg{skip}}]
+% is an API macro to insert a vertical $\arg{skip}$ if
+% $\!\lastskip!<\arg{skip}$, or a skip of $\arg{skip}+\!\lastskip!$
+% otherwise.  The macro is used in \!\pcol@zparacol!  when it finds the
+% \env{paracol} environment to start is at the very beginning of a
+% \env{list}-like environment, to insert \!\@topsep! instead of
+% $\!\parskip!+\!\itemsep!$ going to be inserted by the first \!\item!.
+% 
+% \item[\Uidx{$\!\addpenalty!\arg{pen}$}]
+% is an API macro to insert a page break $\!\penalty!=\arg{pen}$ if
+% $\CSIndex{if@nobreak}={\false}$.  The \!\penalty! is inserted removing the
+% last vertical skip which is reinserted after the \!\penalty!.  The macro
+% is used in \!\pcol@output@start! and \!\pcol@restartcolumn! to insert
+% \!\interlinepenalty! if $\CSIndex{if@nobreak}=\false$, while
+% \!\pcol@zparacol! uses it to insert \!\@beginparpenalty! when it finds the
+% \env{paracol} environment to start is at the very beginning of a
+% \env{list}-like environment.
+% 
+% \item[\Uidx{\!\footnotesize!}]
+% is an API macro to set the font size for footnotes.  It is used in
+% \!\pcol@fntextbody! for footnote typesetting.
+% 
+% \item[\Uidx{\!\rule!\oarg{\mbox{$r$}}$\Arg{w}\Arg{h}$}]
+% is an API macro to draw a vertical rule of $w$ width and $h$ tall,
+% optionally raised by $r$.  It is used in \!\pcol@fntextbody! to have the
+% rule of $w=r=0$ and $h=\!\footnotesep!$ to make the first line of the
+% footnote is at least as tall as \!\footnotesep!.
+% 
+% \item[\Uidx{$\!\addcontentsline!\arg{file}\arg{sec}\arg{entry}$}]
+% is an API macro to put \!\addtocontents! for the arguments to |.aux| file.
+% The orignial definition of the macro is kept in
+% \!\pcol@addcontentsline! so that \!\pcol@ac@disable@toc! and
+% \!\pcol@ac@caption! make the macro regain its original definition after
+% temporarily disabling its function by making it \!\let!-equal to
+% \!\pcol@gobblethree!.
+% 
+% \item[\Uidx{\!\marginpar!}\oarg{left}\marg{right}]
+% is an API macro to put merginal note $\arg{left}$ or $\arg{right}$ to the
+% left or right margin.  In \!\pcol@zparacol! it is made \!\let!-equal to
+% \!\pcol@marginpar! for the emulation of \!\marginnote!, while its original
+% version is kept in \!\pcol@@marginpar!.
+% 
+% \item[\Uidx{\!\footnote!}\oarg{num}\marg{text}]
+% is an API macro to give a footnote $\arg{text}$ optionally with its number
+% $\arg{num}$.  In \!\pcol@zparacol! it is made \!\let!-equal to
+% \!\pcol@footnote!  to implement its starred version and the adjustment of
+% \counter{footnote} at \Endparacol, while its original version is kept in
+% \!\pcol@@footnote!.
+% 
+% \item[\Uidx{\!\footnotemark!}\oarg{num}]
+% is an API macro to give a footnote mark optionally with the number
+% $\arg{num}$ which the mark represents.  In \!\pcol@zparacol! it is made
+% \!\let!-equal to \!\pcol@footnotemark! to implement its starred version
+% and the adjustment of \counter{footnote} at \Endparacol, while its
+% original version is kept in \!\pcol@@footnotemark!.
+% 
+% \item[\Uidx{\!\footnotetext!}\oarg{num}\marg{text}]
+% is an API macro to give a footnote $\arg{text}$ optionally with its number
+% $\arg{num}$ but without putting the mark in the footnoted text.  In
+% \!\pcol@zparacol!  it is made \!\let!-equal to \!\pcol@footnotetext! to
+% implement its starred version, while its original version is kept in
+% \!\pcol@@footnotetext!.
+% 
+% \item[\Uidx{\!\footnoterule!}]
+% is an API macro to draw a horizontal line above footnotes, or to insert
+% whatever it has above them.  With \Scfnote{} typesetting, it is redefined
+% in \!\pcol@zparacol! so that it refers to \!\textwidth! instead of
+% \!\columnwidth! for drawing the horizontal line or whatever defined, while
+% the original version is kept in \!\pcol@footnoterule!.  Then it is used in
+% \!\pcol@putfootins! to separate footnotes from the stuff above them, with
+% the original or modified definition.
+% 
+% \item[\Uidx{\!\newpage!}]
+% is an API macro to break a page.  It is used in \!\pcol@switchcol! as the
+% argument of \!\pcol@visitallcols! to break the \colpage{}s visited in the
+% \cscan{} when the \sync{}ed \cswitch{} requires explicit page breaks.
+% 
+% \item[\Uidx{\!\dblfigrule!}]
+% is an API macro to draw a horizontal line between the last \pwise{}
+% floats and the main vertical list, or to insert whatever it has between
+% them.  The macro is used in \!\pcol@startpage! to build \spanning{} in
+% the page $p$ in $\pp^b(p)$.
+% 
+% \item[\Uidx{\!\topfigrule!}]
+% is an API macro to draw a horizontal line between the last \cwise{}
+% top float and the main vertical list, or to insert whatever it has between
+% them.  The macro is used in \!\pcol@cflt! and \!\pcol@synccolumn! to
+% insert it below the last (real) top float.  It is also made \!\let!-equal
+% to \!\relax! temporarily by \!\pcol@imakeflushedpage! when it put floats in
+% a \fcolumn{} as top floats.  Note that the macro and its bottom
+% counterpart \!\botfigrule! should produce a vertical list whose total
+% height and depth is 0, because \LaTeX's float mechanism and thus our
+% macros believe so.
+% 
+% \item[\Uidx{\!\normalcolor!}]
+% is an API macro to have color specification stuff for normal coloring.
+% The macro is used in \!\pcol@putfootins! to specify the color of footnotes
+% to be put in \!\@outputbox!, in \!\normalcolumncolor!\oarg{c} to
+% define that the default color of the column $c$ is the normal color,
+% in \!\normalcolseprulecolor! to specify that the color for \cseprule{}s is
+% \!\normalcolor!, and in the initial definition of \!\pcol@colseprulecolor!
+% to give the default color for \cseprule{}s.
+% 
+% \item[\Uidx{\!\color!}\oarg{mode}\marg{color}]
+% is an API macro defined in coloring pacakges to start text coloring with
+% $\arg{color}$ optionally with $\arg{mode}$.  The macro is used in
+% \!\pcol@xcolumncolor!\oarg{mode}\~\marg{color}\oarg{c} and
+% \!\pcol@ycolumncolor!\marg{color}\oarg{c} to define the default color of
+% the column $c$ is $\arg{color}$ optionally with $\arg{mode}$, in
+% \!\pcol@defcseprulecolor@x! and \!\pcol@defcseprulecolor@y! to define the
+% color of \cseprule{}s, and in \!\pcol@backgroundcolor@x! to define the
+% color for \bgpaint{} of a region.
+% 
+% \item[\Uidx{\!\pfmtname!}]
+% is an API macro defined in p\LaTeX{} to have its format name |pLaTeX2e|
+% (so far).  It is used in the top level assignment of the constant switch
+% \CSIndex{ifpcol@bfbottom}.
+% 
+% \item[\Uidx{$\!\PackageError!\arg{pkg}\arg{msg}\arg{hlp}$}]
+% is a developer's API macro to stop the exectution showing the error
+% message $\arg{msg}$ with the package identification $\arg{pkg}$ and the
+% help mssage $\arg{hlp}$.  The macro is used in the following macros;
+% \!\pcol@ovf! on \!\@freelist! shortage; \!\pcol@set@color@push! on too
+% many math-mode colorings; in \!\pcol@zparacol! on two-column
+% typesetting outside \env{paracol} and illegal nesting of \env{paracol};
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ on too large $x/y$;
+% \!\pcol@switchcolumn! on invalid target column; \!\pcol@switchenv! on
+% illegal \cswitch{} commands\slash environments in a \csenv;
+% \!\addcontentsonly! on unknown contents type; \!\footnotelayout! on
+% unknown layout;  \!\pcol@twosided! on unknown two-sided typesetting
+% feature;  \!\pcol@backgroundcolor! on unknown region of \bgpaint;  and in 
+% \!\pcol@backgroundcolor@i! on a region not being a column or \csepgap{}
+% but its ordinal being specified.
+% 
+% \item[\Uidx{$\!\PackageWarning!\arg{pkg}\arg{msg}$}]
+% is a developer's API macro to report a warning message $\arg{msg}$ with
+% the package identification $\arg{pkg}$.  The macro is used in
+% \!\pcol@ignore! to complain an API macro appears in \env{paracol}
+% inappropriately, in \!\pcol@fntextbody!  if the footnote is taller than
+% $\!\textheight!-\!\skip!\!\footins!$, in \!\pcol@mn@warning! to show
+% \!\marginnote! is emulated, and in \!\pcol@icolumncolor!,
+% \!\pcol@defcseprulecolor@i! and \!\pcol@backgroundcolor@ii! to complain
+% \!\columncolor!\slash\!\normalcolumncolor!,
+% \!\colseprulecolor!\slash\!\normalcolseprulecolor! or \!\background~color!
+% is used without coloring packages respectively.
+% 
+% \item[\Uidx{\!\@@par!}]
+% is an internal macro to keep \TeX's original primitive \CSIndex{par} in it.
+% The macro is used in \!\pcol@output! to let \CSIndex{par} act with its
+% original definition, and in \!\pcol@switchcol! and \!\pcol@flushclear! as
+% the argument given to \!\pcol@visitallcols! to give \TeX's page builder
+% the chance of page break in \cscan{}ning.
+% 
+% \item[\Uidx{\!\@height!}]
+% is an internal macro having the keyword |height|.  It is used in
+% \!\pcol@buildcolsep~rule!, \!\pcol@buildcselt!, \!\pcol@bg@paintregion@i!,
+% \!\pcol@output@start!, and \!\pcol@putbackmvl! to draw a \!\hrule! for
+% \cseprule{} in the first two, a \!\vrule! to be painted in the third, and
+% an invisible \!\hrule! in the fourth and last.
+% 
+% \item[\Uidx{\!\@width!}]
+% is an internal macro having the keyword |width|.  It is used in
+% \!\pcol@buildcolsep~rule!, \!\pcol@buildcselt!, \!\pcol@bg@paintregion@i!,
+% \!\pcol@output@start!, and \!\pcol@putbackmvl! to draw a \!\hrule! for
+% \cseprule{} in the first two, a \!\vrule! to be painted in the third, and
+% an invisible \!\hrule! in the fourth and last.
+% 
+% \item[\Uidx{\!\@plus!}]
+% is an internal macro having the keyword |plus|.  It is used in the
+% following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! to \!\def!ine \!\@textbottom! with the body of a vertical
+% skip with small infinite stretch and shrink.
+% 
+% \item
+% \!\pcol@combinefloats! for a skip of the same amount in \!\@textbottom!
+% above and that of negative amount to {\em move} the effect.
+% 
+% \item
+% \!\pcol@hfil! for skips having 1\,|fil| infinite stretch with $\gap_c$ or
+% $\gap_c/2$ to make it sure the series of columns and \csepgap{}s does not
+% cause underfull.
+% 
+% \item
+% \!\pcol@synccolumn! to put a $1\,|fil|$ infinte stretch below the
+% main vertical list together with a small infinte shrink in the \colpage{}
+% being flushed and having a \sync{}ation point, and a vertical skip with a
+% small infinite stretch to push up the main vertical list above a
+% \sync{}ation point.
+% 
+% \item
+% \!\pcol@setcw@getspec@i! to add $0\,|pt|\ |plus|\ 1000\,|pt|\ |minus|\
+% 1000\,|pt|$ to \!\@tempskipa! to ensure the register have stretch and
+% shrink components.
+% 
+% \item
+% \!\pcol@setcw@fill! to let $\!\@tempskipa!=0\,|pt|\ |plus|\ f\,|fil|$ as
+% the infinite stretch factor of $f$.
+% \end{itemize}
+% 

+% It is also used in the top level assignment of $0\,|pt|\ |plus|\ 1\,|fil|\
+% |minus|\ 1\,|fil|$ to \!\@tempskipa! for the invocatoin of \!\pcol@defkw!.
+% 
+% \item[\Uidx{\!\@minus!}]
+% is an internal macro having the keyword |minus|.  It is used in the
+% following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! to \!\def!ine \!\@textbottom! with the body of a vertical
+% skip with small infinite stretch and shrink.
+% 
+% \item
+% \!\pcol@combinefloats!  for a skip of the same amount and that of negative
+% amount.
+% 
+% \item
+% \!\pcol@synccolumn! to put a small infinite shrink together with a
+% stretch of $1\,|fil|$ at the bottom of the main vertical list in a
+% \colpage{} being flused and having a \sync{}ation point.
+%
+% \item
+% \!\pcol@setcw@getspec@i! to add $0\,|pt|\ |plus|\ 1000\,|pt|\ |minus|\
+% 1000\,|pt|$ to \!\@tempskipa! to ensure the register have stretch and
+% shrink components.
+% \end{itemize}
+% 

+% It is also used in the top level assignment of $0\,|pt|\ |plus|\ 1\,|fil|\
+% |minus|\ 1\,|fil|$ to \!\@tempskipa! for the invocatoin of \!\pcol@defkw!.
+% 
+% \item[\Uidx{\!\hb@xt@!}]
+% is an internal macro having the sequence ``\!\hbox!| to|''.  It is used in 
+% \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! to
+% put each \colpage{} in a \!\hbox! of \!\columnwidth! wide and to enclose
+% all of them in a \!\hbox! of \!\textwidth! wide.
+% 
+% \item[\Uidx{$\!\@namedef!\arg{cs}\arg{body}$}]
+% is an internal macro to do $\!\def!|\|\arg{cs}\Arg{body}$.  It is used in
+% the following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@zparacol! for \!\column*! and \!\pcol@com@column*!.
+% 
+% \item
+% $\!\pcol@remctrelt!\<\theta\>$ for $|\cl@|{\cdot}\theta$.
+% 

+% \SpecialArrayIndex{\theta}{\cl@}
+% 
+% \item
+% $\!\definethecounter!\<\theta\>\<c\>\arg{rep}$ for
+% $|\pcol@thectr@|{\cdot}\theta{\cdot}c$,
+% 

+% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
+% 
+% \item
+% $\!\pcol@loadctrelt!\<\theta\>\<\val_c(\theta)\>$ for
+% $|\pcol@ctr@|{\cdot}\theta$.
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}
+% 
+% \item
+% \!\pcol@defcolumn! for \!\pcol@com@column*!.
+% 
+% \item
+% \!\pcol@defcseprulecolor@i! for $\!\pcol@colseprulecolor![{\cdot}c]$.
+% 

+% \SpecialArrayIndex{c}{\pcol@colseprulecolor}
+% 
+% \end{itemize}
+% 

+% We also use this macro in top level \!\def!initions of
+% \!\pcol@com@nthcolumn*!, \!\pcol@com@leftcolumn*! and
+% \!\pcol@com@rightcolumn*! for the starter of the environments
+% \env{nthcolumn*}, \env{leftcolumn*} and \env{rightcolumn*}.
+% 
+% \item[\Uidx{$\!\@nameuse!\arg{cs}$}]
+% is an internal macro to do $|\|\arg{cs}$.  It is used in the following
+% macros.
+% 

+% \begin{itemize}
+% \item
+% $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ for
+% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}\{a{\cdot}|@|{\cdot}c,a\}$.
+% 

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}

+%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% 
+% \item
+% \!\pcol@bg@columnleft! for $|\pcol@columnwidth|{\cdot}c$ and
+% $|\pcol@columnsep|{\cdot}c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}
+% \SpecialArrayIndex{c}{\pcol@columnsep}
+% 
+% \item
+% \!\pcol@bg@columnwidth! for $|\pcol@columnwidth|{\cdot}c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}
+% 
+% \item
+% \!\pcol@bg@columnsep! for $|\pcol@columnsep|{\cdot}c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}
+% 
+% \item
+% \!\pcol@ccuse! for
+% $\Celt^c=|\pcol@columncolor@box|{\cdot}c$ or
+% $\Celtshadow^c=|\pcol@columncolor|{\cdot}c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% 
+% \item
+% \!\column*! for \!\pcol@com@column*!.
+% 
+% \item
+% \!\pcol@zparacol! for $|\pcol@colpream|{\cdot}0$.
+% 

+% \SpecialArrayIndex{c}{\pcol@colpream}

+% 
+% \item
+% $\!\pcol@storectrelt!\<\theta\>$ for $|\pcol@ctr@|{\cdot}\theta$.
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 
+% \item
+% $\!\pcol@cmpctrelt!\<\theta\>$ for $|\c@|{\cdot}\theta$
+% 

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

+% 

+% and $|\pcol@ctr@|{\cdot}\theta$.
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 
+% \item
+% \!\pcol@synccounter! for $|\pcol@counters|{\cdot}c$ for the column $c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@counters}

+% 
+% \item
+% $\!\pcol@syncctrelt!\<\theta\>$ for $|\c@|{\cdot}\theta$.
+% 

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

+% 
+% \item
+% $\!\pcol@stepcounter!\<\theta\>$ for $|\pcol@counters|{\cdot}c$ for the
+% column $c$,
+% 

+% \SpecialArrayIndex{c}{\pcol@counters}

+% 

+% and for $|\cl@|{\cdot}\theta$.
+% 

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

+% 
+% \item
+% \!\pcol@switchcol! to the column $c$ for $|\pcol@colpream|{\cdot}c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@colpream}

+% 
+% \item
+% $\!\pcol@aconlyelt!\<t\>\<c\>$ for $|\pcol@ac@def@|{\cdot}t$.
+% 

+% \SpecialIndex{\pcol@ac@def@lof}\SpecialIndex{\pcol@ac@def@lot}

+% 
+% \item
+% $\!\pcol@ac@def@lof!\arg{eord}$ and $\!\pcol@ac@def@lot!\arg{eord}$
+% for $|\pcol@ac@caption@|{\cdot}\~\arg{eord}$.
+% 

+% \SpecialIndex{\pcol@ac@caption@enable}

+% \SpecialIndex{\pcol@ac@caption@disable}

+% 
+% \item
+% $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\arg{cap}$ for
+% $|\pcol@ac@caption@if@|{\cdot}t$
+% 

+% \SpecialIndex{\pcol@ac@caption@if@lof}

+% \SpecialIndex{\pcol@ac@caption@if@lot}

+% 

+% and for $|\ext@|{\cdot}\~\arg{type}$.
+% 

+% \SpecialIndex{\ext@figure}\SpecialIndex{\ext@table}

+% 
+% \item
+% $\!\footnotelayout!\Arg{l}$ for $|pcol@fnlayout@|{\cdot}l$.
+% 

+% \SpecialArrayIndex{l}{\pcol@fnlayout@}

+% \SpecialIndex{\pcol@fnlayout@c}

+% \SpecialIndex{\pcol@fnlayout@p}

+% \SpecialIndex{\pcol@fnlayout@m}

+% 
+% \item
+% $\!\pcol@twosided!|[|T|]|$ for $|pcol@twosided@|{\cdot}t$ where $t\in T$.
+% 

+% \SpecialArrayIndex{t}{\pcol@twosided@}

+% \SpecialIndex{\pcol@twosided@p}

+% \SpecialIndex{\pcol@twosided@c}

+% \SpecialIndex{\pcol@twosided@m}

+% \SpecialIndex{\pcol@twosided@b}

+% \end{itemize}
+% 
+% \item[\Uidx{$\!\@gobble!\arg{arg}$}]
+% discards its argument $\arg{arg}$.  It is used in \!\pcol@output@start!,
+% \!\pcol@icolumncolor! and \!\pcol@set@color@push! for temporarily letting
+% \!\aftergroup! be \!\@gobble! to nullify \!\aftergroup! with
+% \!\reset@color! invoked in \!\pcol@set@color!, being the original version
+% of \!\set@color!, and in \!\pcol@zparacol! to make \!\pcol@bg@paintbox!
+% \!\let!-equal to \!\@gobble! to nullify it if any coloring packages have
+% not been loaded.  In addition, the macros \!\pcol@F! and \!\pcol@Fe! for
+% logging are made \!\let!-equial to \!\@gobble! at the top level to nullify
+% them.
+% 
+% \item[\Uidx{$\!\@ifundefined!\arg{cs}\arg{then}\arg{else}$}]
+% \begin{Hfuzz}{0.8pt}%
+% is an internal macro to do $\arg{then}$ or $\arg{else}$ if $\arg{cs}$ is
+% undefined or defined respectively.
+% It is used in the following macros;
+% $\!\pcol@bg@paintregion!\arg{a}\arg{c}$ to examine if either
+% $|\pcol@bg@color@|{\cdot}a{\cdot}|@|{\cdot}c$ or
+% $|\pcol@bg@color@|{\cdot}a$ is defined;
+% 

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% 

+% \!\add~contentsonly!$\<t\>\<c\>$ to stop the execution if
+% $|\pcol@ac@def@|{\cdot}t$ is not defined;
+% 

+% \SpecialArrayIndex{t}{\pcol@ac@def@}

+% 

+% \!\footnote~layout!$\Arg{l}$ to stop the execution if
+% $|\pcol@fnlayout@|{\cdot}l$ is not defined;
+% 

+% \SpecialArrayIndex{l}{\pcol@fnlayout@}

+% 

+% $\!\pcol@twosided!|[|T|]|$ to stop the execution if $T$ has $t$
+% such that $|\pcol@twosided@|{\cdot}t$ is not defined;
+% 

+% \SpecialArrayIndex{t}{\pcol@twosided@}

+% 

+% \!\pcol@backgroundcolor! to stop the execution if $|\pcol@bg@@|{\cdot}a$
+% is not defined for a region $a$;
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@@}

+% 

+% and \!\pcol@backgroundcolor@i! to stop the execution if
+% $|\pcol@bg@mayhavecol|{\cdot}a$ is not defined for a region $a$.
+% \end{Hfuzz}
+% 
+% \item[\Uidx{$\!\@ifnextchar!\arg{char}\arg{then}\arg{else}$}]
+% is an internal macro to do $\arg{then}$ or $\arg{else}$ if the character
+% following to the macro is $\arg{char}$ or not respectively.  It is used in
+% the following macros to examine if they are followed by a `\texttt{\LB}'.
+% 

+% \begin{quote}\raggedright
+% \!\paracol!,
+% \!\pcol@zparacol!,
+% \!\columnratio!,
+% \!\pcol@com@column*!\hbox{ (initial definition)},
+% \!\pcol@com@switchcolumn!,
+% \!\pcol@iswitchcolumn!,
+% \!\pcol@adjustfnctr!,
+% \!\pcol@ifootnotetext!,
+% \!\twosided!,
+% \!\marginparthreshold!,
+% \!\columncolor!,
+% \!\pcol@columncolor!,
+% \!\normalcolumncolor!.
+% \!\colseprulecolor!,
+% \!\pcol@defcseprulecolor!,
+% \!\normalcolseprulecolor!,
+% \!\pcol@backgroundcolor!,
+% \!\pcol@backgroundcolor@w!.
+% \end{quote}
+% It is also used in \!\pcol@backgroundcolor@iii! and
+% \!\pcol@backgroundcolor@iv! if they are followed by a `\texttt{\LP}'.
+% 
+% \item[\Uidx{$\!\@ifstar!\arg{then}\arg{else}$}]
+% is an internal macro to do $\arg{then}$ or $\arg{else}$ if the character
+% following to the macro is `|*|'.  It is used in \!\pcol@yparacol!,
+% \!\globalcounter!, \!\pcol@switchcolumn!, \!\pcol@footnote!,
+% \!\pcol@footnotemark! and \!\pcol@footnotetext! to examine if the optional
+% `|*|' is specified.
+% 
+% \item[\Uidx{$\!\@whilesw!\arg{sw}\cs{fi}\arg{body}$}]
+% is an internal macro to iterate $\arg{body}$ while the switch $\arg{sw}$
+% is $\true$.  It is used in \!\pcol@output!, \!\pcol@startpage!,
+% \!\pcol@output@clear!, \!\pcol@flushfloats!, \!\pcol@freshpage! and
+% \!\pcol@output@end! to iterate building process of \fcolumn{}s or
+% \fpage{}s while $\CSIndex{if@fcolmade}=\true$, and in \!\pcol@switchcol!
+% and \!\pcol@flushclear! to iterate the height check of \sync{}ed or
+% flushed pages while $\CSIndex{ifpcol@flush}=\true$.
+% 
+% \item[\Uidx{$\!\@whilenum!\arg{ifnum}\cs{do}\arg{body}$}]
+% is an internal macro to interate $\arg{body}$ while the integer comparison
+% expression $\arg{ifnum}$ is $\true$.  The macro is used in the following
+% macros to iterate their own procedures for all columns $c\In0\C$.
+% 

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

+% The macro is also used in the following macros for the ranges following
+% macro name, where $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$ and $c$ is the
+% column they are working on.
+% 

+% \begin{quote}
+% \!\pcol@ioutputelt! $\LBRP\Cfrom\Cto$\\
+% \!\pcol@bg@paint@ii! $\LBRP\CBfrom{\Cto{-}1}$\\
+% \!\pcol@bg@columnleft! $\LBRP\CBfrom{c}$\\
+% \!\pcol@addmarginpar! $\LBRP\Cfrom{c'}$ ($c'\in\{c,\;\Cto-(c-\Cfrom)-1\}$)\\
+% \!\pcol@imakeflushedpage! $\LBRP\Cfrom\Cto$\\
+% \!\pcol@iflushfloats! $\LBRP\Cfrom\Cto$\\
+% \!\pcol@setcw@scan! $\LBRP\Cfrom\Cto$
+% \end{quote}
+% 

+% The other users have a little bit more complicated range as follows.
+% \begin{itemize}
+% \item
+% \!\pcol@flushcolumn! to iterate \fcolumn{} building for a column $c$ in
+% pages $q$ such that $q\in(\cc_c(\vb^p),\ptop)$.
+% 
+% \item
+% \!\pcol@setcolwidth@r! to make assignment of $\w_c$ for
+% $c\In{\min(\Cfrom{+}k,\Cto{-}1)}{\,\Cto}$ where $k$ is the number of
+% fractions given as the first or second argument of
+% \!\columnratio! and kept in \!\pcol@columnratioleft! or
+% \!\pcol@columnratioright!, respectively.
+% 
+% \item
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to calculate
+% $\lceil{y/2^{k_2+k_3}}\rceil$ finding $k_3$ by iterating $y/2$ until the
+% result becomes less than $2^{15}$, to calculate $z'/2^k$ with the range
+% $\LBRP0k$, to calculate $z'/2^{k-16}$ with the range $\LBRP0{\,k{-}16}$,
+% and to calculate $z'\cdot2^{16-k}$ with the range $\LBRP0{\,16{-}k}$,
+% where $z'\cdot2^{16-k}=Z=z\times1\,|pt|$ and $k_2$, $k_3$ and $k$ are
+% scaling parameters for good approximation.
+% \end{itemize}
+% 
+% \item[\Uidx{$\!\@whiledim!\arg{ifdim}\cs{do}\arg{body}$}]
+% is an internal macro to interate $\arg{body}$ while the dimensional
+% comparison expression $\arg{ifdim}$ is $\true$.  The macro is used in
+% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ twice, at first to find
+% $k_1=\min\Set{k}{x\cdot2^k\geq2^{13}\,|pt|}$ and to have $x\cdot2^{k_1}$,
+% and then to find $k_2=\max\Set{k}{y\bmod2^k=0}$ and to have $y/2^{k_2}$.
+% 
+% \item[$\Uidx{\!\@for!}\arg{cs}\texttt{:=}\arg{list}\cs{do}\arg{body}$]
+% is an internal macro to iterate $\arg{body}$ for each element of the
+% comma-separated $\arg{list}$ letting $\arg{cs}$ have the element.  The
+% macro is used in \!\pcol@setcolwidth@r! to scan its argument
+% $\arg{ratio}$ defined by \!\columnratio!, and in \!\pcol@setcw@scan! to
+% scan its argment $\arg{spec}$ defined by \!\setcolumnwidth!.
+% 
+% \item[$\Uidx{\!\@tfor!}\arg{cs}|:=|\arg{list}\cs{do}\arg{body}$]
+% is an internal macro to iterate $\arg{body}$ for each non-space token in
+% $\arg{list}$ letting $\arg{cs}$ have the token.  The macro is used in
+% \!\pcol@bg@paint@ii!, \!\pcol@setcw@getspec! and \!\pcol@twosided! to scan
+% their arguments, in \!\pcol@setcw@getspec@i! to scan a column\slash
+% gap specification to remove spaces from it, and in
+% $\!\pcol@twosided!|[|T|]|$ to scan all tokens being two-sided typesetting
+% features in $T$.
+% 
+% \item[\Uidx{$\!\@next!\arg{elm}\arg{lst}\arg{suc}\arg{fail}$}]
+% is an internal macro to remove the first element from $\arg{lst}$,
+% \!\def!ine $\arg{elm}$ to have the first element, and then do $\arg{suc}$,
+% if $\arg{lst}$ is not empty.  Otherwise, it performs $\arg{fail}$.  The
+% macro is used in the following macros to obtain an \!\insert! from
+% \!\@freelist!.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@opcol! for the completed \colpage{}.
+% 
+% \item
+% \!\pcol@startpage! for \fpage{}s and \spanning{} for \pwise{} top
+% floats.
+% 
+% \item
+% \!\pcol@output@start! for the \preenv{}, and \colpage{}s and $\Celt^c$ of
+% all columns.
+% 
+% \item
+% \!\pcol@output@switch! for the \colpage{} from which we are leaving.
+% 
+% \item
+% \!\pcol@iscancst! for $\Celt^c$.
+% 
+% \item
+% \!\pcol@savefootins! for footnotes.
+% 
+% \item
+% \!\pcol@flushcolumn! for \fcolumn{}s and the empty \colpage{} in $\ptop$.
+% 
+% \item
+% \!\pcol@synccolumn! for an \mvlfloat{} on a \sync{}ation if its point
+% defined by a column whose main vertical list is empty.
+% 
+% \item
+% \!\pcol@output@end! for the \pwise{} floats in the \lpage{} if the
+% main vertical list of the page is empty.
+% 
+% \item
+% \!\pcol@icolumncolor! for $\Celt^c$.
+% \end{itemize}
+% 

+% The macro is also used in \!\pcol@ioutputelt! to obtain completed
+% \colpage{}s from $\S_c$.
+% 
+% \item[\Uidx{%
+%	$\!\@xnext!\cs{@elt}\arg{car}\arg{cdr}\cs{@@}\arg{first}\arg{rest}$}]
+% is an internal macro to remove the first element $|\@elt|\arg{car}$ from a
+% list in the form of $|\@elt|\,e_1\,\cdots\,|\@elt|\,e_n$ where
+% $\arg{cdr}=|\@elt|\,e_2\,\cdots\~\,|\@elt|\,e_n$ and |\def|ine
+% $\arg{first}$ as $\arg{car}$ and globally |\def|ine $\arg{rest}$ as
+% $\arg{cdr}$.  It is used in \!\pcol@addmarginpar! to get the first element
+% of \!\@currlist! being a \!\insert! for a right marginal note without
+% modifying \!\@currlist!.
+% 
+% \item[\Uidx{$\!\@cons!\arg{lst}\arg{elm}$}]
+% is an internal macro to add $\!\@elt!\arg{elm}$ to the tail of $\arg{lst}$.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! to add $\spt(H,h)$ to the tail of $\pp^s(\ptop)$.
+% 
+% \item
+% \!\pcol@opcol! to add the completed \ccolpage{} $\cc_c(\vb)$ to $\S_c$.
+% 
+% \item
+% \!\pcol@startpage! to add $\pp(\ptop-1)$ and \fpage{}s to $\PP$.
+% 
+% \item
+% \!\pcol@outputelt! to return \spanning{} $\pp^i(q)$ in a shipped-out \fpage{}
+% $q$ to \!\@freelist!, or to add $\pp(q)$ to $\PP$ if the page $q$ is kept.
+% 
+% \item
+% \!\pcol@ioutputelt! to return \spanning{} $\pp^i(q)$, \Scfnote{}s
+% $\pp^f(q)$ and/or \colpage{}s $\s_c(q)$ for all $c\In0C$ in a shipped-out
+% page $q$ to \!\@freelist!.
+% 
+% \item
+% \!\pcol@output@start! to return the \ccolpage{} $\cc_0(\vb)$ to
+% \!\@freelist!.
+% 
+% \item
+% \!\pcol@output@switch! to add $\spt(H,h)$ to the tail of $\pp^s(\ptop)$.
+% 
+% \item
+% \!\pcol@restartcolumn! to return the \ccolpage{} $\cc_c(\vb)$ to be resumed,
+% and its footnotes $\cc_c(\ft)$ if any, to \!\@freelist!.
+% 
+% \item
+% $\!\pcol@getmparbottom!\<t\>\<h\>$ to add
+% $\mpar(\max(t,b_n),\max(t,b_n){+}h)$ to the tail of the list
+% $\mpb_{\{L,R\}}^{\{l,r\}}$, and its callee
+% $\!\pcol@getmpbelt!\<t_i\>\<b_i\>$ to add $\mpar(t_i,b_i)$ or
+% $\mpar(\max(t,b_{i-1}),\max(t,b_{i-1}){+}h)$ to the so-far tail of the
+% list in rebuilding.
+% 
+% \item
+% \!\pcol@flushcolumn! to return footnotes $\cc_c(\ft)$ in the \ccolpage{}
+% of $c$ to be flushed to \!\@freelist! if any, and to add the flushed
+% \colpage{} and \fcolumn{}s to $\S_c$.
+% 
+% \item
+% \!\pcol@makefcolelt! to add a float to \!\@toplist! or $\cc_c(\dl)$.
+% 
+% \item
+% \!\pcol@synccolumn! to add an \mvlfloat{} for \sync{}ation to
+% $\cc_c(\tl)$.
+% 
+% \item
+% \!\pcol@makeflushedpage! to return \spanning{} $\pp^i(\ptop)$ and/or
+% \Scfnote{}s $\pp^f(\ptop)$ in the top page to be flushed to \!\@freelist!
+% if any.
+% 
+% \item
+% \!\pcol@imakeflushedpage! to return \Mcfnote{}s in $\cc_c(\ft)$ s.t.\
+% $\cc_c(\vb^p)=\ptop$ to \!\@freelist! if any.
+% 
+% \item
+% \!\pcol@output@end! to return $\pp^f(\ptop)$, all \ccolpage{}s
+% $\cc_c(\vb)$, and all $\Celt^c\neq\bot$ to \!\@freelist!.
+% 
+% \item
+% \!\pcol@end@dblfloat! to add a \pwise{} float in \!\@currbox! to
+% \!\@dbldeferlist!.
+% 
+% \item
+% $\!\globalcounter!\<\theta\>$ to add a \gcounter{} $\theta$ to $\CG$.
+% 
+% \item
+% $\!\pcol@iremctrelt!\<\theta\>$ to add a \lcounter{} $\theta$ to $\CTL$.
+% 
+% \item
+% $\!\pcol@storectrelt!\<\theta\>$ to add a pair $\<\theta,\val_c(\theta)\>$
+% to $\Cc_c$ for a column $c$.
+% 
+% \item
+% $\!\pcol@savectrelt!\<\theta\>$ to add a pair $\<\theta,\val(\theta)\>$ to
+% $\Cc_c$ for a column $c$.
+% 
+% \item
+% $\!\pcol@cmpctrelt!\<\theta\>$ to add a counter $\theta$ to the list of
+% \lcounter{}s to be synchronized.
+% 
+% \item
+% $\!\addcontentsonly!\<t\>\<c\>$ to add a pair $\<t,c\>$ to $\T$.
+% 
+% \item
+% \!\pcol@backgroundcolor@ii! to add a region whose \bground{} is painted to
+% \!\pcol@bg@defined!.
+% \end{itemize}
+% 
+% \item[\Uidx{$\!\@cdr!\<a_1\>\<a_2\>\cdots\<a_n\>\cs{@nil}$}]
+% is an internal macro to be expanded to $\<a_2\>\cdots\<a_n\>$. It is used
+% in $\!\pcol@getcurrpinfo!\arg{cs}$ to extract $\pp(\ptop)$ from
+% $\!\pcol@currpage!=\!\@elt!\arg{\pp(\ptop)}$ and to \!\def!ine $\arg{cs}$
+% letting it have $\pp(\ptop)$.
+% 
+% \item[\Uidx{$\!\protected@edef!\arg{macro}$\marg{body}}]
+% is an internal macro to do \!\edef!$\arg{macro}$\marg{body} with the
+% \!\protect!ion so that \!\protect!$\arg{cs}$ is kept in the expansion.  It
+% is used in \!\pcol@fntextbody! to \!\edef!ine \!\@currentlabel!.
+% 
+% \item[\Uidx{$\!\@latex@warning@no@line!\arg{msg}$}]
+% is an internal macro to report a warning message $\arg{msg}$ without the
+% line number in which the cause lies.  It is used in \!\pcol@output! if
+% a page with floats and very short main vertical list is built.
+% 
+% \item[\Uidx{\!\@eha!}]
+% is an internal macro having a help message saying the command causing an
+% error is ignored.  It is used in \!\pcol@zparacol!, \!\pcol@setcw@calcf!,
+% \!\pcol@switchcolumn!, \!\pcol@switchenv!, and \!\addcontentsonly! as the
+% argument of \!\PackageError!.
+% 
+% \item[\Uidx{\!\@ehb!}]
+% is an internal macro having a help message saying the error causes a
+% serious problem.  It is used in \!\pcol@ovf!, \!\pcol@zparacol! and
+% \!\pcol@set@color@push! as the argument of \!\PackageError!.
+% 
+% \item[\Uidx{\!\@parmoderr!}]
+% is an internal macro to complain about misplacement of a macro or
+% environment which is expected to appear in ``outer par mode''.
+% It is used in \!\pcol@zparacol! if it finds $\CSIndex{ifinner}=\true$.
+% 
+% \item[\Uidx{\!\@Esphack!}]
+% is an internal macro to put back the horizontal skip and space factor
+% saved by \!\@bsphack! at the end of an environment.  It is used in
+% \!\pcol@end@dblfloat!.
+% 
+% \item[\Uidx{\!\reset@font!}]
+% is an internal macro \!\let!-equal to \!\normalfont! to use a starndard
+% font.  It is used in \!\pcol@fntextbody! for footnote typesetting.
+% 
+% \item[\Uidx{\!\set@color!}]
+% is an internal macro to start coloring of texts following it.  By default
+% it is \!\relax! but may have a definition to put a \!\special! for
+% coloring with the color in \!\current@color!.  In the following macros, it
+% is examined if $\!\set@color!=\!\relax!$ and/or some local definition is
+% given to \!\set@color!.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@output! lets $\!\set@color!=\!\pcol@set@color!$ i.e., lets it
+% regain its original definition because we don't need any special
+% operations in \!\output! routine.
+% 
+% \item
+% \!\@outputpage! performs \bgpaint{} if $\!\set@color!\neq\!\relax!$.
+% 
+% \item
+% \!\pcol@zparacol! performs set-up operations for text coloring, including
+% making \!\set@color! \!\let!-equal to \!\pcol@set@color@push! saving
+% its original definition into \!\pcol@set@color!, and enabling \bgpaint{}
+% macros if $\!\set@color!\neq\!\relax!$, while these \bgpaint{} macros are
+% nullified otherwise.
+% 
+% \item
+% \!\pcol@icolumncolor! complains that no color packages have been loaded if
+% \!\set@color!${}={}$\!\relax!, and then otherwise temporarily lets it be
+% the original saved in \!\pcol@set@color! to \!\insert! a \!\vbox! to
+% update $\Celt^c$ or to do the update immediately.
+% 
+% \item
+% \!\pcol@iicolumncolor! temporarily lets $\!\set@color!=\!\relax!$ so that
+% \!\color! or \!\normalcolor! invoked in the macro just defines
+% \!\current@color! to be set into $\Celtshadow^c$ without doing any other
+% coloring operations.
+% 
+% \item
+% \!\pcol@defcseprulecolor@i! complains that no color packages have been
+% loaded if $\!\set@color!=\!\relax!$, while otherwise the macro temporarily
+% lets $\!\set@color!=\!\relax!$ to invoke \!\color! (or \!\normalcolor!) to
+% check if its arguments are properly given.
+% 
+% \item
+% \!\pcol@backgroundcolor@ii! complains that no color packages have been
+% loaded if $\!\set@color!=\!\relax!$, while otherwise its descendent 
+% \!\pcol@backgroundcolor@x! temporarily lets
+% $\!\set@color!=\!\pcol@backgroundcolor@y!$ to \!\def!ine
+% $|\pcol@bg@|\~|color@|a[|@|{\cdot}c]$ to be \!\current@color!.
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% \end{itemize}
+% 
+% \item[\Uidx{\!\reset@color!}]
+% is an internal macro to finish text coloring started by \!\set@color!.  By
+% default it is undefined but may have some definition to put a \!\special!
+% to finish coloring.  It is used in \!\pcol@clearcolorstack! so as to apply
+% it to all elements in $\CST^c$, in \!\pcol@iscancst! to put it to the
+% main vertical list in the case that $\Celt^c$ was $\bot$ and then updated,
+% in \!\pcol@icolumncolor! to apply it to all elements in $\CSTshadow^c$,
+% and in \!\pcol@reset@color@pop! and \!\pcol@reset@color@mpop! to have an
+% uncoloring \!\special! in the \!\vbox! for $\celt_i$ and $\mcelt_{i,m}$.
+% 
+% \item[\Uidx{\!\color@begingroup!}]
+% is an internal macro to open a group in which a color is specified.  It is
+% used in \!\pcol@putfootins! to enclose footnotes with \!\normalcolor!, and
+% in \!\pcol@fntextbody!\marg{text} to enclose the coloring in the footnote
+% $\arg{text}$.
+% 
+% \item[\Uidx{\!\color@endgroup!}]
+% is an internal macro to close a group in which a color is specified.  It is
+% used in \!\pcol@putfootins! to enclose footnotes with \!\normalcolor!, and
+% in \!\pcol@fntextbody!\marg{text} to enclose the coloring in the footnote
+% $\arg{text}$.
+% 
+% \item[\Uidx{$\!\@stpelt!\<\theta\>$}]
+% is an internal macro to zero-clear the counter $\theta$ for the
+% implementation of \!\stepcounter!.  It is used in \!\pcol@stepcounter! to
+% clear the descendent counters of a \gcounter{} $\cg$ listed in
+% $|\pcol@cl@|{\cdot}\cg$.
+% 

+% \SpecialArrayIndex{\theta}{\pcol@cl@}
+% 
+% \item[\Uidx{\!\@nbitem!}]
+% is an internal macro to insert a vertical skip of
+% $\!\@outerparskip!-\!\parskip!$ above the first \!\item! of a
+% \env{list}-like environment when $\CSIndex{if@nobreak}=\true$.  It is used
+% by \!\pcol@zparacol! when it finds the \env{paracol} environment to start
+% is at the very beginning of a \env{list}-like environment and
+% $\CSIndex{if@nobreak}=\true$.
+% 
+% \item[\Uidx{\!\@parboxrestore!}]
+% is an internal macro to set up typesetting paramenters for paragraphs
+% encapsulated in a box.  It is used in \!\pcol@fntextbody! for paragraphs
+% in a footnonte.
+% 
+% \item[\Uidx{\!\@finalstrut!}$\arg{box}$]
+% is an internal macro to add an invisible vertical rule whose depth is that
+% of a $\arg{box}$.  It is used in \!\pcol@fntextbody! to make the last line
+% of the footnotes is as deep as \!\strutbox! at shallowest.
+% 
+% \item[\Uidx{\!\@sect!}]
+% is an internal macro to implement sectioning commands.  The original
+% definition of the macro is kept in \!\pcol@ac@enable@toc!, while
+% \!\pcol@ac@def@toc! makes it \!\let!-equal to \!\pcol@ac@enable@toc! or
+% \!\pcol@ac@disable@toc!, the latter of which uses the original version
+% temporarily disabling \!\addcontentsline!.
+% 
+% \item[\Uidx{\!\@svsechd!}]
+% is an internal macro (locally) \!\def!ined in \!\@sect! and \!\@ssect! to
+% keep the section header of a sectioning command such as \!\paragraph!
+% which puts the header as the leading text of the paragraph following the
+% command rather than putting it as an individual paragraph.  The macro is
+% \!\global!ized in \!\pcol@sptext! so that it is properly referred to in
+% \!\everypar! for the paragraph led by the text in case that a \mctext{}
+% has the sectioning command only and thus the \!\def!inition of the macro
+% must survive after we close the group in which the \mctext{} is put.
+% 
+% \item[\Uidx{\!\@svsec!}]
+% is an internal macro (locally) \!\def!ined in \!\@sect! to keep
+% \!\thesection!  etc.\ to be displayed as the leading part of the section
+% header.  The macro is \!\global!ized in \!\pcol@sptext! together with
+% \!\@svsechd!  because it is in the body of \!\@svsechd!.
+% 
+% \item[\Uidx{\!\@caption!}]
+% is an internal macro to implement \!\caption!.  The original definition of
+% the macro is kept in \!\pcol@ac@caption@latex!, while
+% \!\pcol@ac@caption@def! makes it \!\let!-equal to \!\pcol@ac@caption!
+% which uses the original version temporarily disabling \!\addcontentsline!
+% if necessary.
+% 
+% \item[\Uidx{\!\end@float!}]
+% is an internal macro to close a \cwise{} float environment.  It is used in
+% \!\pcol@end@dblfloat! (but never invoked because we havd \cs{if@twocolumn}
+% true always).
+% 
+% \item[\Uidx{\!\end@dblfloat!}]
+% is an internal macro to close a \pwise{} float environment.  It is replaced
+% with our own \!\pcol@end@dblfloat!.
+% 
+% \item[\Uidx{\!\@endfloatbox!}]
+% is an internal macro to close a \!\vbox! for a float.  It is used in
+% \!\pcol@end@dblfloat!.
+% 
+% \item[\Uidx{\!\@largefloatcheck!}]
+% is an internal macro to examine if a float is too large.  It is used in
+% \!\pcol@end@dblfloat!.
+% 
+% \item[\Uidx{\!\@floatplacement!}]
+% is an internal macro for \!\output! routine to reinitialize \cwise{}
+% float placement parameters.  It is used in our own version of it,
+% \!\pcol@floatplacement!.
+% 
+% \item[\Uidx{\!\@dblfloatplacement!}]
+% is an internal macro for \!\output! routine to reinitialize \pwise{}
+% float placement paramenters.  It is used in \!\pcol@startpage! and
+% \!\pcol@output@clear! prior to processing \pwise{} floats in
+% \!\@dbldeferlist!.  As discussed in
+% item-(\ref{item:ovv-float-@dblfloatplacement}) of
+% \secref{sec:imp-ovv-float}, this macro in 2015 or later version of
+% \LaTeX{} lets $\!\f@depth!=|1sp|$.
+% 
+% \item[\Uidx{\!\@xympar!}]
+% is an interal macro to perform the last operations for \!\marginpar!.  In
+% \!\pcol@zparacol! it is made \!\let!-equal to \!\pcol@xympar! for the
+% emulation of \!\marginnote!, while its original version is kept in
+% \!\pcol@@xympar!.
+% 
+% \item[\Uidx{\!\p@footnote!}]
+% is an internal macro to have the prefix to \!\thefootnote! in the printed
+% reference of the counter \counter{footnote}.  It is used in
+% \!\pcol@fntextbody! to produce \!\@currentlabel!.
+% 
+% \item[\Uidx{\!\@thefnmark!}]
+% is an internal macro to have \!\thefootnote!\footnote{

+% 

+% Or \cs{thempfootnote} in \env{minipage} environment.}.
+% 

+% It is used in \!\pcol@fntextbody! to produce \!\@currentlabel!.
+% 
+% \item[\Uidx{\!\@footnotetext!}\marg{text}]
+% is an internal macro to implement \!\footnote! and \!\footnotetext! for
+% $\arg{text}$.  In \!\pcol@zparacol!, it is made \!\let!-equal to
+% \!\pcol@fntext!.
+% 
+% \item[\Uidx{\!\@makefntext!}\marg{fn}]
+% is an internal macro to typeset the footnote $\arg{fn}$.  It is used in
+% \!\pcol@fntextbody!\marg{text} to typeset the footnote $\arg{text}$ with
+% some other stuff.
+% 
+% \item[\Uidx{\!\@emptycol!}]
+% is an internal macro for \!\output! routine to put back an empty page to
+% the main vertical list.  It is used \!\pcol@output! if a page with floats
+% and very short main vertical list is built.
+% 
+% \item[\Uidx{\!\@specialoutput!}]
+% is an internal macro for \!\output! routine to process an \!\output!
+% request made by \LaTeX's original \!\clearpage!, $\!\end!\Arg{float}$ and
+% \!\marginpar!.  It is used in \!\pcol@specialoutput! to process the
+% request for floats or marginal notes.
+% 
+% \item[\Uidx{\!\@opcol!}]
+% is an internal macro for \!\output! routine to output a page or to keep
+% the first column until the second one is completed.  This macro is used in
+% \!\pcol@output! to process a sneaked \!\output! request from outside of
+% \env{paracol}, and in \!\pcol@output@end! for the case \pwise{} floats
+% are left at \Endparacol{} and they are put in \fpage{}s.
+% 
+% \item[\Uidx{\!\@makecol!}]
+% is an internal macro for \!\output! routine to build the ship-out
+% image of a column in \!\@outputbox! consisting of top floats, main
+% vertical list in \!\box!|255|, footnotes in \!\footins!, and bottom
+% floats\footnote{

+% 

+% In p\LaTeX, the order of footnotes and bottom floats are reversed.}.
+% 

+% It is used in \!\pcol@output! to process a sneaked \!\output!  request
+% from outside of \env{paracol}, in \!\pcol@@makecol! for a \colpage{} to be
+% flushed by \!\pcol@flushcolumn! and \!\pcol@makeflushedpage!, in
+% \!\pcol@makecol! for an ordinary \colpage{}, and in \!\pcol@output@start!
+% and \!\pcol@makenormalcol! for \preenv{}.
+% 
+% \item[\Uidx{\!\@textbottom!}]
+% is an internal macro for \!\output! routine to be put at the bottom of
+% \!\@outputbox! in which a \colpage{} is stored, by \!\@makecol!.  This
+% macro is temporarily re\!\def!ined by \!\pcol@makecol! for a \colpage{}
+% having \sync{}ation points so that it has a vertical skip of inifinite
+% stretch and shrink to push up/down the stuff below the last \sync{}ation
+% point in order to adjust its top to the point.  After that, its original
+% definition kept in \!\pcol@textbottom! is restored.  Another modifiers of
+% the macro are as follows; \!\pcol@makenormalcol! to make the macro
+% \!\let!-equal to \!\relax! temporarily to avoid the insertion of whatever
+% the macro has in \!\@makecol!; and \!\pcol@makeflushedpage! to let the
+% macro have \!\vfil! temporarily so that empty columns in a \lpage{} are
+% made {\em full size} without underfull.
+% 
+% \item[\Uidx{\!\@outputpage!}]
+% is an internal macro for \!\output! routine to output a page kept in
+% \!\@outputbox! together with the header and footer.  The original
+% definition of this macro is saved in \!\pcol@@outputpage! to be used in
+% \!\pcol@outputpage@l! and \!\pcol@outputpage@r! being callees of our own
+% revised version of \!\@outputpage!.  Therefore, any \!\output! request to
+% result in page ship-out reaches our own \!\@outputpage! and then \LaTeX's
+% one after we perform operations for \parapag{}ing and \bgpaint{} onto the
+% ship-out image.
+% 
+% \item[\Uidx{\!\@combinefloats!}]
+% is an internal macro for \!\output! routine to combine top and bottom
+% floats in \!\@toplist! and \!\@botlist! respectively with \!\@outputbox!
+% in which the main vertical list and footnotes\footnote{
+% 

+% In p\LaTeX, footnotes are not in \cs{@outputbox} because of the reversal of
+% footnotes and bottom floats.}
+% 

+% have been put by \!\@makecol!, and to have the result in \!\@outputbox!
+% again.  In \!\pcol@zparacol!, it is made \!\let!-equal to our own
+% \!\pcol@combinefloats!  so that \!\@makecol! and \!\pcol@makenormalcol!
+% uses it instead of the original one.  However, if \!\pcol@output! finds
+% that the \!\output!  request for a page break outside \env{paracol} is
+% sneaked into our own \!\output! routine, it makes this macro \!\let!-equal
+% to \!\pcol@@combinefloats! in which \LaTeX's version is kept so that
+% \LaTeX's original \!\output! routine works perfectly as original.
+% 
+% \item[\Uidx{\!\@cflt!}]
+% is an internal macro for \!\output! routine to put all top floats in
+% \!\@toplist! and related stuff such as the vertical skip of
+% \!\textfloatsep! into \!\@outputbox!  together with its old contents being
+% the main vertical list and footnotes

+% 

+% \addtocounter{footnote}{-1}\footnotemark.
+% 

+% It is used in \!\pcol@combinefloats! if the \colpage{} being processed
+% does not have \sync{}ation points.
+% 
+% \item[\Uidx{\!\@cflb!}]
+% is an internal macro for \!\output! routine to put all bottom floats in
+% \!\@botlist! and related stuff such as the vertical skip of
+% \!\textfloatsep! into \!\@outputbox!  together with its old contents being
+% top floats, the main vertical list and footnotes

+% 

+% \addtocounter{footnote}{-1}\footnotemark.
+% 

+% It is used in \!\pcol@combinefloats!.
+% 
+% \item[\Uidx{$\!\@comflelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine to put $\arg{flt}$ being a
+% \cwise{} top or bottom float to the tail of \!\@tempboxa! which
+% finally has all top\slash bottom floats in a column.  It is used in
+% \!\pcol@cflt! to apply it to each element of \!\@toplist!.
+% 
+% \item[\Uidx{$\!\@comdblflelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine to put $\arg{flt}$ being a
+% \pwise{} float to the tail of \!\@tempboxa! which finally has the
+% \spanning{} for \pwise{} floats.  It is used in \!\pcol@startpage! to
+% apply to each element of \!\@dbltoplist! to have the \spanning.
+% 
+% \item[\Uidx{\!\@startcolumn!}]
+% is an internal macro for \!\output! routine which tries to build a
+% \fcolumn{} for the floats in \!\@deferlist! and, if the column
+% is not built, tries to move floats to \!\@toplist! and \!\@botlist!.  This
+% macro is used in \!\pcol@output! to process a sneaked \!\output! request
+% from outside of \env{paracol}, and in \!\pcol@output@end! for the case
+% \pwise{} floats are left at \Endparacol{} after which they become
+% \cwise{} ones.
+% 
+% \item[\Uidx{$\!\@tryfcolumn!\arg{lst}$}]
+% is an internal macro for \!\output! routine which examines if a \fcolumn{}
+% or a \fpage{} can be built with some floats in $\arg{lst}$ and, if so,
+% builds the page in \!\@outputbox! removing floats put in the page from
+% $\arg{lst}$.  It is used in \!\pcol@startpage! for \pwise{} floats in
+% \!\@dbldeferlist!, and in \!\pcol@startcolumn! for \cwise{} floats in
+% $\cc_c(\dl)$.
+% 
+% \item[\Uidx{$\!\@scolelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine which examines if a
+% \cwise{} float $\arg{flt}$ can be added to \!\@toplist! or
+% \!\@botlist! being the list of the floats to be put at the top or bottom
+% of a page respectively.  Then, if the examination succeeds, $\arg{flt}$ is
+% added to \!\@toplist! or \!\@botlist!, while it is added to
+% \!\@deferlist! otherwise.  It is used in \!\pcol@trynextcolumn! to
+% apply to each element of (the copy of) $\cc_c(\dl)$.
+% 
+% \item[\Uidx{$\!\@sdblcolelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine which examines if a
+% \pwise{} float $\arg{flt}$ can be added to \!\@dbltoplist! being the
+% list of the floats to be put at the top of a page, and if so, adds
+% $\arg{flt}$ to \!\@dbltoplist!, while it is added to \!\@dbldeferlist! or
+% \!\@deferlist! depending on \LaTeX's version otherwise as discussed in
+% item-(\ref{item:ovv-float-@addtodblcol}) of \secref{sec:imp-ovv-float}.
+% It is used in \!\pcol@startpage! to apply to each element of (the copy of)
+% \!\@dbldeferlist!.
+% 
+% \item[\Uidx{\!\@addmarginpar!}]
+% is an internal macro for \!\output! routine to add a marginal note.  Its
+% original definition is kept in \!\pcol@@addmarginpar! and used in
+% \!\pcol@addmarginpar! being our own \!\@addmarginpar!.
+% 
+% \item[\Uidx{$\!\@makefcolumn!\arg{lst}$}]
+% is an internal macro for \!\output! routine to build a \fcolumn{} with
+% some floats at the head of a float list $\arg{lst}$ and to remove the
+% floats from the list.  It is used in \!\pcol@flushcolumn! and
+% \!\pcol@iflushfloats! for $\cc_c(\dl)$ of \cwise{} floats, and in
+% \!\pcol@output@clear! for \!\@dbldeferlist! of \pwise{} floats.
+% \end{description}
+%
+% 
+% 
+% \subsubsection{Structural Macros}
+% 
+% \begin{description}
+% \item[\Uidx{$\!\@elt!\<a_1\>\cdots\<a_n\>$}]
+% is an internal control sequence to represent a list element having $n$
+% subelements.  The sequence is often made \!\let!-equal to a macro which
+% processes $\<a_1\>\cdots\<a_n\>$ and is applied to all members in a list.
+% It is also made \!\let!-equal to \!\relax! on a manipulation of a list,
+% such as element addition and concatenation, by \!\edef! or \!\xdef!.  The
+% usages of the sequence are as follows.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@F@count! \!\def!ines \!\@elt! as a macro to increment
+% \!\@tempcnta! by one to measure the cardinality of \!\@freelist!.
+% 
+% \item
+% \!\pcol@cflt! lets $\!\@elt!=\!\@comflelt!$ for $\cc_c(\tl)$, and then
+% $\!\@elt!=\!\relax!$ to concatenate \!\@freelist! and $\cc_c(\tl)$.
+% 
+% \item
+% \!\pcol@setpageno! lets $\!\@elt!=\!\pcol@setpnoelt!$ for $\PP$.
+% 
+% \item
+% \!\pcol@setpnoelt! and \!\pcol@setmpbelt! let $\!\@elt!=\!\relax!$ to add
+% $\pp(q)$ to $\PP$.  It also uses \!\@elt! to \!\def!ine \!\pcol@currpage!
+% with $\!\@elt!
+% \Arg{\pp^p(q)}\<\pp^i(q)\>\<\pp^f(q)\>\~\Arg{\pp^s(p)}\Arg{\pp^m(p)}$.
+% 
+% \item
+% \!\pcol@defcurrpage! lets $\!\@elt!=\!\relax!$ to \!\xdef!ine
+% \!\pcol@currpage! with
+% $\!\@elt!\Arg{\pp^p(q)}\<\pp^i(q)\>\<\pp^f(q)\>\Arg{\pp^s(p)}\Arg{\pp^m(p)}$.
+% 
+% \item
+% \!\pcol@nextpage! lets $\!\@elt!=\!\pcol@nextpelt!$ for $\PP$.
+% 
+% \item
+% \!\pcol@getcurrpage! lets $\!\@elt!=\!\pcol@getpelt!$ for $\PPP$.
+% 
+% \item
+% \!\pcol@startpage! lets $\!\@elt!=\!\@sdblcolelt!$ for (the copy of)
+% \!\@dbldeferlist!, and $\!\@elt!=\!\@comdblflelt!$ for \!\@dbltoplist!.  It
+% also lets $\!\@elt!=\!\relax!$ for the concatenation of \!\@dbldeferlist!
+% and \!\@deferlist!, and that of \!\@freelist! and \!\@dbltoplist!.
+% 
+% \item
+% \!\pcol@outputcolumns! lets $\!\@elt!=\!\pcol@outputelt!$ with two arguments
+% for (the copy of) $\PP$.
+% 
+% \item
+% \begin{Sloppy}{2400}%
+% \!\pcol@ioutputelt! \!\def!ines \!\pcol@bg@footnoteheight! and
+% \!\pcol@bg@float~height! with \!\@elt! to let painting macros add elements
+% in them to have the height of the \bground{} regions $\bgr_{\{n,N\}}$ and
+% $\bgr_{\{f,F\}}$ to be painted.
+% \end{Sloppy}
+% 
+% \item
+% \!\pcol@buildcolseprule! lets $\!\@elt!=\!\pcol@buildcselt@S!$ and then
+% $\!\@elt!=\!\pcol@buildcselt!$ for $\pp^s(p)$, and then \!\def!ines
+% \!\pcol@bg@columnheight! with \!\@elt! to add $H'_n$ and $\!\@maxdepth!$
+% or 0 for the \bground{} region $\bgr_{\{c,g\}}^c(n+1)$ where
+% $n=\Abs{\pp^s(p)}$.
+% 
+% \item
+% \!\pcol@buildcselt@S! \!\def!ines \!\pcol@bg@spanningtop! and
+% \!\pcol@bg@spanning~height! with \!\@elt! to define the region
+% $\bgr_S(i)$.
+% 
+% \item
+% \begin{Hfuzz}{0.55pt}
+% \!\pcol@buildcselt! \!\def!ines \!\pcol@bg@columnheight!,
+% \!\pcol@bg@spanningtop! and \!\pcol@bg@spanningheight! with \!\@elt! to
+% define regions $\bgr_{\{c,g\}}^c(i)$ and $\bgr_s(i)$.
+% \end{Hfuzz}
+% 
+% \item
+% $\!\pcol@bg@calculate!\arg{z}\arg{z_0}\Arg{F}$ lets
+% $\!\@elt!=\!\pcol@bg@advance!$ to let $\!\@elt!\arg{f}$ in $F$ do
+% $z\gets z+f$.
+% 
+% \item
+% $\!\pcol@bg@negative!\Arg{F^-}$ lets $\!\@elt!=\!\pcol@bg@nadvance!$ to
+% let $\!\@elt!\arg{f}$ in $F^-$ do $z\gets z-f$, and then lets
+% $\!\@elt!=\!\pcol@bg@advance!$ to go back to addition.
+% 
+% \item
+% \!\pcol@output@start! lets all floats $f$ imported in \!\@dbldeferlist!
+% have depth 0 by \!\def!ining $\!\@elt!\arg{f}$ to do it, \!\edef!ines
+% \!\pcol@bg@textheight! with \!\@elt!  having height-plus-depth of
+% \preenv{} for \bgpaint{} of it, and \!\def!ines $\pp^m(0)$ having one
+% element in $\mpb_L^l$ or $\mpb_L^r$ for \!\@mparbottom! in \preenv{}.
+% 
+% \item
+% \!\pcol@makenormalcol! lets $\!\@elt!=\!\relax!$ to concatenate
+% \!\@freelist! and \!\@midlist!.
+% 
+% \item
+% \!\pcol@trynextcolumn! lets $\!\@elt!=\!\@scolelt!$ for (the copy of)
+% $\cc_c(\dl)$.
+% 
+% \item
+% \!\pcol@setcurrcol! lets $\!\@elt!=\!\relax!$ to \!\xdef!ine $\cc_c$ with
+% $\cc_c(\tl)=\!\@toplist!$, $\cc_c(\ml)=\!\@midlist!$,
+% $\cc_c(\bl)=\!\@botlist!$  and $\cc_c(\dl)=\!\@deferlist!$.
+% 
+% \item
+% \!\pcol@scancst! and \!\pcol@iscancst! let $\!\@elt!=\!\relax!$ to
+% \!\edef!ine the list $M=(m\,\Bar\,\mceltpop_{j,m}\in\cstraw,\;j\geq i)$ for
+% $\mceltpop_{i,*}$, and then the latter \!\def!ines \!\@elt! as a macro with
+% an argument $m$ to examine $m\in M$ for $\mcelt_{i,m}$.
+% 
+% \item
+% \!\pcol@addmarginpar! lets $\!\@elt!=\!\pcol@setmpbelt!$ for $\PPP$.
+% 
+% \item
+% \!\pcol@getmparbottom! lets $\!\@elt!=\!\pcol@getmpbelt!$ for the list
+% $\mpb_{\{L,R\}}^{\{l,r\}}$.  It also lets $\!\@elt!=\!\relax!$ for the
+% addition of $\mpar(h_i,t_i)$ to the list by itself and
+% \!\pcol@getmpbelt!.
+% 
+% \item
+% \!\pcol@mparbottom@zero! has \!\@elt! in its body to have $\mpar(0,0)$ for
+% each $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$ the macro has.
+% 
+% \item
+% $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$ has \!\@elt!
+% in its argument specification, and \!\def!ines \!\reserved@b! with
+% \!\@elt! for $\mpar(t+y,b+y)$.
+% 
+% \item
+% \begingroup\def\,{\mskip0mu plus2mu\relax}
+% $\!\pcol@getmparbottom@last@i!\,
+% \Arg{y}\,\mpar(t_1,b_1)\,\cdots\,\mpar(t_n,b_n)\,\!\@nil!$ at first
+% \!\def!\-ines \!\reserved@b! with \!\@elt! for $\mpar(y,y)$ and then
+% \!\def!ines \!\@elt!  to do it for $\mpar(t_i,b_i)$ for all $i\in[1,n]$.
+% \endgroup
+% 
+% \item
+% \!\pcol@makefcolumn! lets $\!\@elt!=\!\pcol@makefcolelt!$ for (the copy
+% of) $\cc_c(\dl)$ to examine if each float in it can be put in a \fcolumn{}
+% to be built, and then \!\def!ine it to put floats in $\cc_c(\tl)$ into
+% $\cc_c(\vb^b)$.
+% 
+% \item
+% \!\pcol@addflhd! lets $\!\@elt!=\!\pcol@hdflelt!$ for its argument
+% $\cc_c(\tl)$ or $\cc_c(\bl)$, and then $\!\@elt!=\!\relax!$ to give the
+% default.
+% 
+% \item
+% \!\pcol@makeflushedpage! \!\edef!ines \!\pcol@bg@floatheight! with
+% \!\@elt! letting it be \!\relax!.
+% 
+% \item
+% \!\pcol@imakeflushedpage! \!\def!ines \!\pcol@bg@footnoteheight! with
+% \!\@elt!.
+% 
+% \item
+% \!\pcol@output@end! uses \!\@elt! in the argument specification of the
+% \!\def!inition of \!\pcol@do@mpbout@elem!, lets $\!\@elt!=\!\relax!$ to
+% add the \spanning{} of the last page to the head of \!\@dbldeferlist!, and
+% uses it in the body of \!\pcol@bg@textheight! and
+% \!\pcol@bg@footnoteheight! to be \!\def!ined for \bgpaint{} of
+% \Scfnote{}s.
+% 
+% \item
+% \begin{Hfuzz}{0.14pt}%
+% \!\pcol@zparacol! lets $\!\@elt!=\!\pcol@remctrelt!$ for $\CG$,
+% $\!\@elt!=\!\pcol@thectrelt!$ for $\CTL$, $\!\@elt!=\!\pcol@loadctrelt!$
+% for $\Cc_0$, $\!\@elt!=\!\pcol@cmpctrelt!$ for $\CTL$,
+% $\!\@elt!=\!\pcol@defcomelt!$ for \!\pcol@localcommands!, and then
+% $\!\@elt!=\!\relax!$ to give the default.
+% \end{Hfuzz}
+% 
+% \item
+% \!\globalcounter!\marg{ctr} defeines \!\@elt!\marg{\theta} for $\CG$ to
+% check if there is $\theta\in\CG$ such that $\theta=\arg{ctr}$.
+% 
+% \item
+% \!\pcol@localcommands! has the sequence of $\!\@elt!\ARg{com}$ for all
+% \lcommand{}s $|\|\arg{com}$.
+% 
+% \item
+% \!\pcol@gcounters! has \!\@elt!|{page}| as its initial definition.
+% 
+% \item
+% $\!\pcol@removecounter!\arg{\Theta'}\arg{\theta}$ lets
+% $\!\@elt!=\!\pcol@iremctrelt!$ for (the copy of) its argument
+% $\mathit{\Theta}'$ to remove $\theta$ from it.
+% 
+% \item
+% $\!\pcol@sscounters!\arg{elt}$ lets $\!\@elt!=\arg{elt}$, where
+% $\arg{elt}=\!\pcol@storectrelt!$ or $\arg{elt}=\!\pcol@savectrelt!$, for
+% $\CTL$, and then $\!\@elt!=\!\relax!$ to \!\xdef!ine $\Cc_c$.
+% 
+% \item \begingroup\hfuzz1.4pt
+% $\!\pcol@com@synccounter!\<\theta\>$ gives $\!\@elt!\Arg{\theta}$ as the
+% argument of |\pcol@synccounter|.

+% 

+% \SpecialIndex{\pcol@synccounter}

+% \par\endgroup
+% 
+% \item \begingroup\hfuzz0.51pt
+% $\!\pcol@synccounter!\arg{lst}$ lets $\!\@elt!=\!\relax!$ to have the list
+% $\arg{lst}$ in \!\reserved@a! by \!\edef!, $\!\@elt!=\!\pcol@loadctrelt!$
+% for $\CC_c$, and then $\!\@elt!=\!\pcol@syncctrelt!$ for $\arg{lst}$.
+% \par\endgroup
+% 
+% \item
+% $\!\pcol@stepcounter!\<\theta\>$ lets $\!\@elt!=\!\pcol@stpldelt!$ for
+% $\CTL$, $\!\@elt!=|\pcol@|\~|stpclelt|$
+% 

+% \SpecialIndex{\pcol@stpclelt}

+% 

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

+% \SpecialIndex{\pcol@aconlyelt}

+% 

+% for $\T$, and then $\!\@elt!=\!\relax!$ to give the default.
+% 
+% \item
+% \!\pcol@icolumncolor! \!\def!ines $\!\@elt!\arg{\celtshadow_i}$ to apply
+% \!\reset@color! for rewinding and \!\pcol@set@color! for reestablishing
+% to each $\celtshadow_i\in\CSTshadow^c=(\Celtshadow^c,\cstshadow)$
+% by \!\pcol@scancst@shadow!, in which \!\@elt! is explicitly applied to
+% $\Celtshadow^c$ if it is defined and then implicitly done to
+% $\cstshadow=\!\pcol@colorstack@shadow!$.
+% 
+% \item
+% \!\pcol@set@color@push! lets $\!\@elt!=\!\relax!$ to push a color
+% information into $\cstshadow$, with save\slash restore of its original
+% value.
+% 
+% \item
+% \!\resetbackgroundcolor! lets $\!\@elt!=\!\pcol@resetbackgroundcolor!$ to
+% scan \!\pcol@bg@defined! containing $\!\@elt!\Arg{a'_i}$ to let
+% $|\pcol@bg@color|{\cdot}a'_i$ for each of $i$.
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% \end{itemize}
+% 
+% \item[\Uidx{\!\@empty!}]
+% is a macro always having nothing.  Its major usages are to examine if a
+% macro often having a list is empty, and to make such a macro empty.  The
+% following macros use \!\@empty! to examine the emptiness of the objects in
+% parentheses.
+% 

+% \begin{quote}
+% \!\pcol@combinefloats! ($\cc_c(\tl)$, $\cc_c(\bl)$)\\
+% \!\pcol@checkshipped! ($S_c$)\\
+% \!\pcol@startpage! ($\pp(\ptop)$, \!\@dbltoplist!)\\
+% \!\pcol@makenormalcol! (\!\@botlist! in \preenv)\\
+% \!\pcol@getmparbottom! ($\pp^m(p)$)\\
+% \!\pcol@getmparbottom@last! ($\pp^m(\ptop)$)\\
+% \!\pcol@setmpbelt! ($\pp^m(p)$)\\
+% \!\pcol@flushcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\tl)$, $\cc_c(\dl)$)\\
+% \!\pcol@measurecolumn! ($\cc_c(\bl),\cc_c(\dl)$)\\
+% \!\pcol@addflhd! ($\cc_c(\tl)$, $\cc_c(\bl)$)\\
+% \!\pcol@synccolumn! ($\cc_c(\tl)$)\\
+% \!\pcol@makeflushedpage! ($\cc_c(\dl)$)\\
+% \!\pcol@imakeflushedpage! ($\cc_c(\dl)$)\\
+% \!\pcol@iflushfloats! ($\cc_c(\dl)$)\\
+% $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$ ($x'_d$)\\
+% $\!\pcol@setcw@fill!\<f\>\!\fill!$ ($f$)
+% \end{quote}
+% 

+% The following macros use \!\@empty! to empty the objects in parentheses.
+% 

+% \begin{quote}
+% \!\pcol@cflt! ($\cc_c(\tl)$)\\
+% \!\pcol@setpageno! ($\PP$, $\pp(\ptop)$)\\
+% \!\pcol@startpage! ($\cc_c(\dl)$, \!\@dbldeferlist!, \!\@deferlist!,
+% 	\!\@dbltoplist!)\\
+% \!\pcol@trynextcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@output@start! ($\PP$, $\pp(\ptop)$, $\cc_c(\dl)$)\\
+% \!\pcol@makenormalcol! (\!\@midlist! in \preenv)\\
+% \!\pcol@addmarginpar! ($\PP$, $\pp(\ptop)$)\\
+% \!\pcol@getmparbottom! ($\mpb_{\{L,R\}}^{\{l,r\}}$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\dl)$, $\cc_c(\tl)$)\\
+% \!\pcol@makeflushedpage! ($\cc_c(\tl)$)\\
+% \!\pcol@freshpage! ($\PP$, $\pp(\ptop)$)\\
+% \!\pcol@zparacol! (\!\@gtempa!)\\
+% \!\pcol@removecounter!$\<\mathit{\Theta}'\>\Arg{\theta}$
+% ($\mathit{\Theta}'\in\{\CG,\CL\}$)\\
+% \!\pcol@sscounters! ($\Cc_c$)
+% \end{quote}
+% 
+% \item[\Uidx{\!\@currentlabel!}]
+% is an internal macro to have the reference to be associated with the
+% \!\label! following it.  It is defined in \!\pcol@fntextbody! to have the
+% reference to the footnote with \!\@thefnmark!.
+% 
+% \item[\Uidx{\!\ext@figure!}]
+% is an internal macro having ``|lof|'' being the extention of the file for
+% list of figures.  It is used in
+% $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\<cap\>$ to have ``|lof|''
+% when $\arg{type}=|figure|$.
+% 
+% \item[\Uidx{\!\ext@table!}]
+% is an internal macro having ``|lot|'' being the extention of the file for
+% list of tables.  It is used in
+% $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\<cap\>$ to have ``|lot|''
+% when $\arg{type}=|table|$.
+% 
+% \item[\Uidx{\!\@currbox!}]
+% is an internal macro which conventionally has an \!\insert! for floats,
+% etc.  The follwing macros use \!\@currbox! having the objects in
+% parentheses.
+% 

+% \begin{quote}
+% \!\pcol@opcol! ($\cc_c(\vb)$)\\
+% \!\pcol@startpage! ($\pp^i(\ptop)$)\\
+% \!\pcol@ioutputelt! ($\s_c(q)$)\\
+% \!\pcol@output@start! ($\pp^i(0)$, $\cc_c(\vb)$, $\Celt^c$)\\
+% \!\pcol@output@switch! ($\cc_c(\vb)$)\\
+% \!\pcol@restartcolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@igetcurrcol! ($\cc_c(\vb)$)\\
+% \!\pcol@setcurrcol! ($\cc_c(\vb)$)\\
+% \!\pcol@putbackmvl! ($\cc_c(\vb)$)\\
+% \!\pcol@iscancst! ($\Celt^c$)\\
+% \!\pcol@addmarginpar! (left marginal note)\\
+% \!\pcol@flushcolumn! ($\cc_c(\vb), \s_c(q)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@measurecolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@synccolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@imakeflushedpage! ($\cc_c(\vb)$)\\
+% \!\pcol@freshpage! ($\cc_c(\vb)$)\\
+% \!\pcol@output@end! (top float, $\cc_c(\vb)$)\\
+% \!\pcol@end@dblfloat! (\pwise{} float)\\
+% \!\pcol@icolumncolor! ($\Celt^c$)
+% \end{quote}
+% 
+% \item[\Uidx{\!\@marbox!}]
+% is an internal macro which has an \!\insert! for left marginal notes.  It
+% is used in \!\pcol@xympar!.
+% 
+% \item[\Uidx{\!\@currlist!}]
+% is an internal macro which has an list of \!\insert!s for floats and
+% marginal notes given to \!output!.  It is used in \!\pcol@addmarginpar! to
+% get the right marginal note from its head.
+% 
+% \item[\Uidx{\!\@freelist!}]
+% is an internal macro having available \!\insert!s for floats originially,
+% but also \colpage{}s, \spanning{}, footnotes and default column-color in
+% our usage.  Besides the acquisition of an \!\insert! from it shown in the
+% description of \!\@next!, it is used by the following macros to return the
+% the objects in parentheses to \!\@freelist!.
+% 

+% \begin{quote}
+% \!\pcol@cflt! ($\cc_c(\tl)$)\\
+% \!\pcol@startpage! (\!\@dbltoplist!)\\
+% \!\pcol@outputelt! ($\pp^i(q)$)\\
+% \!\pcol@ioutputelt! ($\pp^i(q)$, $\pp^f(q)$, $\s_c(q)$)\\
+% \!\pcol@startcolumn! ($\pp^f(\ptop)$)\\
+% \!\pcol@output@start! ($\cc_0(\vb)$)\\
+% \!\pcol@makenormalcol! (\!\@midlist! in \preenv)\\
+% \!\pcol@restartcolumn! ($\cc_c(\vb)$, $\pp^f(p)$ or $\cc_c(\ft)$)\\
+% \!\pcol@savefootins! ($\pp^f(p)$ or $\cc_c(\ft)$)\\
+% \!\pcol@flushcolumn! ($\cc_c(\ft)$)\\
+% \!\pcol@makefcolpage! ($\cc_c(\tl)$)\\
+% \!\pcol@makeflushedpage! ($\pp^i(\ptop)$, $\pp^f(\ptop)$)\\
+% \!\pcol@imakeflushedpage! ($\cc_c(\ft)$)\\
+% \!\pcol@output@end! ($\pp^f(\ptop)$, $\cc_c(\vb)$, $\Celt^c$)
+% \end{quote}
+% 

+% In addition \!\pcol@F@count! scans its element to have its cardinality.
+% 
+% \item[\Uidx{\!\@nil!}]
+% is an internal control sequence which is conventionally used to terminate
+% a variable length argument.  It is used in the following macros.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@getcurrpinfo! for the invocation of \!\@cdr!.
+% 
+% \item
+% $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$ to capture
+% $t$ and $b$ following the convention in \!\pcol@do@mpb@all@ii!.
+% 
+% \item
+% \begingroup\def\,{\mskip0mu plus2mu\relax}
+% $\!\pcol@getmparbottom@last@i!\,
+% \Arg{y}\,\mpar(t_1,b_1)\,\cdots\,\mpar(t_n,b_n)\,\!\@nil!$ to capture
+% $\mpar(t_i,b_i)$ for all $i\in[1,n]$.
+% \endgroup
+% 
+% \item
+% $\!\pcol@do@mpb@all@i!
+% \Arg{\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$ to terminate the
+% list $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$ in the invocation of
+% \!\pcol@do@mpb@all@ii!.
+% 
+% \item
+% $\!\pcol@do@mpb@all@ii!
+% \Arg{y}\mpar(t_1,b_1)\cdots\mpar(t_n,b_n)\!\@nil!$ to capture
+% $\mpar(t_i,b_i)$ for all $i\in[1,n]$, and then to terminate them
+% passed to \!\pcol@bias@mpbout@i! or \!\pcol@getmparbottom@last!.
+% 
+% \item
+% \!\pcol@setcw@scan! for the invocation of\\\mbox{}\qquad
+% $\!\pcol@setcw@getspec!\<w'_d\>|/|\<g'_d\>|/|\arg{garbage}\~\!\@nil!$.
+% 
+% \item
+% \!\pcol@setcw@getspec@i! for the invocation of\\\mbox{}\qquad
+% $\!\pcol@extract@fil!\<n\>| plus |\<f\>| minus|\arg{garbage}\!\@nil!$\\
+% and thus in the \!\def!inition of it in \!\pcol@def@extract@fil!.
+% 
+% \item
+% \!\pcol@defkw! has \!\@nil! in its argument specification to terminate the
+% argument $0\,|pt|\ |plus|\ 1\,|fil|\ |minus|\ 1\,|fil|$.
+% 
+% \item
+% \!\pcol@extract@fil@i!, \!\pcol@extract@fil@ii! and
+% \!\pcol@extract@fil@iii! have \!\@nil! in their argument specifications as
+% the terminator, and thus \!\@nil! appears in their invocations in
+% \!\pcol@extract@fil!, \!\pcol@extract@fil@i! and \!\pcol@extract@fil@ii!
+% respectively, and in the \!\def!inition of \!\pcol@extract@fil@iii! in
+% \!\pcol@def@extract@fil@iii!.
+% 
+% \item
+% \!\pcol@iadjustfnctr! and \!\pcol@iifootnotetext! to terminate their
+% argument |[|$[|+-|]\meta{disp}$|]| passed to \!\pcol@calcfnctr!.
+% 
+% \item
+% \!\backgroundcolor! and \!\nobackgroundcolor! to terminate their first
+% argument given to \!\pcol@backgroundcolor! so that its descendants
+% \!\pcol@backgroundcolor@x! and \!\pcol@backgroundcolor@z! finally capture
+% everything not processed by their ancestors.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\current@color!}]
+% is an internal macro having color information to be put into |.dvi| as a
+% part of the argument of coloring \!\special!.  It is referred to by
+% \!\pcol@bg@paintregion@i!,
+% \!\pcol@output@start!,
+% \!\pcol@icolumncolor!,
+% \!\pcol@iicolumncolor!, and
+% \!\pcol@set@color@push!,
+% \!\pcol@backgroundcolor@y!.
+% 
+% \item[\Uidx{\!\@dbldeferlist!}]
+% is an internal macro having the list of \pwise{} floats whose page
+% appearance are not yet fixed.  It is scanned and then updated in
+% \!\pcol@startpage! and \!\pcol@output@clear!, while \!\pcol@output@start!
+% lets it have \!\@deferlist! made before \beginparacol, and
+% \!\pcol@output@end! adds \pwise{} floats to be put in the empty
+% \lpage{} to it and then move the whole of the list to \!\@deferlist!.
+% As discussed in \secref{sec:imp-ovv-float}, 2015 or later version of
+% \LaTeX{} no longer uses this list, but we stick with it for \pwise{}
+% floats produced in \env{paracol} environments and thus have its top level
+% definition with empty body in \Paracol.
+% 
+% \item[\Uidx{\!\@dbltoplist!}]
+% is an internal macro having the list of \pwise{} floats which
+% \!\@sdblcolelt! decided to be put in the new page.  The macro
+% \!\pcol@startpage! scans it to put all floats into the page $\ptop$ as its
+% \spanning{} $\pp^i(\ptop)$, and then empties it after returning all floats
+% to \!\@freelist!.
+% 
+% \item[\Uidx{\!\@deferlist!}]
+% is an internal macro having the list of \cwise{} floats whose page
+% appearance are not yet fixed.  It is scanned and then updated in
+% \!\pcol@startcolumn!, \!\pcol@trynextcolumn!, \!\pcol@flushcolumn!,
+% \!\pcol@makefcolumn! and \!\pcol@iflushfloats!, while the following macros
+% also act on it.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@output@start! moves it to \!\@dbldeferlist! because it is created
+% before \beginparacol.
+% 
+% \item
+% \!\pcol@startpage! uses it as the interface with \!\@addtodblcol! of 2015
+% or later version of \LaTeX{} as discussed in
+% item-(\ref{item:ovv-float-@addtodblcol}) of
+% \secref{sec:imp-ovv-float}.
+% 
+% \item
+% \!\pcol@setcurrcol! and \!\pcol@igetcurrcol! saves\slash restores it
+% into/from $\cc_c(\dl)$, respectively.
+% 
+% \item
+% \!\pcol@makefcolelt!$\arg{flt}$ returns $\arg{flt}$ to the list if
+% $\arg{flt}$ cannot be put in the \fcolumn{} which the macro is working on.
+% 
+% \item
+% \!\pcol@measurecolumn! examines its emptiness to let
+% $\CSIndex{ifpcol@dfloats}=\true$ iff not empty.
+% 
+% \item
+% \!\pcol@output@end! lets it have \!\@dbldeferlist! so that it processed as
+% \cwise{} floats after \Endparacol.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@toplist!}]
+% is an internal macro having the list of \cwise{} floats which is
+% decided to be put at the top of the \ccolpage{} by float environments or by
+% \!\pcol@trynextcolumn!.  This list is scanned by \!\pcol@cflt! if its
+% invoker \!\pcol@combinefloats! finds the macro is not empty.  The list is
+% also scanned by \!\pcol@makecol!, \!\pcol@output@switch! and
+% \!\pcol@measurecolumn! using \!\pcol@addflhd! for the measurement of the
+% combined size of top floats, while \!\pcol@setcurrcol! and
+% \!\pcol@igetcurrcol!  saves\slash restores the list into/from $\cc_c(\tl)$
+% respectively.  In addition our macros may add an element or build the
+% entire list in the following two cases.  One case is for a \sync{}ation
+% for which \!\pcol@synccolumn! lets the main vertical list in
+% $\cc_c(\vb^b)$ be a float, namely {\em\mvlfloat} to be added to this list.
+% Another case is for a \fcolumn{} in the \lpage{} for which
+% \!\pcol@makefcolumn! and \!\pcol@makefcolelt! build this list for deferred
+% floats.  In the latter case, the list is scanned by \!\pcol@makefcolpage!
+% invoked from \!\pcol@makefcolumn! itself, \!\pcol@flushcolumn! and
+% \!\pcol@makeflushedpage!.
+% 
+% \item[\Uidx{\!\@botlist!}]
+% is an internal macro having the list of \cwise{} floats which is
+% decided to be put at the bottom of the \ccolpage{} by float environments or
+% by \!\pcol@trynextcolumn!.  The emptiness of this list examined by
+% \!\pcol@combinefloats! to invoke the scanner \!\@cflb! unless empty,
+% by \!\pcol@output@start! to calculate the room for each \colpage{} in the
+% \spage, and by \!\pcol@makenormalcol! to decide whether \!\@makecol! is
+% used or not for building \preenv.  The list is also scanned by
+% \!\pcol@measurecolumn! for the measurement of the combined size of bottom
+% floats, while \!\pcol@setcurrcol! and \!\pcol@igetcurrcol! saves\slash
+% restores the list into/from $\cc_c(\bl)$ respectively.
+% 
+% \item[\Uidx{\!\@midlist!}]
+% is an internal macro having the list of in-text floats which has already
+% been put in the \ccolpage{} but is kept to check the ordering of the
+% succeeding floats.  The list is emptied by \!\pcol@makenormalcol! after
+% returning all elements in it to \!\@freelist!, while \!\pcol@setcurrcol!
+% and \!\pcol@igetcurrcol! saves\slash restores the list into/from
+% $\cc_c(\ml)$ respectively.
+% 
+% \item[\Uidx{\!\f@depth!}]
+% is an internal macro having |1sp| or being \!\let!-equal to \!\z@! to
+% specify the float category, \pwise{} or \cwise{} respectively, which
+% float-related macros work on.  As discussed in
+% item-(\ref{item:ovv-float-@dblfloatplacement}) of
+% \secref{sec:imp-ovv-float}, this feature introduced in 2015 version
+% of \LaTeX{} is nullified in \env{paracol} environments and thus the
+% setting with |1sp| done by \!\@dblfloatplacement! is overriden by
+% \!\pcol@startpage! and \!\pcol@output@clear! when they invoke the macro.
+% 
+% \item[\Uidx{\!\cl@@ckpt!}]
+% is an internal macro having the list of all counters defined by
+% \!\newcounter! and the counter \counter{page}.  The original usage of this
+% macro is to log the values of all counters into |.aux| by \!\include!, but
+% we use it to obatin all counters in \!\pcol@zparacol! and
+% \!\pcol@globalcounter@s!.
+% 
+% \item[$\cs{cl@}{\cdot}\theta$]
+% is an internal macro having the list $\clist(\theta)$ of descendant
+% counters of the counter $\theta$ whose increment by \!\stepcounter! lets
+% them 0.  The macro \!\pcol@remctrelt! moves it to
+% $|\pcol@cl@|{\cdot}\theta$
+% 

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

+% 

+% and re\!\def!ines it to have $\!\pcol@stepcounter!\Arg{\theta}$.
+% 
+% \item[\Uidx{\!\reserved@a!}]
+% is an internal macro for temporary use.  Its usages are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@Fe!, it is used to keep the cardinality of \!\@freelist! in
+% \!\pcol@F@n! to log it by \!\pcol@FF! after \!\pcol@F@n! is let have
+% another measurement result.
+% 
+% \item
+% In $\!\pcol@iLogLevel!\<l\>\arg{name}$, it is used to implement
+% $\!\let!|\|\arg{name}=|\|\arg{name}{\cdot}l'$ where $l'$ is the roman
+% representation of the level $l$.
+% 
+% \item
+% In \!\pcol@setpageno!, it has $\PPP$ so that we update $\PP$ and
+% $\pp(\ptop)$ scanning their original contents.
+% 
+% \item
+% In \!\pcol@getcurrpinfo!, it has $\pp(\ptop)$ so that we give its five
+% components to \!\pcol@getpinfo! as its first five arguments.
+% 
+% \item
+% In \!\@outputpage!, it has a sequence of \bgpaint{} for both left and
+% right \parapag{}es to be shipped out outside \env{paracol} environment.
+% 
+% \item
+% In \!\pcol@outputpage@ev!, it has the expansion result of
+% \!\meaning!\!\yoko! to be compared with \!\reserved@b! having
+% \!\string!\!\yoko! for examining if \!\yoko! is a primitive of underlying
+% \TeX{}.
+% 
+% \item
+% In $\!\pcol@bg@paintregion!\arg{a}\arg{c}$, it is let have
+% $a'=a{\cdot}|@|{\cdot}c$ or $a'=a$, and then referred to by
+% \!\pcol@bg@paintregion@i! to use $|\pcol@bg@color|{\cdot}a'$, and by
+% $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ to use
+% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'$.
+% 

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}

+%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% 
+% \item
+% In \!\pcol@specialoutput!, it is \!\let!-equal to $|\pcol@output@|{\cdot}f$
+% corresponding to $\!\outputpenalty!=|\pcol@op@|{\cdot}f$, or
+% \!\@specialoutput!.
+% 
+% \item
+% In \!\pcol@output@start!, it is let have a \bgpaint{} macro
+% \!\pcol@bg@paintbox! and the definition of a parameter
+% \!\pcol@bg@textheight! for it.
+% 
+% \item
+% In \!\pcol@output@switch!, it is \!\let!-equal to \!\@nobreaktrue! or
+% \!\@nobreakfalse! according to \CSIndex{if@nobreak} in the leaving column
+% to broadcast it to other columns.
+% 
+% \item
+% In \!\pcol@ifempty!$\arg{box}\arg{then}\arg{else}$, it has $\arg{then}$ or
+% $\arg{else}$ according to the emptiness of $\arg{box}$.
+% 
+% \item
+% In \!\pcol@clearcolorstack!, it is \!\def!ined to put an uncoloring
+% \!\special! by \!\reset@color! for its argument $\celt_i$ in
+% \!\pcol@iscancst!.
+% 
+% \item
+% In \!\pcol@restorecst!, it is \!\def!ined to put a coloring \!\special! in
+% its argument $\celt_i$ by \!\unvbox! done in \!\pcol@iscancst!.
+% 
+% \item
+% In \!\pcol@addmarginpar!, at first it is made let equal to 0 or $\CL$
+% according to $c<\CL$ or not.  Then it is let have $\PPP$ to be scanned to
+% find $\pp^m(p)$.
+% 
+% \item
+% In \!\pcol@getmparbottom@i!, it is let have one of
+% $\mpb_{\{L,R\}}^{\{l,r\}}$ according to the side margin which the marginal
+% note to be added goes to, and then it is referred to by
+% \!\pcol@getmparbottom!.
+% 
+% \item
+% In \!\pcol@setmpbelt@i!, it is let have what $\pp^m(p)$ should have after
+% the update of a list of marginal notes in it, and then \!\pcol@setmpbelt!
+% updates $\pp(p)$ with the new $\pp^m(p)$ in the macro.
+% 
+% \item
+% In $\!\pcol@bias@mpbout!\Arg{y}$ and $\!\pcol@getmparbottom@last!\Arg{y}$,
+% it is let have $\!\pcol@bias@mpbout@i!\Arg{y}$ and
+% $\!\pcol@getmparbottom@last@i!\Arg{y}$ respectively, so that they are
+% invoked in \!\pcol@do@mpb@all@ii!.
+% 
+% \item
+% In \!\pcol@makeflushedpage!, it is let have an invocation of
+% \!\pcol@bg@paintbox! for \pwise{} floats in $\pp^i(\ptop)$ together with
+% the condition of the \bgpaint.
+% 
+% \item
+% In \!\pcol@output@end!, it is let have the invocation of
+% \!\pcol@bg@paintbox!  for \bgpaint{} of \Scfnote{}s with the condition to
+% do it and a \!\def!inition of \!\pcol@bg@footnoteheight!.
+% 
+% \item
+% In $\!\pcol@defcomelt!\arg{com}$, it is used to implement
+% $\!\let!|\|\arg{com}=|\pcol@com@|{\cdot}\~\arg{com}$.
+% 
+% \item
+% In \!\pcol@setcolumnwidth!, it is made \!\let!-equal to
+% \!\pcol@setcolwidth@s! or \!\pcol@setcolwidth@r! according to
+% $\!\pcol@columnratioleft!=\!\relax!$ or not.
+% 
+% \item
+% In \!\pcol@setcolwidth@r!, it is used to have the fraction $r_d$ being a
+% comma-seperated list element in its argument $\arg{ratio}$ defined by
+% \!\columnratio! and scanned by a \!\@for! loop.
+% 
+% \item
+% In $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\Arg{spec}$, at first it is let
+% have $\arg{spec}$, then the result of adding `|,|' as many as
+% $\Cto-\Cfrom$ to the tail, and finally each element in the extended
+% $\arg{spec}$ in a \!\@for! loop.
+% 
+% \item
+% In $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$, it is let have
+% $\<x'_d\>$ from which all space tokens are removed.
+% 
+% \item
+% In \!\pcol@setcw@calcfactors!, it is used as a waste bascket to throw away
+% $(\WT-W)/(F\times1\,|pt|)$ calculated by \!\pcol@setcw@calcf!.
+% 
+% \item
+% In $\!\pcol@extract@fil@i!\<n\>|.|\<m{\cdot}\mathit{unit}\>\!\@nil!$, it has
+% $\<n\>|.|\<m{\cdot}\mathit{unit}\>$, and is referred to by
+% \!\pcol@extract@fil@ii!.
+% 
+% \item
+% In \!\globalcounter!\marg{ctr}, it is used to have $\arg{ctr}$ for the
+% \CSIndex{ifx}-comparison with each $\theta\in\CG$.
+% 
+% \item
+% In $\!\pcol@remctrelt!\<\theta\>$, it is used to implement
+% $\!\let!|\pcol@cl@|{\cdot}\theta=|\cl@|{\cdot}\theta$,
+% 

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

+% 
+% \item
+% In $\!\pcol@removecounter!\<\mathit{\Theta}'\>\Arg{\theta}$, it is used to
+% have $\theta$ for the \CSIndex{ifx}-comparison in \!\pcol@iremctrelt!.
+% 
+% \item
+% In $\!\pcol@thectrelt!\<\theta\>$, it is used to implement
+% $\!\let!|\pcol@thectr@|{\cdot}\theta=|\the|{\cdot}\theta$,
+% 

+% \SpecialArrayIndex{\theta}{\pcol@thectr@}\SpecialArrayIndex{\theta}{\the}

+% 

+% and then is made \!\let!-equal to $|\pcol@thectr@|{\cdot}\theta{\cdot}0$.
+% 

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

+% 
+% \item
+% In $\!\pcol@synccounter!\arg{lst}$, it has $\arg{lst}$.
+% 
+% \item
+% In $\!\pcol@setctrelt!\<\theta\>\<\val_c(\theta)\>$, it is made
+% \!\let!-equal to $|\pcol@thectr@|{\cdot}\theta$
+% 

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

+% 

+% or
+% $|\pcol@thectr@|{\cdot}\theta{\cdot}c$.
+% 

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

+% 
+% \item
+% In \!\pcol@switchenv!, it is used to save \!\switchcolumn! which is
+% redefined in the macro, and then to invoke \!\switchcolumn! with the
+% original definition.
+% 
+% \item
+% In \!\pcol@fntext!\marg{text}, it is \!\let!-equal to \!\pcol@fntextother!
+% or \!\pcol@fntext~top! according to the footnote $\arg{text}$ is deferred
+% or not.
+% 
+% \item
+% \begin{Hfuzz}{0.6pt}%
+% In \!\pcol@calcfnctr!$\arg{num}$\!\@nil!, it has the first token of
+% $\arg{num}$ for \CSIndex{ifx}-comparison with `|+|' and `|-|'.
+% \end{Hfuzz}
+% 
+% \item
+% In $\!\pcol@twosided!|[|T|]|$, it is let have each non-space token in $T$
+% given by a \!\@tfor! loop.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\reserved@b!}]
+% is an internal macro for temporary use.  It is used in the following
+% macros to keep a list shown in paraentheses so that we update the list in
+% the scan of list elements. 
+% 

+% \begin{quote}
+% \!\pcol@startpage! (\!\@dbldeferlist!)\\
+% \!\pcol@outputcolumns! ($\PP$)\\
+% \!\pcol@trynextcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@removecounter!$\<\mathit{\Theta}'\>\Arg{\theta}$
+% ($\mathit{\Theta}'\in\{\CG,\CC\}$)
+% \end{quote}
+% 

+% In addition, it is used in the following macros.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@outputpage@ev!, it has the expansion result of
+% \!\string!\!\yoko! to be compared with \!\reserved@a! having
+% \!\meaning!\!\yoko! for examining if \!\yoko! is a primitive of underlying
+% \TeX{}.
+% 
+% \item
+% In \!\pcol@bg@paint@ii!, it has a token in the arguments $K_b$, $K_g$ and
+% $K_c$ of the macro scanned by \!\@tfor!.
+% 
+% \item
+% In \!\pcol@output@switch!, it is \!\let!-equal to |\@afterindenttrue| or
+% |\@after|\~|indentfalse| according to \CSIndex{if@afterindent} in the
+% leaving column to broadcast it to other columns.
+% 
+% \item
+% In \!\pcol@clearcolorstack!, it is \!\def!ined to put an uncoloring
+% \!\special! by \!\reset@color! for its argument $\Celt^c$ in
+% \!\pcol@scancst!.
+% 
+% \item
+% In \!\pcol@restorecst!, it is \!\def!ined to put a coloring \!\special! in
+% its argument $\Celt^c$ by \!\unvcopy! done in \!\pcol@scancst!.
+% 
+% \item
+% In \!\pcol@scancst! and \!\pcol@iscancst!, after the reference for the
+% purposes shown in the two items above, it has
+% $M=(m\,\Bar\,\mceltpop_{j,m}\in\cstraw,\;j\geq i)$ for $\mceltpop_{i,*}$
+% and in the latter is scanned to find $m$ for $\mcelt_{i,m}$ in $M$.
+% 
+% \item
+% In \!\pcol@addmarginpar!, it is made let equal to $\CL$ or $\C$
+% according to $c<\CL$ or not.
+% 
+% \item
+% In $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$, it is
+% let have $\mpar(t+y,b+y)$, and in $\!\pcol@getmparbottom@last@i!
+% \Arg{y}\mpar(t_1,b_1)\cdots\mpar(t_n,b_n)\!\@nil!$ it is let have
+% $\mpar(y,y)$ or $\mpar(t_n,b_n)$, so that they are let be a
+% $\mpb_{\{L,R\}}^{\{l,r\}}$ by \!\pcol@do@mpb@all@ii!.
+% 
+% \item
+% In $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$, it is let have each
+% non-space token in $\<x'_d\>$ to remove space tokens from it.
+% 
+% \item
+% In $\!\pcol@setcw@fill!\<f\>\!\fill!$, it is let have $f$.
+% 
+% \item
+% In $\!\pcol@extract@fil@ii!\arg{unit}\!\@nil!$, it is let have
+% $\arg{unit}$.
+% 
+% \item
+% In \!\globalcounter!$\Arg{\theta}$, it has $\cg_i\in\CG$ for
+% \CSIndex{ifx}-comparison with $\theta$.
+% 
+% \item
+% In $\!\pcol@iremctrelt!\<\mathit{\Theta}'\>\Arg\theta$, it has $\theta$ for
+% \CSIndex{ifx}-comparison with $\theta'$ to be removed from $\CG$ or $\CC$.
+% 
+% \item
+% In \!\pcol@calcfnctr!$\arg{num}$\!\@nil!, it has `|+|' and then `|-|' for
+% \CSIndex{ifx}-comparison with the first token of $\arg{num}$.
+% 
+% \item
+% In \!\pcol@backgroundcolor@ii!, it has \!\pcol@backgroundcolor@x! or
+% \!\pcol@back~groundcolor@z! according that the region of \bgpaint{} and its
+% color is defined or undefined.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\reserved@c!}]
+% is an internal macro for temporary use.  It is used in \!\pcol@startpage!
+% to save \!\@deferlist! in it and then to restore the list from it, and in
+% \!\pcol@iscancst! to have \!\relax! or the macro itself to iterate the
+% macro recursively.
+% 
+% \item[\Uidx{\!\reserved@d!}]
+% is an internal macro for temporary use.  It is used in
+% \!\pcol@iscancst! as a \!\chardef! register to have 0 if $m$ for
+% $\mcelt_{i,m}$ is not in the list
+% $M=(n\,\Bar\,\mceltpop_{j,n}\in\cstraw,\;j\geq i)$, or 1 if found.
+% 
+% \item[\Uidx{\!\@gtempa!}]
+% is an internal macro used as a \!\global!ly modifiable scratchpad.  Its
+% usages are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@ifempty!$\arg{box}\arg{then}\arg{else}$, it has \!\lastpenalty!
+% in a \!\vbox! whose value is examined outside the \!\vbox! for the
+% emptiness check of $\arg{box}$.
+% 
+% \item
+% In \!\pcol@addmarginpar!, it is given to \!\@xnext! as the target to have
+% the second and successive elements of \!\@currlist! which we cannot modify.
+% 
+% \item
+% In \!\pcol@zparacol! and \!\pcol@cmpctrelt!, it has the list of counters
+% to be synchronized.
+% 
+% \item
+% In $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$, it is made
+% \!\@empty! or \!\relax! according to $x'_d$ has \!\fill! or not.
+% 
+% \item
+% In \!\pcol@storectrelt!, \!\pcol@savectrelt! and \!\pcol@sscounters!, it
+% has the new version of $\CC_c$.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+%\iffalse
+%<*paracol>
+%\fi
+% 
+% \section{Register Declaration}
+% \label{sec:imp-decl}
+% 
+% \subsection{\cs{count} Registers}
+% 
+% Here we declare registers and switches.  The first group is for \!\count!
+% registers.
+% 

+% \begin{macro}{\pcol@currcol}
+% \changes{v1.2-1}{2013/05/11}
+%	{Add initialization to 0 after the declaration.}

+% 

+% The register \!\pcol@currcol! has the zero-origin ordinal $c$ of the
+% column which we were in when \!\output! is invoked.  Therefore, for
+% example, in the process of \!\switchcolumn!, the register has $c$ from
+% which we are switching to another column.  The register is initialized to
+% be 0 by \!\pcol@output@start!, and then set to $\!\pcol@nextcol!=d$ by
+% \!\pcol@restartcolumn! to switch to (or stay in) $d$.  Note that these two
+% assignments are \!\global! while other macros may {\em locally} use the
+% register to, for example, scan all columns $c\In0\C$.  Besides two macros
+% above, the following macros refer to the register to know which column we
+% are in (or which column is processed by their invokers).
+% 

+% \begin{quote}\raggedright
+% \!\pcol@Log@iii!,
+% \!\pcol@Log@ii!,
+% \!\pcol@FF!,
+% \!\pcol@makecol!,
+% \!\pcol@opcol!,
+% \!\pcol@bg@columnleft!,
+% \!\pcol@bg@columnwidth!,
+% \!\pcol@bg@columnsep!,
+% \!\pcol@output@switch!,
+% \!\pcol@getcurrcol!,
+% \!\pcol@setcurrcol!,
+% \!\pcol@clearcolorstack!,
+% \!\pcol@restorecolorstack!,
+% \!\pcol@addmarginpar!,
+% \!\pcol@getmparbottom@i!,
+% \!\pcol@setmpbelt@i!,
+% \!\pcol@invokeoutput!\footnote{

+% 

+% Only for logging.},
+% 

+% \!\thecolumn!,
+% \!\pcol@sscounters!,
+% \!\pcol@setctrelt!,
+% \!\pcol@com@switchcolumn!,
+% \!\pcol@switchcol!,
+% \!\pcol@visitallcols!,
+% \!\pcol@aconlyelt!,
+% \!\pcol@flushclear!.
+% \!\pcol@columncolor!,
+% \!\normalcolumncolor!,
+% \!\pcol@icolumncolor!,
+% \end{quote}
+% 

+% Among the macros above, \!\columncolor! and \!\normalcolumncolor! could
+% refer to the register outside \env{paracol} environment and thus before
+% the initialization by \!\pcol@output@start!.  Therefore, the register is
+% also initialized to be 0 after its declaration to assure safe reference.
+% 
+% The following macros use the register for the scan of all $c\In0\C$ by
+% themselves or their invokers.
+% 

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

+% The macros \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! also use
+% the register for scanning but for $\LBRP\Cfrom\Cto$ given by their
+% arguments.
+% 
+% In addition \!\pcol@ccuse!, \!\pcol@ifccdefined! and \!\pcol@ccxdef!
+% refer to the register to have the control sequence
+% $|\pcol@columncolor|\cdot c=\Celtshadow^c$ or
+% $|\pcol@columncolor@box|\cdot c=\Celt^c$ where $c$ is for the current
+% column or for all columns depending on their invokers.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% \end{macro}
+% 

+% \begin{macro}{\pcol@nextcol}
+% The register \!\pcol@nextcol! has the zero-origin ordinal $d$ of the
+% column to which we are switching, or in which we are staying, to be set
+% into \!\pcol@currcol! by \!\pcol@restartcolumn!.  The main usage of the
+% register is to set the switching target in \!\pcol@switchcolumn!, but
+% other macros use it to specify the (temporary) target of
+% \!\pcol@switchcol!; the tallest column in \!\pcol@sync!; 0 in
+% \!\pcol@zparacol!, \!\pcol@sptext! and \!\endparacol!; all in $\LBRP0\C$
+% but $c=\!\pcol@currcol!$ in \!\pcol@visitallcols!; and $c$ in
+% \!\pcol@flushclear! to stay in the current column $c$.  The other user of
+% this register is \!\pcol@invokeoutput! but only for logging.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@ncol}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add initial zero-clearing for safe reference in \cs{@outputpage}
+%	 invokded prior to the first \string\texttt{paracol}.}

+% \begin{macro}{\pcol@ncolleft}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to specify the number of columns in left
+%	 parallel-pages.}

+% 

+% The register \!\pcol@ncol! has the number of columns $\C$ given as the
+% argument of \!\paracol!, whose callee \!\pcol@zparacol! being the sole
+% modifier of the register \!\global!ly assigns $C$ to the register to give
+% safe reference to \!\@outputbox! invoked after a \env{paracol} is closed.
+% In addition for the reference in \!\@outputbox! before the first
+% \env{paracol}, the register is initialized with zero after the declaration.
+% 
+% The following macros refer to the register to scan all columns $c\In0\C$.
+% 

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

+% The register \!\pcol@ncolleft! has $\Uidx\CL$ being the number of columns
+% in the left {\em\Uidx\parapag{}e} if \parapag{}ing is in effect, or have
+% $\C$ otherwise.  Similar to $\C$, the number $\CL$ is given as the
+% optional argument of \!\pcol@zparacol! and is \!\global!ly assigned to the
+% register by the sole modifier \!\pcol@zparacol!, unless the optional
+% arugment is not less than $\C$ which is assigned to $\CL$ if this
+% exception is found.  The reason of the \!\global! assignment and the
+% initial zero-clearing after the declaration is same as that for $C$, i.e.,
+% for the reference in \!\@outputpage! outside \env{paracol}.
+% 
+% The following macros examines if $\Uidx\CL<\C$, i.e., if \parapag{}ing is
+% in effect.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@outputelt!,
+% \!\@outputpage!,
+% \!\pcol@output@start!,
+% \!\pcol@output@flush!,
+% \!\pcol@output@clear!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@flushfloats!,
+% \!\pcol@output@end!,
+% \!\pcol@zparacol!,
+% \end{quote}
+% 

+% \begin{Sloppy}{2350}
+% In the macros listed above, \!\pcol@outputelt!, \!\pcol@makeflushedpage!
+% and \!\pcol@flushfloats! passes $\LBRP0\CL$ and $\LBRP\CL\C$ to their
+% respective callees \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage!  and
+% \!\pcol@iflushfloats! as their argument pair
+% $\LBRP{\Uidx\Cfrom}{\Uidx\Cto}$ to let them work on the left and right
+% \parapag{}es repsectively.  The callees above also pass the pair to
+% \!\pcol@swapcolumn! to swap the scanning order of columns if \cswap{} is
+% in efect.
+% 
+% They also pass the pair to \!\pcol@buildcolseprule! which then passes it
+% to \!\pcol@bg@paintcolumns!  and \!\pcol@bg@paintbox! by binding it to
+% $\LBRP\CBfrom\CBto=\LBRP{\!\pcol@bg@from!}{\~\!\pcol@bg@to!}$ referred to
+% by \!\pcol@bg@paint@i! and its callee \!\pcol@bg@paint@ii! to define the
+% range of columns to be painted is $\LBRP\CBfrom\CBto$.  Similar passing is
+% done by (our own version of) \!\@outputpage!, but it directly uses
+% $\LBRP0\CL$ and $\LBRP\CL\C$ as the sources and the target painting macros
+% are \!\pcol@bg@paintpage!, \!\pcol@bg@@paintpage! and
+% \!\pcol@bg@paintbox!.  Note that $\CBto$ is initialized to be
+% \!\let!-equal to $\C$ because it may be referred to without
+% binding\footnote{

+% 

+% This meaningless reference has no harmful side effects.}.
+% \end{Sloppy}
+% 
+% The macro \!\pcol@addmarginpar! also referes to $\CL$ to know if the
+% column $c$ on which it is working on is in the left or right \parapag{}e,
+% i.e., $c<\CL$ or not, to decide the margin to which a marginal note is put,
+% and to pass $\LBRP0\CL$ or $\LBRP\CL\C$ to \!\pcol@swapcolumn! to
+% calculate the distance to the left or right margin from the column.  The
+% examination of $c<\CL$ is also done in related macros
+% \!\pcol@getmparbottom@i! and \!\pcol@setmpbelt@i!.
+% 
+% Similar column-range specification is done for the argument pair
+% $\LBRP\Cfrom\Cto$ of \!\pcol@setcolumnwidth!  invoked from
+% \!\pcol@zparacol!.  Then the arguments are passed to the callees
+% \!\pcol@setcolwidth@r! or \!\pcol@setcolwidth@s!, the latter of
+% which also passes them to its callee \!\pcol@setcw@scan!, to define the
+% width of columns in $\LBRP\Cfrom\Cto$ and thier separators.
+% 
+% The other references to $\C$ are made by \!\pcol@com@switchcolumn! and
+% \!\pcol@switchcolumn! to examine $c<\C$, to wraparound $\C-1$ to 0 for the
+% former and to complain if $c\geq\C$ for the latter.
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@page}
+% The register \!\pcol@page! has the zero-orgin ordinal $p$ of the page
+% which we are in.  The register is initialized to be 0 not only by
+% \!\pcol@output@start! to give the obvious starting point, but also by
+% \!\pcol@freshpage! for page flushing which clears $\PP=\!\pcol@pages!$ to
+% give us another type of starting point.  Then the register is incremented
+% by \!\pcol@nextpage! to advance one page, by \!\pcol@nextpelt! to skip a
+% \fpage, and by \!\pcol@startpage! for a \fpage{} to be created.  The other
+% type of updates of the register is done by \!\pcol@restartcolumn! which
+% lets $p$ be $\cc_c(\vb^p)$ when we revisit the column $c$ belonging to the
+% page $p$.  Note that, besides these \!\global!  updates,
+% \!\pcol@flushcolumn! locally updates the register to scan
+% $\PP=\!\pcol@pages!$, and \!\pcol@freshpage! also performs local updates
+% but in more weird manner.  Besides the updates discussed above, the
+% macros \!\pcol@Log@iii!, \!\pcol@Log@ii!, \!\pcol@FF!, \!\pcol@makecol!,
+% \!\pcol@opcol!, \!\pcol@setpageno!, \!\pcol@getcurrpage!,
+% \!\pcol@startcolumn!, \!\pcol@output@switch!, \!\pcol@addmarginpar! and
+% \!\pcol@fntext! refer to the register to know which page they are
+% operating on.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@basepage}
+% The register \!\pcol@basepage! has the ordinal $\pbase$ of the \bpage{}
+% being the oldest page not shipped out yet.  The register is initialized to
+% be 0 by \!\pcol@output@start! and \!\pcol@freshpage! together with
+% \!\pcol@page!, and then incremented by \!\pcol@outputelt! when it ships
+% the page $\pbase$ out.  The macros \!\pcol@setpageno!, \!\pcol@nextpage!,
+% \!\pcol@getcurrpage! and \!\pcol@addmarginpar! refer to the register in
+% their scans of $\PP$ or $\PPP$ to know the zero-origin ordinal of the
+% element for the current page $p$ is $p-\pbase$.
+% \end{macro}
+% 

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

+% 

+% The register \!\pcol@toppage! has the ordinal $\ptop$ of the \tpage{}
+% having the most advanced \colpage{}s, or {\em\Uidx\lcolpage{}s} in short.
+% The register is initialized to be 0 by \!\pcol@output@start! and
+% \!\pcol@freshpage! together with \!\pcol@page!, and then let be
+% $p=\!\pcol@page!$ by \!\pcol@startpage! to start a new page $p$.  The
+% macros \!\pcol@makecol!, \!\pcol@opcol!, \!\pcol@startcolumn!,
+% \!\pcol@output@switch! and \!\pcol@restartcolumn!  refer to the register
+% to examine if they are working on a \colpage{} in the \tpage, while
+% \!\pcol@flushcolumn! and \!\pcol@fntext! examines if the \ccolpage{} is
+% behind the \tpage.  The register is also referred to by \!\pcol@Log@iii!,
+% \!\pcol@Log@ii! and \!\pcol@FF! for logging.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@footnotebase}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for page-wise footnotes.}

+% 

+% The register \!\pcol@footnotebase! is let have the value of \!\c@footnote!
+% at the start of a \env{paracol} environment by \!\pcol@zparacol! to give
+% the base value $\Uidx\bf$ for relative numbering of \counter{footnote}
+% done in \!\pcol@calcfnctr! for the starred versions of \!\footnote!,
+% \!\footnotemark! and \!\footnotetext!.  The register is also referred to
+% by \!\endparacol!  to let \!\c@footnote! have $\bf+\nf$ where
+% $\nf=\!\pcol@nfootnotes!$ shown below is the number of footnotes in the
+% \env{paracol} environment to be closed.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@nfootnotes}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for page-wise footnotes.}

+% 

+% The register \!\pcol@nfootnotes! is to accumulate the number of footnotes
+% $\Uidx\nf$ in a \env{paracol} environment.  Therefore, it is zero-cleared
+% by \!\pcol@zparacol!, then incremented by \!\pcol@ifootnote! and
+% \!\pcol@ifootnotemark! for \!\footnote! and \!\footnotemark!, and finally
+% referred to by \!\endparacol! to let $\!\c@footnote!=\bf+\nf$.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@mcid}
+% \changes{v1.24}{2013/07/27}
+%	{Introduced for coloring specified in math mode.}

+% \changes{v1.34}{2018/05/07}
+% 	{Change its meaning and operations with it a little bit according to
+%	 the new text coloring with \cs{insert}.}
+% 

+% The register \!\pcol@mcid! has the number of pushes of
+% \colorstack{} by coloring commands in math mode between two consecutive
+% invocations of \!\output!.  The register is
+% zero-cleared by \!\pcol@output! because we are definitely in the main
+% vertical mode and thus all pops corresponding to pushes in math mode must
+% have been applied to |.tex|'s \colorstack.  Then the register
+% is referred to by \!\pcol@set@color@push! when it is invoked in math mode,
+% to increment it and then examine if it does not exceed the limit
+% \!\pcol@mcpushlimit! to mean the math-mode coloring still can be made.  The
+% macro then uses the value of the register as the identifier of the push
+% operation given to \!\output! through an \!\insert!ion.
+% \end{macro}
+%    \begin{macrocode}
+
+%% Register Declaration
+
+\newcount\pcol@currcol \global\pcol@currcol\z@
+\newcount\pcol@nextcol
+\newcount\pcol@ncol \global\pcol@ncol\z@
+\newcount\pcol@ncolleft \global\pcol@ncolleft\z@
+\newcount\pcol@page
+\newcount\pcol@basepage
+\newcount\pcol@toppage
+\newcount\pcol@footnotebase
+\newcount\pcol@nfootnotes
+\newcount\pcol@mcid
+%    \end{macrocode}
+% 
+% 
+% 
+% \subsection{Switches}
+% 
+% The second declaration group is for switches.
+% 

+% \begin{macro}{\ifpcol@output}
+% \changes{v1.2-7}{2013/05/11}
+% 	{Introduced to solve the \cs{output} request sneaking.}

+% \changes{v1.22}{2013/06/30}
+%	{Add a user \cs{pcol@reset@color@pop} to inhibit uncoloring if
+%	 $\mathit{false}$.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add a user \cs{@outputpage} for parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add a user \cs{@outputpage} for background-painting.}

+% 

+% The switch \CSIndex{ifpcol@output} is $\true$ iff \!\pcol@output@start!
+% which turns the switch $\true$ has been invoked but \!\pcol@output@end!
+% which does $\false$ has not yet.  Then the switch is examined by
+% \!\pcol@output! to detect an \!\output! request sneaked from outside of
+% the \env{paracol} environment.  The other users \!\@outputpage! and
+% \!\pcol@reset@color@pop! examine this switch to know if the macro is
+% invoked inside or outside of \env{paracol} environment, while the macro
+% \!\pcol@output@start!  temporarily turns the switch $\false$ when it ships
+% out a page having \preenv{} only.
+% \end{macro}
+% 
+% \begin{macro}{\ifpcol@nospan}
+% \changes{v1.0}{2011/10/10}
+%	{Renamed from \cs{pcol@textonly}.}

+% 

+% The switch |\ifpcol@nospan| is $\true$ iff a page $p$ does not have
+% \spanning, i.e., $\pp^i(p)=\bot$.  It is set by by
+% \!\pcol@getpinfo! for the examination in \!\pcol@ioutputelt!,
+% \!\pcol@makeflushedpage! and \!\pcol@output@end!.
+% \end{macro}
+% 

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

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{pcol@switchcol} and \cs{pcol@flushclear} to the macros
+%	 turning the switch $\string\mathit{true}$ due to column scanning
+%	 and pre-flushing column height check.}

+% 

+% The switch |\ifpcol@sync| is $\true$ iff \!\pcol@output@switch! is invoked
+% for \sync{}ed \cswitch{} by \!\switchcolumn!|*| or its relative
+% enviroment openers, or \pfcheck{} prior to page flushing or environment
+% closing.  Therefore, the switch is \!\global!ly turned $\true$ by
+% \!\pcol@iswitchcolumn! and \!\pcol@sptext! for the \sync{}ing
+% \cswitch{}ing but then temporarily turned $\false$ by \!\pcol@switchcol!
+% invoked by them for \cscan{}ning and then turned $\true$ again by the
+% macro.  For \pfcheck{}, the macro \!\pcol@flushclear! turns the switch
+% $\true$.  The other macro turns this switch is \!\pcol@output@switch! at
+% the end of which the switch is turned $\false$ to go back to the default
+% state.  The macros examining this switch are \!\pcol@output@switch!,
+% \!\pcol@putbackmvl!, \!\pcol@sync!, \!\pcol@invokeoutput! (for logging) and
+% \!\pcol@switchcol!.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@sptextstart}
+% \changes{v1.3-1}{2013/09/17}
+%	{Introduced to capture the starting point of a spanning text so that
+%	 the text is split from other main vertical list stuff.}

+% \begin{macro}{\ifpcol@sptext}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to restrict the broadcast of \cs{if@nobreak} and
+%	 \cs{everypar} only when a column-switching is accompanied with
+%	 spanning text.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Renamed from \cs{ifpcol@mctext} following the naming convention, and
+%	 move the timing of turning $\string\mathit{true}$ from the end
+%	 of a spanning text to its beginning.}

+% 

+% The switch |\ifpcol@sptextstart| is $\true$ iff \!\pcol@output@switch! is
+% invoked from \!\pcol@sptext! prior to a \mctext.  That is, the switch is
+% \!\global!ly\footnote{

+% 

+% Not necessary to be \cs{global}ly turned but we dare to do that to clearly
+% distinguish that from the local turning in \cs{pcol@putbackmvl}.}
+% 

+% let $\true$ and then $\false$ by \!\pcol@sptext! before and
+% after the invocation of \sync{}ed \!\pcol@switchcol! prior to the
+% \mctext.  Then the switch is examined by \!\pcol@putbackmvl! after
+% the \sync{}ation to save the {\em\Uidx\prespan}, being all stuff in main
+% vertical list prior to the \sync{}ation, so that the \mctext{} is split
+% from the stuff and is captured afterward by \!\pcol@makecol! and/or
+% \!\pcol@output@switch!.  The macro also locally turns the switch
+% $\false$ if it does not follow the \sync{}ation, i.e., its invocation is
+% for \cscan{}ning or is caused by pre-\sync{}ation page break, to do the
+% saving only when it follows the \sync{}ation.  The switch is also examined
+% in \!\pcol@output! to inhibit the warning and forced page break even when
+% $\cc_0(\vb^r)=\!\@colroom!<1.5\!\baselineskip!$, because we may let it have
+% a small value when the \mctext{} starts near the page bottom to capture
+% the text portion in the page by \!\pcol@makecol!.  In addition, it is
+% examined by \!\pcol@switchcol! to invoke $|\pcol@colpream|{\cdot}c$,
+% where $c=-1$ if $\true$ or $c=\!\pcol@currcol!$ otherwise.
+% 

+% \SpecialArrayIndex{c}{\pcol@colpream}
+% 
+% The macro \!\pcol@sptext! then \!\global!ly turns another switch
+% \CSIndex{ifpcol@sptext} $\true$ before putting the \mctext{} into the main
+% vertical list so that \!\pcol@makecol! for the page break in the text and
+% \!\pcol@output@switch! for closing capture the text to place it
+% appropriately especially when \cswap{} is in effect.  Then the switch 
+% is \!\global!ly turned $\false$ by \!\pcol@output@switch! to give the
+% default state after it {\em broadcasts} \CSIndex{if@nobreak},
+% \CSIndex{if@afterindent} and \!\everypar! to all columns.
+% \end{macro}\end{macro}
+% 

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

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{pcol@flushclear} to the macros turning the switch
+%	 $\string\mathit{true}$ due to the pre-flushing column height
+%	 check.}

+% 

+% The switch |\ifpcol@clear| is $\true$ iff \!\pcol@output@switch! is
+% invoked for \pfcheck{}, page flushing or environment closing.  Therefore,
+% the switch is turned $\true$ by \!\pcol@flushclear! in the first case, and
+% by \!\pcol@makeflushedpage! in the latter two.  These two macros also
+% turned the switch $\false$ after the direct\slash indirect invocation of
+% \!\pcol@output@switch! to give the default state.  The switch is examined
+% by \!\pcol@output@switch! and its descendants \!\pcol@sync!,
+% \!\pcol@flushcolumn! and \!\pcol@synccolumn!  for \sync{}ation, and by
+% \!\pcol@invokeoutput!  for logging.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@flush}
+% \changes{v1.2-3}{2013/05/11}
+%	{Introduced to fix the problem with a too-tall page at
+%	 synchronization.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add uses for page-wise footnote functions.}

+% 

+% The switch |\ifpcol@flush| is turned $\true$ by \!\pcol@sync! iff it finds
+% that the page to be \sync{}ed or to be flushed is too tall because the
+% sum of the total height of top floats and main text in a column and that
+% of bottom floats and footnotes in another column is larger than
+% $\pp^h(\ptop)-v^f-\VE$, where $v^f$ is the total heigth-plus-depth of the
+% \Scfnote{}s if $\ptop$ has them or 0 otherwise, and $\VE$ is the amount
+% given by \!\ensurevspace! in \sync{}ation or 0 in flushing.  Then the
+% switch is examined in \!\pcol@sync! itself to restart the tallest column
+% if $\true$, in \!\pcol@putbackmvl! to check if a \mctext{} is really to
+% start, in \!\pcol@switchcol! to have a explicit page break in each column
+% if $\true$, and in \!\pcol@flushclear! also to have a page break if
+% $\true$.  The last examiner \!\pcol@flushclear!  may turn the switch
+% $\true$ when it is invoked from \!\endparacol! if the last page leaves
+% deferred and non-merged \Scfnote{}s for which an explicit page break is
+% also required.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@outputflt}
+% \changes{v1.0}{2011/10/10}
+%	{Renamed from \cs{ifpcol@stopoutput} with the reversal.}

+% 

+% The switch |\ifpcol@outputflt| is used in \!\pcol@outputelt! to know
+% whether a \fpage{} is to be shipped out ($\true$) or not.  The switch is
+% initialized to be $\true$ by \!\pcol@outputcolumns! which invokes
+% \!\pcol@outputelt! for all $\pp(p)\in\PP$.  Then if \!\pcol@outputcolumns! is
+% invoked from \!\pcol@opcol! to ship the oldest page $\pbase$ out, the
+% switch is turned $\false$ when we visit the second non-\fpage.  That is,
+% all \fpage{}s following the first (oldest) page are shipped out but others
+% are not.  On the other hand, if \!\pcol@outputcolumns! is invoked from
+% \!\pcol@sync! to ship out all pages including \fpage{}s in $\PP$, the
+% switch is kept $\true$ throughout all invocations of \!\pcol@outputelt!.
+% \end{macro}
+% 

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

+% \begin{macro}{\ifpcol@lastpagesave}
+% \changes{v1.2-7}{2013/05/11}
+%	{Introduced to fix the bug that \cs{@makecol} and
+%	 \cs{pcol@makefcolumn} in \cs{pcol@flushcolumn} misunderstand that
+%	 non-last pages are last.}
+% 

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

+% \begin{itemize}
+% \item
+% \!\pcol@combinefloats! adds \!\textfloatsep! below bottom floats of each
+% column if any so that the floats are well sepearated from the \postenv.
+% 
+% \item
+% \!\pcol@sync! examines $\VPP$ instead of $\VP$ for the \pfcheck.
+% 
+% \item
+% \!\pcol@makefcolumn! trys to make deferred floats as top floats.
+% 
+% \item
+% \!\pcol@makeflushedpage! builds a short page of $\VPP$ tall, leaves
+% \spanning{} from ship-out if $\VPP=\!\pcol@colht!=-\infty$ so that it
+% becomes a float in \postenv, and leaves \Scfnote{}s untouched if
+% \Mgfnote{} typesetting is in effect.  This macro itself turns this switch
+% $\false$ if $\CSIndex{ifpcol@dfloats}=\true$ to mean one or more columns
+% in the \lpage{} have deferred \cwise{} floats and thus the \lpage{}
+% must be {\em full size}.
+% 
+% \item
+% \!\pcol@imakeflushedpage! leaves the \bground{} of \Scfnote{}s unpainted,
+% and lets the depth of the \lpage{} be 0 in \bgpaint{} and packing of
+% \colpage{}s.
+% \end{itemize}
+% 

+% The switch is initialized to be $\false$ by \!\pcol@zparacol!, then turned
+% $\true$ by \!\endparacol!, and then finally turned $\false$ by
+% \!\pcol@output@end! again for
+% \fpage{}s following the \lpage{} if any.  The macro \!\pcol@flushcolumn!
+% saves the switch into \CSIndex{ifpcol@lastpagesave} then turning it
+% $\false$ during it works on \colpage{}s in non-top and thus non-\lpage{}s
+% to keep \!\@makecol! and \!\pcol@makefcolumn! from misunderstanding the
+% pages are last, and then restore the switch when the macro reaches to the
+% \tpage.  This saving and temporary turning $\false$ is also done in
+% \!\pcol@flushclear! when it forces a page break so that the \!\output!
+% routine working on the broken non-\lpage{} correctly recognizes that.
+% Another temporary turning is made by \!\pcol@makenormalcol! but in reverse
+% to let the switch be $\true$ so that its indirect callee
+% \!\pcol@combinefloats!  puts a vertical skip of \!\textfloatsep! below the
+% bottom floats in \preenv.
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\ifpcol@scfnote}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for page-wise footnote functions.}

+% 

+% The switch \!\ifpcol@scfnote! is turned $\true$ by \!\pcol@fnlayout@p!
+% and \!\pcol@fnlayout@m! (through \!\pcol@fnlayout@p!) to indicate
+% footnotes in all columns are merged and \scfnote, while
+% \!\pcol@fnlayout@c! turns it $\false$ to make footnote typesetting
+% \mcfnote{}, being default as well.  The switch is examined by the
+% following macros to do special operations for \Scfnote{}s if
+% it is $\true$.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! shrinks \!\@colht! and put the stretch\slash shrink
+% factor of \!\skip!\!\footins! at the bottom of the \colpage{} to be built
+% by the macro if the page has footnotes.  If the \colpage{} is in the
+% \tpage{} $\ptop$, the macro also saves \!\footins! into \!\pcol@currfoot!
+% which then will be saved into $\pp^f(\ptop)$ by \!\pcol@startpage!, or
+% \!\footins! is discarded otherwise.
+% 
+% \item
+% \!\pcol@startcolumn!, if it is invoked from \!\pcol@output! to start a
+% \colpage{} in a page $p$, \!\insert!s $\pp^f(p)$ through \!\footins!, and
+% also the deferred footnotes in $\df$ by \!\pcol@deferredfootins!, if
+% $p=\ptop$.
+% 
+% \item
+% \!\pcol@output@switch! saves \!\footins! into $\pp^f(\ptop)$ if the macro
+% is to leave a \colpage{} in the \tpage, or discards it otherwise.
+% 
+% \item
+% \!\pcol@restartcolumn! to restart a \colpage{} in a page $p$ \!\insert!s
+% $\pp^f(p)$ through \!\footins!, and also the deferred footnotes in $\df$
+% by \!\pcol@deferredfootins!, if $p=\ptop$.
+% 
+% \item
+% \!\pcol@sync! examines whether the total height of \Scfnote{}s is too
+% large to let them reside in the page to be synchronized or flushed as a
+% whole.
+% 
+% \item
+% \!\pcol@zparacol! redefines \!\footnoterule! so that it refers to
+% \!\textwidth!  rather than \!\column~width! to determine the width of the
+% rule above footnotes.
+% 
+% \item
+% \!\pcol@fntext! invokes \!\pcol@fntextother! to add the footnote given to
+% it to $\df$ as a deferred footnote if $p<\ptop$.
+% 
+% \item
+% \!\pcol@fntextbody! lets \!\hsize! be \!\textwidth! rather than
+% \!\columnwidth! to typeset the footnote given to it.
+% \end{itemize}
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@mgfnote}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for page-wise footnote functions.}

+% 

+% The switch \!\ifpcol@mgfnote! is turned $\true$ by \!\pcol@fnlayout@m!
+% to indicate footnotes in the \spage{} and \lpage{} of a \env{paracol}
+% environment are merged with those in pre- and \postenv{}, while
+% \!\pcol@fnlayout@p! and \!\pcol@fnlayout@c! turn it $\false$ to
+% put them above\slash below the columns in the starting\slash\lpage{}
+% respectively, being default as well.  The switch is examined by the
+% following macros to do special operations for \mgfnote{} \Scfnote{}s
+% if it is $\true$.
+% 

+% \Index{pre-environment stuff}
+% \Index{starting page}
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makenormalcol! leaves \!\footins! untouched rather than putting it
+% as a part of \preenv.
+% 
+% \item
+% \!\pcol@makeflushedpage! leaves \!\footins! untouched rather than putting it
+% as a part of the \lpage{} of \env{paracol} if it works on the page.
+% 
+% \item
+% \!\endparacol! does not let \!\pcol@flushclear! examine the existence of
+% deferred footnotes in \pfcheck{} for the \lpage.
+% \end{itemize}
+% \end{macro}
+% 

+% \begingroup\let\small\footnotesize
+% \begin{macro}{\ifpcol@fncounteradjustment}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for page-wise footnote functions.}

+% 

+% The switch \!\ifpcol@fncounteradjustment! is turned $\true$ by the API
+% macro \!\fncounter~adjustment!, which is also invoked from
+% \!\pcol@fnlayout@p! and \!\pcol@fnlayout@m! (through \!\pcol@fnlayout@p!),
+% to let $\!\c@footnote!=\bf+\nf$ by \!\endparacol!.  The macro
+% \!\nofncounter~adjustment! turns the switch $\false$ to give the default
+% state.
+% \end{macro}
+% \endgroup
+% 

+% \begin{macro}{\ifpcol@inner}
+% \changes{v1.22}{2013/06/30}
+%	{Introduced to know if we are in a \cs{vbox}.}

+% 

+% The switch \cs{ifpcol@inner} is turned $\false$ by \!\pcol@zparacol! to
+% mean we are outside any \!\vbox!es, while the macro also lets
+% \!\everyvbox! in the \env{paracol} environment has the operation to turn
+% the switch $\true$ so that it is true whenever we are in a \!\vbox!.  The
+% switch is examined by \!\pcol@set@color@push! and \!\pcol@icolumncolor!,
+% the former of which also turns it $\true$ if we are in restricted
+% horizontal mode, to make an \!\output! request for \colorstack{}
+% manipuratoin and, in the former, to reserve the stack popper by
+% \!\aftergroup!, iff the switch is $\false$.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@firstpage}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to know if a spanning stuff is pre-environment one.}

+% 

+% The switch \cs{ifpcol@firstpage} is \!\global!ly turned $\true$ or
+% $\false$ by \!\pcol@output@start! if it captures \preenv{} as a
+% \spanning{} or not because it is too large, respectively.  Then the switch
+% is examined by \!\pcol@ioutputelt! or \!\pcol@makeflushedpage! when they
+% finds a \spanning{} to be combined to the page to be printed so as to
+% paint the \bground{} for the color of \pwise{} floats unless the switch is
+% $\true$ to mean the stuff is pre-environment one rather than floats.  Then
+% \!\pcol@outputelt! or \!\pcol@makeflushedpage! itself \!\global!ly turns
+% the switch $\false$ after printing a page because we no longer have
+% \preenv{} in the \env{paracol} environment we are in.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@havelastpage}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to know if a page to be put has the last page of a
+%	 \string\texttt{paracol} environment.}

+% 

+% The switch \cs{ifpcol@havelastpage} is, after intiailized $\false$,
+% \!\global!ly turned $\true$ by \!\pcol@output@end! if it finds the
+% \lpage{} of the \env{paracol} environment is connected to the \postenv, or
+% $\false$ otherwise.  Then the switch is examined by (our own version of)
+% \!\@outputpage! which paints the \bground{} of the page to be printed iff
+% the switch is $\true$ because a part of the page was prodcued by a
+% \env{paracol} environment.  Then the macro \!\global!ly turns the switch
+% $\false$ because so far \bgpaint{} should be disabled.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@paired}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for parallel-paging which has paired and non-paired mode.}

+% 

+% The switch \cs{ifpcol@paired} is $\true$ if the \parapag{}ed typesetting
+% should be done in {\em\paired} mode in which the pair of left and right
+% \parapag{}es comprises a virtual page, while it is $false$ if
+% \npaired{} to treat the left and right pages as individual ones.
+% Therefore, the switch is \!\global!ly turned $\false$ by \!\pcol@yparacol!
+% when \beginparacol{} has the optional argument for the number of columns
+% in the left \parapag{}e followed by |*|, or turned $\true$
+% otherwise by \!\paracol! for giving default or by \!\pcol@zparacol! if it
+% finds $\CL\geq\C$ to mean \parapag{}ing is not in effect
+% in reality\footnote{

+% 

+% The initialization to let the switch $\false$ is not necessary because it
+% is examined only after the first \cs{paracol} even in the
+% \cs{@outputpage} outside \texttt{paracol} environment, but we dare to do
+% this for the sake of clearity.}.
+% 
+% Then the switch is examined by \!\pcol@setpnoelt! and \!\pcol@startpage!
+% so that, if the switch is $\false$, they let $\page(q)=\page(q-1)+2$ where
+% $\cc_0(\vb^p)<q\leq\ptop$ in the former and $q=\ptop$ in the latter,
+% instead of $\page(q)=\page(q-1)+1$ in the usual $\true$ case, because the
+% left\slash right pair of \parapag{}es is treated as two pages rather than
+% one.
+% 
+% The other macros \!\pcol@ioutputelt!, (our own version of) \!\@outputpage!,
+% \!\pcol@output@start!, \!\pcol@imakeflushedpage!, \!\pcol@iflushfloats! and
+% \!\pcol@output@end! also refer to the switch so that, if $\false$, they
+% temporarily let $\!\c@page!=\page(p)+1$ in building the shipout image of
+% the right component of the \parapag{}e pair of the page $p$ in order to
+% have the appropriate page number parity for the right component.  Among
+% them, \!\@outputpage! has another mode dependant operation, if the switch
+% is $\true$, to decrement \!\c@page! by one before shipping out the right
+% component to cancel the increment in the ship-out process of the left
+% component.  The macro \!\pcol@addmarginpar! also examines the switch to
+% decide the margin for marginal notes in \npaired{} \parapag{}es.  Another
+% examiner \!\pcol@zparacol! lets $\CSIndex{ifpcol@swapcolumn}=\false$
+% only in the \env{paracol} environment to start if the switch is $\true$
+% because \cswap{} is meaningless in \npaired{} \parapag{}ing.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@swapcolumn}
+% \changes{v1.2-4}{2013/05/11}
+%	{Introduced for column-swapping in even pages.}

+% \begin{macro}{\ifpcol@swapmarginpar}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced for marginal-note-swapping in even pages.}

+% \begin{macro}{\ifpcol@bg@swap}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for mirrored backgournd painting for even numbered
+%	 pages.}

+% \begin{macro}{\ifpcol@bg@@swap}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for mirrored backgournd painting for even numbered
+%	 pages.} 

+% 

+% The switch \cs{ifpcol@swapcolumn}, \cs{ifpcol@swapmarginpar} and
+% \cs{ifpcol@bg@swap} specify that, if $\true$, columns, marginal notes,
+% and \bgpaint{} in even numbered pages are swapped, respectively.
+% That is, \cs{ifpcol@swapcolumn} lets columns be put from right to left,
+% \cs{ifpcol@swapmarginpar} lets marginal notes go to the opposite side from
+% that in odd numbered pages, and \cs{ifpcol@bg@swap} makes \bgpaint{}
+% \mirror{}ed.
+% 
+% Besides the initial setting to let them $\false$ \!\global!ly after the
+% declaration, the switches are \!\global!ly turned $\false$ by
+% \!\pcol@twosided! for the cases in which API macro \!\twosided! does not
+% have `|c|', `|m|' or `|b|' in its optional argument respectively, and then
+% \!\global!ly turned $\true$ by $|\pcol@twosided@|{\cdot}k$
+% ($k\in\{|c|,|m|,|b|\}$ )
+% 

+% \SpecialIndex{\pcol@twosided@c}

+% \SpecialIndex{\pcol@twosided@m}

+% \SpecialIndex{\pcol@twosided@b}

+% 

+% which is invoked when the argument contains `|c|', `|m|' or `|b|'
+% respectively, or the API macro does not have the argument at
+% all\footnote{

+% 

+% \cs{ifpcol@swapcolumn} is also turned $\true$ and $\false$ by backward
+% compatible API macros \cs{swapcolumn}\~\texttt{inevenpages} and
+% \cs{noswapcolumninevenpages} respectively.}.
+% 

+% \SpecialIndex{\swapcolumninevenpages}

+% \SpecialIndex{\noswapcolumninevenpages}

+% 

+% The switch \CSIndex{ifpcol@swapcolumn} is also turned $\false$ by
+% \!\pcol@zparacol! but locally if \npaired{} \parapag{}ing is specified
+% because \cswap{} is meaningless in the environment.  Another modifier is (our
+% own version of) \!\@outputpage!, but setting and examining the switch in
+% this macro is also local and is to decide the ship-out order of left and
+% right \parapag{}es.
+% 
+% Besides the local use by \!\@outputpage!, \CSIndex{ifpcol@swapcolumn} is
+% then examined by the following macros to do special operations if it is
+% $\true$ and we are in an even numbered page.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@swapcolumn! to reverse the order of column visiting in
+% \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats!.
+% 
+% \item
+% \!\pcol@shiftspanning! to shift a \mctext{} to the left edge of text area.
+% 
+% \item
+% \!\pcol@bg@paint@ii! to \mirror{} the \bgpaint{} of columns and \csepgap{}s.
+% \end{itemize}
+% 

+% On the other hand, examiners of \CSIndex{ifpcol@swapmarginpar} and
+% \CSIndex{ifpcol@bg@swap} are sole for each, namely \!\pcol@addmarginpar!
+% and \!\pcol@bg@paint@i! respectively.  If each switch is $\true$ and we
+% are in an even numbered page, the former reverses \CSIndex{if@firstcolumn}
+% from the value having been set for non-swapping case, while the latter
+% \mirror{}s the \bgpaint{} of the regions excepting columns and
+% \csepgap{}s.
+% 
+% A related switch \CSIndex{ifpcol@bg@@swap} is let be $\true$ if
+% \CSIndex{ifpcol@swapcolumn} or \cs{ifpcol@bg@}\~\texttt{swap}
+% 

+% \CSINDEX{ifpcol@bg@swap}

+% 

+% is $\true$ and we are working on a even numbered page by
+% \!\pcol@bg@swappage! for \mirror{}ed \bgpaint{} of columns and
+% \csepgap{}s, or other regions respectively, and then examined by
+% \!\pcol@bg@paintregion@i! for \mirror{}ing.
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\ifpcol@bg@painted}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to examine if a set of regions are painted.}

+% 

+% The switch \cs{ifpcol@bg@painted} is \!\global!ly turned $\false$ at the
+% beginning of \!\pcol@bg@paint@i!, and then \!\global!ly turned $\true$ by
+% \!\pcol@bg@paintregion! if it paint the region specified by its argument,
+% i.e., \!\backgroundcolor! for the region is declared.  Then the switch is
+% examined by \!\pcol@bg@paint@i! to combine the painted region with others,
+% by (our own version of) \!\@outputpage! and \!\pcol@outputpage@r! to
+% incorporate painted regions into ship-out image.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@bfbottom}
+% \changes{v1.3-6}{2013/09/17}
+%	{Introduced to know which column-wise footnotes or bottom floats
+%	 are put at the bottom of a column.}

+% 

+% The switch \cs{ifpcol@bfbottom} is $\true$ if \!\@makecol! puts bottom
+% floats at the bottom of a column as done by the macro in \LaTeX's standard
+% implementation, or $\false$ otherwise and thus bottom floats can be
+% followed by footnotes as done in p\LaTeX.  Since we know only p\LaTeX{} is 
+% exceptional, we let the switch $\false$ iff \!\pfmtname! is defined and
+% has |pLaTeX2e| in its body.  The switch is examined by
+% \!\pcol@measurecolumn! to determine which footnotes or bottom floats
+% determine $\DP$ if both of them exist.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@dfloats}
+% \changes{v1.3-6}{2013/09/17}
+%	{Introduced to know if the last page has deferred column-wise floats.}
+% 

+% The switch \cs{ifpcol@dfloats} is $\true$ iff one or more columns (in a
+% \lpage) have deferred \cwise{} floats.  Therefore, it is turned
+% $\false$ by \!\pcol@sync! before it invokes \!\pcol@measurecolumn! which
+% turns it $\true$ when it finds a column $c$ such that
+% $\cc_c(\dl)\neq\emptyset$.  Then the switch is examined by
+% \!\pcol@makeflushedpage! to make a \lpage{} {\em full size}, and by
+% \!\pcol@output@end! to flush these floats.
+% \end{macro}
+%    \begin{macrocode}
+\newif\ifpcol@output \global\pcol@outputfalse
+\newif\ifpcol@nospan
+\newif\ifpcol@sync \pcol@syncfalse
+\newif\ifpcol@sptextstart \pcol@sptextstartfalse
+\newif\ifpcol@sptext \pcol@sptextfalse
+\newif\ifpcol@clear \pcol@clearfalse
+\newif\ifpcol@flush
+\newif\ifpcol@outputflt
+\newif\ifpcol@lastpage
+\newif\ifpcol@lastpagesave
+\newif\ifpcol@scfnote \pcol@scfnotefalse
+\newif\ifpcol@mgfnote \pcol@mgfnotefalse
+\newif\ifpcol@fncounteradjustment \pcol@fncounteradjustmentfalse
+\newif\ifpcol@inner
+\newif\ifpcol@firstpage
+\newif\ifpcol@havelastpage \global\pcol@havelastpagefalse
+\newif\ifpcol@paired \global\pcol@pairedtrue
+\newif\ifpcol@swapcolumn \global\pcol@swapcolumnfalse
+\newif\ifpcol@swapmarginpar \global\pcol@swapmarginparfalse
+\newif\ifpcol@bg@swap \global\pcol@bg@swapfalse
+\newif\ifpcol@bg@@swap
+\newif\ifpcol@bg@painted
+\newif\ifpcol@bfbottom
+\def\reserved@a{pLaTeX2e}
+\ifx\reserved@a\pfmtname \pcol@bfbottomfalse \else \pcol@bfbottomtrue \fi
+\newif\ifpcol@dfloats
+%    \end{macrocode}
+% 
+% 
+% 
+% \subsection{\cs{dimen} and \cs{skip} Registers}
+% 
+% The next declaration group is for six \!\dimen! and one \!\skip!
+% registers.
+% 

+% \begin{macro}{\pcol@prevdepth}
+% The \!\dimen! register \!\pcol@prevdepth! is set to the depth of the last
+% item added to the main vertical list of column $c$ from which we switch to
+% another column $d$, i.e., \!\prevdepth! seen in \!\pcol@invokeoutput!
+% before \!\output! request.  The value of the register is then  set into
+% \!\prevdepth! also by \!\pcol@invokeoutput! after \!\output! for the
+% column $d$.  The value of the register is stored in $\cc_c(\pd)$ by
+% \!\pcol@setcurrcol! and then restored into the register by
+% \!\pcol@igetcurrcol! for the use in \!\pcol@invokeoutput! above and in
+% \!\pcol@measurecolumn!, which may let the register and $\cc_c(\pd)$ have
+% $\infty$ if the \colpage{} $c$ is empty.  The register is also updated by
+% \!\pcol@synccolumn! for empty main vertical list case, and by
+% \!\pcol@output@end!  to be set into \!\prevdepth! for the first vertical
+% item of \postenv.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@colht}
+% The \!\dimen! register \!\pcol@colht! has $\VPP$ being the height of the
+% tallest column in the \lpage{} taking \!\textfloatsep! below bottom floats
+% into account if any.  The register is initialized to be $-\!\maxdimen!$ by
+% \!\pcol@sync! and then is examined and updated in \!\pcol@measurecolumn!
+% to find the tallest column.  Besides the internal use of this exploration,
+% its result is referred to by \!\pcol@sync! as the threshold of \pfcheck,
+% and by \!\pcol@makeflushedpage! through its argument given by
+% \!\pcol@output@end! to know the height of multi-column stuff in the
+% \lpage{}.  The macro \!\pcol@makeflushedpage! also lets the register have
+% 0 if the \lpage{} has nothing but non-\mgfnote{} \Scfnote{}.  The other
+% usage of this register is in \!\pcol@freshpage! to keep the value of
+% \!\@colht! of the page made by \!\flushpage! or \!\clearpage! so that it
+% is given to $\!\@colroom!=\cc_c(\vb^r)$ of each column $c$ in case a
+% column $c'$ s.t.\ $c'<c$ made another page for \fcolumn{}s updating
+% \!\@colht!.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@textfloatsep}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for the bug fix of float space enlargement.}

+% 

+% The \!\dimen! (not \!\skip!) register \!\pcol@textfloatsep! has
+% \!\maxdimen! if a \colpage{} does not have \sync{}ation points, to let top
+% floats are inserted in usual way.  If it has, the register may hold the
+% vertical space amount inserted after top floats in a \colpage{} instead of
+% \!\textfloatsep! so that, if a column only with top floats defines the
+% first \sync{}ation point, the space for floats are extended to the
+% \sync{}ation point.  In this extension case, the register has the amount
+% above biased by 10000\,|pt| to distinguish the case from another case with
+% ordinary top floats in which the register has non-biased \!\textfloatsep!.
+% In addition, if the register is less than \!\maxdimen! including a value
+% equal to \!\textfloatsep!, top floats are packed in a \!\vbox! so that
+% stretch\slash shrink factor of \!\floatsep!  cannot move \sync{}ation
+% points.  After the default setting to be \!\maxdimen! by \!\pcol@zparacol!
+% and \!\pcol@floatplacement!, the value of the register is stored in
+% $\cc_c(\tf)$ by \!\pcol@setcurrcol! and then restored into the register by
+% \!\pcol@igetcurrcol! for the use in \!\pcol@makecol!,
+% \!\pcol@combinefloats!, \!\pcol@cflt!, \!\pcol@output@switch!,
+% \!\pcol@measurecolumn!, \!\pcol@addflhd! and \!\pcol@synccolumn!.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@lrmargin}
+% \changes{v1.2-5}{2013/05/11}
+%	{Introduced to let \cs{linewidth} for each column has the value
+%	 according to $w_c$ and the list-like environment surrounding
+%	 \string\texttt{paracol} envrionment.}

+% \begin{macro}{\pcol@bg@leftmargin}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The \!\dimen! register \!\pcol@lrmargin! is let have
+% $\Uidx\lrm=\!\textwidth!-\!\linewidth!$ by \!\pcol@zparacol!, so that
+% \!\linewidth! for column $c$ is let have $\w_c-\lrm$ by
+% \!\pcol@invokeoutput!, which also sets \!\parshape! if $\lrm>0$.
+% 
+% The other usage of this register is to have the left or right margin for
+% \bgpaint{} in the alias \!\pcol@bg@leftmargin! for strict local use in
+% \!\pcol@bg@paint@i! and its descendent macros for \bgpaint.  That is, the
+% register is aliased as \!\pcol@bg@leftmargin! by \!\pcol@bg@paint@i!, let
+% have left or right margin by \!\pcol@bg@swappage!, and then referred to by
+% \!\pcol@bg@pageleft!.
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pagerim}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to specify the page rim size for backgournd coloring.}

+% 

+% The API \!\dimen! register \!\pagerim! has the size of {\em\Uidx\prim{}s}
+% specified by users.  Since the rims are the area for which \bgpaint{}
+% is inhibited, the register is used in area specification macros
+% \!\pcol@bg@paperwidth!, \!\pcol@bg@paperheight!, \!\pcol@bg@pageleft!  and
+% \!\pcol@bg@pagetop!, in which the register has the negative counterpart of
+% the specified value set by \!\pcol@bg@paint@i!.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@topskip}
+% The \!\skip! register \!\pcol@topskip! keeps the value of \!\topskip! at
+% \beginparacol{} for the ordinary usage of \!\topskip! which may have 0 in
+% the starting and \lpage{} temporarily.  After the initialization by
+% \!\pcol@zparacol!, it is referred to by \!\pcol@getpinfo! for pages without
+% \spanning{} and thus \preenv, by \!\pcol@startpage! to let \!\topskip! and
+% $\pp^t(p)$ has it for non-\spage{} $p$, by \!\pcol@output@start! for the
+% second page if it finds \preenv{} is too large to combine with the
+% multi-column stuff, and by \!\endparacol! to recover \!\topskip! for the
+% pages following the \lpage.
+% \end{macro}
+% 

+% \begin{macro}{\belowfootnoteskip}
+% \changes{v1.35-4}{2018/12/31}
+% 	{Introduced to specify the additional space below the non-merged
+%	 pre-environment footnotes.}

+% 

+% The API \!\skip! register \!\belowfootnoteskip! has the amount of the space
+% added below non-merged \Preenv{} footnotes.  The register is initialized
+% with the default 0\,pt, and then used in \!\pcol@output@start! to measure
+% the room in the first page, and in \!\pcol@combinefootins! to add the
+% space.
+% \end{macro}
+% 

+%    \begin{macrocode}
+\newdimen\pcol@prevdepth
+\newdimen\pcol@colht
+\newdimen\pcol@textfloatsep
+\newdimen\pcol@lrmargin
+\newdimen\pagerim \pagerim\z@
+\newskip\pcol@topskip
+\newskip\belowfootnoteskip \belowfootnoteskip\z@
+%    \end{macrocode}
+% 
+% 
+% 
+% \subsection{\cs{box} Registers}
+% 
+% The next declaration group is for the following \!\box! registers.
+% 

+% \begin{macro}{\pcol@topfnotes}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for page-wise footnote functions.}

+% 

+% The \!\box! register \!\pcol@topfnotes! is the implementation of $\df$ to
+% have the list of deferred footnotes.  The register is made void by
+% \!\pcol@output@start! and then is made grown by \!\pcol@fntextother!  with
+% a deferred footnote added by the macro.  The macro
+% \!\pcol@deferredfootins! invoked from \!\pcol@startcolumn! and
+% \!\pcol@restartcolumn!  tries to \!\insert! the contents of the register
+% through \!\footins! but may keep some of trailing ones in it if the total
+% height of the footnotes is too large, while \!\pcol@output@end! does the
+% \!\insert!ion without height capping.  The macro \!\endparacol! with
+% non-\mgfnote{} \Scfnote{} typesetting also refers to the register to pass
+% it to \!\pcol@flushclear! as its argument so as to make an explicit page
+% break if the register has some deferred footnotes.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@prespan}
+% \changes{v1.3-1}{2013/09/17}
+%	{Introduced to save pre-spanning-text stuff.}

+% 

+% The \!\box! register \!\pcol@prespan! keeps the \prespan{} during a
+% \mctext{} is processed by \TeX{} and our own \!\output! routine.  That is, 
+% the macro \!\pcol@putbackmvl! saves the contents $\cc_0(\vb^b)$ of
+% the column 0 to be restarted into the register instead of putting it back
+% to the main vertical list, or makes the register $\bot$ if the column has
+% nothing, when the restart follows the \sync{}ation with
+% $\CSIndex{ifpcol@sptextstart}=\true$.  Then the contents of the register
+% is put back to the main vertical list together with the box having
+% \mctext{} after its vertical size is registered in the list $\pp^s(p)$ of
+% \mctext{} postions and heights, by \!\pcol@makecol! when the text sees a
+% page break, or by \!\pcol@output@switch! when the text is completed.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@rightpage}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to have the ship-out image of a right parallel-page.}

+% 

+% The \!\box! register \!\pcol@rightpage! is used to build (a part of) the
+% ship-out image of a right \parapag{}e in it.  The macros;
+% 

+% \begin{quote}\raggedright
+% \!\pcol@outputelt!,
+% \!\pcol@ioutputelt!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@flushfloats!,
+% \!\pcol@output@flush!, and
+% \!\pcol@output@clear!
+% \end{quote}
+% 

+% work on the register together with \!\@outputbox! for
+% the left \parapag{}e to pass both of them to (our of version of)
+% \!\@outputpage!.  The macro \!\pcol@output@end! also uses the register to
+% paint the \bground{} of the empty counterpart of non-merged \Scfnote{}s in
+% it, or to make the register $\bot$ when it have an empty \lpage{} but with
+% \spanning{} of \pwise{} floats.  After closing a \env{paracol}
+% environment, the contents of the register 
+% will be shiped out by
+% \!\@outputpage! invoked outside \env{paracol} environment when the
+% \postenv{} sees a page break, or referred to by \!\pcol@output@start! as
+% the \preenv{} in the right \parapag{}e.  This right \preenv{} then will be
+% combined with \colpage{}s in the right \parapag{}e by \!\pcol@ioutputelt!
+% or \!\pcol@imakeflushedpage! for shipping-out, or by
+% the latter indirectly invoked from \!\pcol@output@end!  as the
+% last\Index{last page}{} right \parapag{}e again.  Therefore the \!\setbox!
+% of the register in \!\pcol@output@start!, \!\pcol@makeflushedpage!,
+% \!\pcol@imakeflushedpage! and \!\pcol@output@end!  must be done
+% \!\global!ly\footnote{

+% 

+% The \!\global! setting in \!\pcol@makeflushedpage! and
+% \!\pcol@imakeflushedpage!, together with \!\@outputbox! which does not
+% need \!\global! assignment, is also required by the sake of simplicity in
+% its implementation, incidentally.}.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@colorstack@saved}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced as $\mathit{\Gamma}_s$ to keep the color stack
+%	 $\mathit{\Gamma}^c$ until a column-page of $c$ becomes non-empty.}
+% 

+% The \!\box! register \!\pcol@colorstack@saved! is $\csts$ to keep the
+% \colorctext{} $\CST^c$ of column $c$ until its \ccolpage{} becomes non-empty
+% to avoid that the \colpage{} only has coloring \!\special!s for
+% \colorstack{} establishing and rewinding to let \!\pcol@ifempty! misjudge
+% the \colpage{} is non-empty.  It is let have $\Celt^c$, if defined,
+% and $\cst$ by \!\pcol@savecolorstack! invoked from \!\pcol@startcolumn!
+% and \!\pcol@output@start!, and from \!\pcol@restartcolumn! through
+% \!\pcol@putbackmvl! when we know or find the (re)starting \colpage{} is
+% empty.  The macro \!\pcol@putbackmvl! also makes the \!\box! register
+% $\bot$ when the restarting \colpage{} is not empty and thus the \colpage{}
+% has had coloring \!\special!s for establishing \colorctext{} at its
+% beginning.  Then the register is given to \!\pcol@restorecst! by
+% \!\pcol@clearcst@unvbox! to put leading coloring \!\special!s for
+% establishing of the \colpage{} when we complete it by \!\pcol@opcol!  or
+% leave from it by \!\pcol@output@switch!.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@tempboxa}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to have materials temporarily for column-separatig rule
+%	 drawing or background painting.}

+% \changes{v1.34}{2018/05/07}
+%	{Renamed from \cs{pcol@tempbox} because its relative
+%	 \cs{pcol@tempboxb} is introduced.}
+% \changes{v1.34}{2018/05/07}
+%	{Add ussage in \cs{pcol@scancst} and \cs{pcol@iscancst}.}
+% 

+% The \!\box! register \!\pcol@tempboxa! is used to have stuff temporarily as
+% follows.
+% 

+% \begin{itemize}
+% \item
+% The macro \!\pcol@buildcolseprule! and its callee \!\pcol@buildcselt!
+% builds the \cseprule{} in the register for a page to be shipped out, while
+% its contents is put into each \csepgap{} by \!\pcol@hfil!.
+% 
+% \item
+% In (our own version of) \!\@outputpage!, the register has the \bgpaint{}
+% of the (left parallel-) page,
+% 

+% \Index{parallel-paging}

+% 

+% which is inserted into the ship-out image by its callee
+% \!\pcol@outputpage@l! through \!\everyvbox! and its contents
+% \!\pcol@outputpage@ev!.
+% 
+% \item
+% In \!\pcol@scancst! and its callee \!\pcol@iscancst! to scan $\CSTraw^c$,
+% $\CST^c$ or $\csts$, the sequence of (un)coloring \!\special!s to be put
+% into the main vertical list is build in it.
+% \end{itemize}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@tempboxb}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to extract the top of color stack $\mathit{\Gamma}$,
+%	 $\mathit{\Gamma}_r$ or $\mathit{\Gamma}_s$.}
+% 

+% The \!\box! register \!\pcol@tempboxb! is used in \!\pcol@iscancst!
+% to extract the top (last) element of $\cst$, $\cstraw$ or $\csts$.
+% \end{macro}
+% 

+%    \begin{macrocode}
+\newbox\pcol@topfnotes
+\newbox\pcol@prespan \setbox\pcol@prespan\box\voidb@x
+\newbox\pcol@rightpage \global\setbox\pcol@rightpage\box\voidb@x
+\newbox\pcol@colorstack@saved
+\newbox\pcol@tempboxa
+\newbox\pcol@tempboxb
+%    \end{macrocode}
+% 
+% 
+% 
+% \subsection{\cs{insert} Register Set}
+% \changes{v1.34}{2018/05/07}
+%	{Add \Sec3.6 ``\cs{insert} Register Set'' for \cs{pcol@colorins}.}
+% 
+% The next declaration is for the following \!\insert! register set.
+% 

+% \begin{macro}{\pcol@colorins}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to present text-coloring operations to \cs{output}
+%	 synchronously with column-pages.}
+% 

+% The register set \!\pcol@colorins! is to \!\insert! a \!\vbox! containing a
+% (un)coloring \!\special! for color pushing or popping, or the definition
+% of a new default color of the current column.  In order to make it sure
+% that an \!\insert!ion does not affect \!\pagetotal! and is given to
+% \!\output!  with |\box255| containing the corresponding coloring
+% \!\special! put in the main vertical list, \!\count!\!\pcol@colorins! and
+% \!\skip!\!\pcol@colorins! are let be 0, while \!\dimen!\!\pcol@colorins! is
+% let be \!\maxdimen! to allow a \colpage{} to have vitually infinite number
+% of \!\insert!ions.
+% 
+% The \!\insert!ion is done by \!\pcol@icolumncolor! for a default color
+% definition, \!\pcol@set@color@push! for color pushing, and
+% \!\pcol@reset@color@pop! and \!\pcol@reset@color@mpop! for color popping
+% in non-math and math mode respectrively.  Then \!\insert!ed \!\vbox!es are
+% packed into \!\box!\!\pcol@colorins! and is given to \!\output! as
+% $\cstraw$ to be scanned by \!\pcol@clearcolorstack! to reform it as
+% $\cst$, and then scanned by \!\pcol@restorecolorstack! or saved into
+% $\csts=\!\pcol@colorstack@saved!$ by \!\pcol@savecolorstack!.  The
+% register is also referred to by $\!\pcol@scancst!\arg{box}$ to examine if
+% $\arg{box}$ is this register or \!\pcol@colorstack@saved!, and is made
+% $\bot$ by \!\pcol@output@end! after the final reestablishment of the
+% \colorstack.
+% 

+%    \begin{macrocode}
+\newinsert\pcol@colorins
+\count\pcol@colorins\z@ \skip\pcol@colorins\z@ \dimen\pcol@colorins\maxdimen
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \subsection{\cs{toks} Register}
+% 
+% The last declaration is for the following \!\toks! register.
+% 

+% \begin{macro}{\pcol@everyvbox}
+% \changes{v1.22}{2013/06/30}
+%	{Introduced to keep \cs{everyvbox} work as usual while having
+%	 \cs{pcol@innertrue} in it always.}
+% 

+% The register \!\pcol@everyvbox! acts as \!\everyvbox! in \env{paracol}
+% environments.  That is, by \!\pcol@zparacol!, \!\everyvbox! is made
+% \!\let!-equal to this register so that updates and references of
+% \!\everyvbox! is made to this register, while the real \!\everyvbox! is
+% let have the reference to the register and |\pcol@innertrue| to make
+% $\CSIndex{ifpcol@inner}=\true$ in every \!\vbox!.  Besides
+% \!\pcol@zparacol!, the register is reffered to by
+% \!\pcol@restoreeveryvbox! to examine if it has been \!\global!ly updated,
+% i.e., its contents is not \!\pcol@dummytoken!.
+% \end{macro}
+% 

+%    \begin{macrocode}
+\newtoks\pcol@everyvbox
+
+%    \end{macrocode}
+% 
+% 
+% 
+% \section{Logging Tools}
+% \label{sec:imp-logging}
+% 
+% Prior to the \!\def!initions of macros to implement \textsf{paracol}'s
+% functions, we define a few macros for debug logging.
+% 

+% \begin{macro}{\pcol@ShowBox}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Change \cs{unvcopy} to \cs{copy} to make sure the argument box
+%	 causes overfull if its height is positive and even if it has
+%	 nothing.}

+% \changes{v1.34}{2018/05/07}
+%	{Add messaging {\tt (VOID)} if $\langle b\rangle\EQ\bot$,
+%	 $\cs{vfuzz}\gets0$ to ensure overfull, and \cs{vskip} of 1\,{\tt
+%	 pt} if $\langle b\rangle$'s height is 0 to ensure overfull too.}
+% 

+% The macro $\!\pcol@ShowBox!\arg{b}$ puts a logging \!\message! showing the
+% height, depth and width of the \!\box! (or \!\insert!) register $b$, or
+% ``|(VOID)|'' if $b=\bot$.  Then, if $b\neq\bot$, $b$'s contents is dumped
+% into |.log| file making overfull intentionally by putting $b$ into
+% \!\box!|0| of null height, together with \!\vskip! of 1\,|pt| if $b$'s
+% height is 0, with setting $\!\vfuzz!=0$.
+% \end{macro}
+% 

+% \KeepSpace{13}
+% \begin{macro}{\pcol@LogLevel}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@iLogLevel}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Log}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Log@iii}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Log@ii}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Log@i}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logstart}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logstart@ii}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logstart@i}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logend}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logend@ii}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logend@i}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logfn}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logfn@ii}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% \begin{macro}{\pcol@Logfn@i}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for debugging page-wise footnote functions.}

+% 

+% The macro $\!\pcol@LogLevel!\arg{l_1}\arg{l_2}\arg{l_3}$ defines the
+% detailedness of logging done by logging macros.  It invokes
+% $\!\pcol@iLogLevel!\Arg{l_i}\Arg{cs}$ to let the following $|\|\arg{cs}$
+% be $|\|\arg{cs}|@|\arg{l'_i}$ where $l'_i$ is the \!\romannumeral!
+% representation of $l_i$.
+% 

+% \begin{itemize}
+% \item
+% $\!\pcol@Log!\arg{cs}\Arg{m}\arg{f}$ is to log the contents of the \!\insert!
+% register $f$ containing footnotes which is referred to by the macro
+% $\arg{cs}$ in a context shown by $m$.  The macro \!\pcol@Log@iii!
+% ($l_1=3$) logs the detailed contents of $f$ by \!\pcol@ShowBox!, while
+% \!\pcol@Log@ii! ($l_1=2$) just shows the height of $f$ and \!\pcol@Log@i!
+% ($l_1=1$) does nothing.
+% 
+% \item
+% $\!\pcol@Logstart!\Arg{m}$ and $\!\pcol@Logend!\Arg{m}$ put logging
+% \!\message!s `$|S:|m$' and `$|E:|m$' respectively to show the beginning
+% and end of a procedure in the macro whose name is at the head of $m$, if
+% $l_2=2$ and thus they are \!\let!-equal to \!\pcol@Logstart@ii! and
+% \!\pcol@Logend@ii!.  If $l_2=1$, \!\pcol@Logstart@i! and \!\pcol@Logend@i!
+% do nothing.
+% 
+% \item
+% $\!\pcol@Logfn!\Arg{m}$ puts a logging \!\message! $m$ whose head is the
+% macro name for footnotes whose information such as the ordinal number of
+% the footnote processed by the macro may be shown in $m$ as well, if
+% $l_3=2$ and thus it is \!\let!-equal to \!\pcol@Logfn@ii!.  If $l_3=1$,
+% \!\pcol@Logfn@i! does nothing.
+% \end{itemize}
+% \end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}
+% 

+%    \begin{macrocode}
+%% Logging Tools
+
+\def\pcol@ShowBox#1{%
+  \ifvoid#1\message{(VOID)}%
+  \else
+    \message{(\the\ht#1+\the\dp#1)x(\the\wd#1)}%
+    {\vfuzz\z@ \showboxdepth\@M \showboxbreadth\@M
+     \setbox\z@\vbox to\z@{\ifdim\ht#1=\z@ \vskip1\p@\fi \copy#1}}%
+  \fi}
+\def\pcol@LogLevel#1#2#3{%
+  \pcol@iLogLevel{#1}{pcol@Log}%
+  \pcol@iLogLevel{#2}{pcol@Logstart}%
+  \pcol@iLogLevel{#2}{pcol@Logend}%
+  \pcol@iLogLevel{#3}{pcol@Logfn}}
+\def\pcol@iLogLevel#1#2{%
+  \expandafter\let\expandafter\reserved@a
+    \csname #2@\romannumeral#1\endcsname
+  \expandafter\let\csname #2\endcsname\reserved@a}
+\def\pcol@Log@iii#1#2#3{\message{\string#1{#2%
+    (\number\pcol@page:\number\pcol@currcol/\number\pcol@toppage)}}%
+  \pcol@ShowBox#3\message{end\string#1}}
+\def\pcol@Log@ii#1#2#3{\message{\string#1{#2%
+    (\number\pcol@page:\number\pcol@currcol/\number\pcol@toppage)}=\the\ht#3}}
+\def\pcol@Log@i#1#2#3{}
+\def\pcol@Logstart@ii#1{\message{S\string#1}}
+\def\pcol@Logend@ii#1{\message{E\string#1}}
+\def\pcol@Logstart@i#1{}
+\def\pcol@Logend@i#1{}
+\def\pcol@Logfn@ii#1{\message{\string#1}}
+\def\pcol@Logfn@i#1{}
+\pcol@LogLevel111
+
+%    \end{macrocode}
+% 
+% \begin{macro}{\pcol@F@write}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% \begin{macro}{\pcol@F}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% \begin{macro}{\pcol@FF}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% \begin{macro}{\pcol@F@count}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% \begin{macro}{\pcol@F@n}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% \begin{macro}{\pcol@Fb}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% \begin{macro}{\pcol@Fe}
+% \changes{v1.32-2}{2015/10/10}
+%	{Introduced for debugging memory leak problems.}

+% Another debugging tool is for investigating memory leak problems.  Since
+% \Paracol{} uses \!\insert! registers for various purposes, management
+% operations of them especially that for proper release of them are crusial
+% for the correctness of the implmentation.  A source of toughness in
+% debugging {\em memory leak} caused by missing a release of a register back
+% to \!\@freelist! is that the resulting shortage is revealed long after the
+% leakage to make it hard to find the point of the leakage.
+% 
+% The set of macros is to help such debugging by logging the aquire and
+% release of \!\insert! registers into a file named $\arg{job}|.fls|$
+% associated with \!\pcol@F@write! where $\arg{job}$ is given by
+% \!\jobname!.  After opened when \Paracol{} is loaded, the file is written by
+% $\!\pcol@FF!\Arg{m_a}\Arg{m_b}$ with a line of the following form with
+% text messages $m_a$ and $m_b$, where $p=\!\pcol@page!$,
+% $c=\!\pcol@currcol!$, $\ptop=\!\pcol@toppage!$, $\pi=\page(p)=\!\c@page!$,
+% and $n_b=\!\pcol@F@n!$ is the cardinality of \!\@deferlist! counted by
+% \!\pcol@F@count!.
+% 

+% \begin{itemize}\item[]
+% $\arg{m_a}|(|\arg{p}|:|\arg{c}|/|\arg{\ptop}|:|\arg{\pi}|)=|
+% \arg{n_b}\arg{m_b}$
+% \end{itemize}
+% 

+% The argument $\arg{m_b}$ is empty when $\!\pcol@FF!$ is invoked from
+% $\!\pcol@F!\arg{m_a}$ for snapshot, while
+% $\arg{m_b}=\hbox{`|<=|$\arg{n_b}$'}$ when invoked from
+% $\!\pcol@Fe!\arg{m_a}$ paired by $\!\pcol@Fb!=\!\pcol@F@count!$ by which
+% the cardinality of \!\@freelist! is given to $\arg{n_b}$ through
+% \!\pcol@F@n! and then \!\reserved@a!.  Therefore, by the pair of
+% \!\pcol@Fb! and \!\pcol@Fe!, the consumption or restitution in a series of
+% operations surrounded by the pair is logged in the file.
+% 
+% In the production version, the logging is disabled of course by \!\let!ting
+% \!\pcol@F! and \!\pcol@Fe! be \!\@gobble! and \!\pcol@F! be \!\relax!,
+% while the open of \!\pcol@F@write! is disabled as well by a pair of
+% \cs{iffalse} and \cs{fi}.
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 

+%    \begin{macrocode}
+\iffalse
+\newwrite\pcol@F@write
+\immediate\openout\pcol@F@write\jobname.fls
+\fi
+\def\pcol@F#1{\pcol@FF{#1}{}}
+\def\pcol@FF#1#2{\pcol@F@count
+  \immediate\write\pcol@F@write{#1(\number\pcol@page:\number\pcol@currcol/%
+    \number\pcol@toppage:\number\c@page)=\pcol@F@n #2}}
+\def\pcol@F@count{{\@tempcnta\z@
+    \def\@elt##1{\advance\@tempcnta\@ne}\@freelist
+    \xdef\pcol@F@n{\number\@tempcnta}}}
+\let\pcol@Fb\pcol@F@count
+\def\pcol@Fe#1{{\let\reserved@a\pcol@F@n \pcol@FF{#1}{<=\reserved@a}}}
+\let\pcol@F\@gobble
+\let\pcol@Fb\relax
+\let\pcol@Fe\@gobble
+
+%    \end{macrocode}
+% 
+% 
+% 
+% \section{\cs{output} Routine}
+% \label{sec:imp-output}
+% 
+% \begin{macro}{\pcol@ovf}
+% Before giving the definitions of macros in \!\output! routine, we define
+% the macro \!\pcol@ovf! invoked if \!\@freelist! is empty on an acquision
+% of an \!\insert! by \!\@next! and thus we have to abort the execution by
+% \!\PackageError! with a message notifying the shortage.  The additional
+% help message is \!\@ehb! as in \!\@fltovf!.  This macro is used in
+% \!\pcol@opcol!, \!\pcol@startpage!, \!\pcol@output@start!,
+% \!\pcol@output@switch!, \!\pcol@iscancst!, \!\pcol@savefootins!,
+% \!\pcol@flushcolumn!, \!\pcol@synccolumn!, \!\pcol@output@end! and
+% \!\pcol@icolumncolor!.
+% \end{macro}
+% 

+%    \begin{macrocode}
+%% \output Routine
+
+\def\pcol@ovf{%
+  \PackageError{paracol}{Too many unprocessed columns/floats}\@ehb}
+
+%    \end{macrocode}
+% 
+% \begin{macro}{\pcol@output}
+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add the examination of \cs{ifpcol@output} and \protect\LaTeX's
+%	 original sequence for \cs{output} request sneaked from outside of
+%	 \texttt{paracol} environment.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add the assignment of \cs{@maxdepth} to \cs{maxdepth} to nullify
+%	 the temproary setting done by \cs{@addtobot}.}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add a space after \cs{@opcol} to obey the coding convention.}

+% 

+% The macro \!\pcol@output! is the \Paracol's version of \!\output! which
+% is let have this macro as its sole token by \!\pcol@zparacol!.  The
+% structure of this macro is same as that of \LaTeX's \!\output! but the
+% following replacements are made\footnote{
.
+% 

+% Besides the logging with \cs{pcol@Logstart} and \cs{pcol@Logend}.}.
+% 

+% \begin{itemize}
+% \item
+% $\!\@specialoutput!\to\!\pcol@specialoutput!$ to process \LaTeX's genuine
+% functions including the customized marginal note placement, and \Paracol's
+% own special output functions; starting first page, \colorctext{} management,
+% \cswitch, page flushing with\slash without float flusing, and building the
+% multi-column part of the \lpage.
+% 
+% \item
+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{@makecol} with \cs{pcol@makecol} for a special care for
+% 	 column-pages with synchronization points.}

+% 

+% $\!\@makecol!\to\!\pcol@makecol!$ for a special care for \ccolpage{} having
+% \sync{}ation point and/or \Scfnote{}s.
+% 
+% \item
+% $\!\@opcol!\to\!\pcol@opcol!$ to hold the \ccolpage{} which just has
+% completed.
+% 
+% \item
+% \changes{v1.2-2}{2013/05/11}
+%	{Add an argument \cs{@ne} to \cs{pcol@startcolumn} to distinguish it
+%	 from the invocation in \cs{pcol@freshpage}.}

+% 

+% $\!\@startcolumn!\to\!\pcol@startcolumn!$ to creat a new \colpage{}.  The
+% argument \!\@ne! is to distinguish the invocation in this macro from
+% that in \!\pcol@freshpage! so that the \!\insert!ions of $\pp^f(p)$ and
+% $\df$ are done only when a new \colpage{} is created with ordinary page
+% break.
+% \end{itemize}
+% 

+% \changes{v1.22}{2013/06/30}
+%	{Add reset of \cs{set@color}.}

+% \changes{v1.24}{2013/07/27}
+%	{Add zero-clear of \cs{pcol@mcid}.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Add $\cs{ifpcol@sptextstart}\EQ\string\mathit{false}$ to the
+%	 condition for the warning of too small \cs{vsize}.}

+% 

+% In addition, before we start the main body of \!\output! routine, we add
+% two operations for coloring.  One is to make
+% \!\set@color! \!\let!-equal to \!\pcol@set@color!, i.e, to let it regain
+% its original definition throughout \!\output! routine, because
+% no manipulation of \colorstack{} is necessary\footnote{

+% 

+% Though this operation is not necessary because \cs{everyvbox} should work
+% for any \cs{set@color} because they should be in a \cs{vbox}, we dare to
+% do it for clearity.}.
+% 

+% The other is to zero-clear the counter \!\pcol@mcid! because we are
+% definitely in the main (non-internal) vertical mode and thus all push/pop
+% pairs of the coloring in math mode have been processed.
+% 
+% Further, before we start the sequence for non-special \!\output!  request
+% on page breaks, we examine if $\CSIndex{ifpcol@output}=\true$ to mean
+% \!\pcol@output@start! has already been invoked in order to cope with
+% \!\output! request {\em sneaking}.  This sneaking happens when
+% \beginparacol{} is at a crtical position of page breaking at which the
+% \preenv{} has already exceeds \!\vsize! but \TeX{} cannot make the
+% \!\output! request for the page break at \CSIndex{par} at the beginning of
+% \!\pcol@zparacol! because it sees $\!\penalty!=10000$ due to, e.g., a
+% sectioning command just preceding \beginparacol.  In this case, the
+% request is postponed until \TeX{} see a \!\penalty! less than 10000 and
+% thus it is made with some non-special \!\outputpenalty! greather than
+% $-10000$ when \TeX{} sees the dummy request of $\!\penalty!=-10004$ in
+% \!\pcol@invokeoutput! for \!\pcol@output@start!.  At this timing,
+% \!\pcol@zparacol! has already let \!\output! have \!\pcol@output! of
+% course but the request must be processed by original \!\output! because it
+% is made {\em outside} of the \env{paracol} environment which has just
+% started.  Therefore, if $\CSIndex{ifpcol@output}=\false$, we have to
+% perform the operation sequence as the original \!\output! does.
+% Furthermore, we have to take care of the fact that a few our own settings
+% related to \!\output!  routine has already been made in \!\pcol@zparacol!,
+% namely $\CSIndex{if@twocolumn}=\true$ and
+% $\!\@combinefloats!=\!\pcol@combinefloats!$, which should make the macros
+% in the original sequnce confused especially by the former.  Therefore, we
+% turns $\CSIndex{if@twocolumn}=\false$ and let \!\@combinefloats! have the
+% original definition kept in \!\pcol@@combinefloats!\footnote{

+% 

+% Though we know \cs{pcol@combinefloats} acts exactly as \cs{@combinefloats}
+% because \cs{pcol@zparacol} initializes $\cs{pcol@textfloatsep}=\infty$ and
+% $\cs{ifpcol@lastpage}=\false$.  On the other hand, we don't cancel the
+% re\cs{def}itnition of \cs{footnoterule} because it should be
+% $\cs{textwidth}=\cs{columnwidth}$ outside of \env{paracol} environments.}
+% 

+% temporarily, i.e., only in the group automatically surrounding the
+% invocation of \!\output!.
+% 
+% Another addition is to assign \!\@maxdepth! to \!\maxdepth! in order to
+% nullify the temporary setting to 0 done in \!\@addtobot!.  By this
+% assignment, in \env{paracol} environments \TeX's page builder always
+% refers to the value in \!\@maxdepth!.  Yet another addition is to add
+% $\CSIndex{ifpcol@sptextstart}=\false$ to the condition for the warning of
+% too short \!\vsize!, because a \mctext{} can start near the bottom of a
+% page with a small \!\@colroom! less than $1.5\times\!\baselineskip!$ and
+% thus the warning is unnecessary and inappropriate when
+% $\CSIndex{ifpcol@sptextstart}=\true$.
+% 

+%    \begin{macrocode}
+\def\pcol@output{\let\par\@@par \let\set@color\pcol@set@color
+  \global\pcol@mcid\z@
+  \pcol@Logstart{\pcol@output\number\outputpenalty
+    (\number\c@page:\number\pcol@currcol)}%
+  \ifnum\outputpenalty<-\@M
+    \pcol@specialoutput
+  \else\ifpcol@output
+    \pcol@makecol
+    \pcol@opcol
+    \pcol@startcolumn\@ne
+    \@whilesw\if@fcolmade\fi{\pcol@opcol \pcol@startcolumn\@ne}%
+  \else
+    \@twocolumnfalse \let\@combinefloats\pcol@@combinefloats
+    \@makecol
+    \@opcol
+    \@startcolumn
+    \@whilesw\if@fcolmade\fi{\@opcol \@startcolumn}%
+  \fi\fi
+  \global\maxdepth\@maxdepth
+  \ifnum\outputpenalty>-\@Miv
+    \ifdim\@colroom<1.5\baselineskip
+      \ifdim\@colroom<\textheight
+        \ifpcol@sptextstart
+          \global\vsize\@colroom
+        \else
+          \@latex@warning@no@line{Text page \thepage\space
+                                  contains only floats}%
+          \@emptycol
+        \fi
+      \else
+        \global\vsize\@colroom
+      \fi
+    \else
+      \global\vsize\@colroom
+    \fi
+  \else
+    \global\vsize\maxdimen
+  \fi
+  \pcol@Logend\pcol@output}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Completing Column-Page}
+% \label{sec:imp-opcol}
+% 
+% \begin{macro}{\pcol@@makecol}
+% \changes{v1.2-7}{2013/05/11}
+%	{Introduced to cope with the careless implementaion of \cs{@makecol}
+%	 in p\string\LaTeX.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add an argument $d$ to be assigned to \cs{boxmaxdepth} to let it
+%	 have 0 rather than \cs{@maxdepth} for last page.}

+% 

+% The macro $\!\pcol@@makecol!\<d\>$ is used in \!\pcol@flushcolumn! and
+% \!\pcol@imakeflushedpage! which simply require \LaTeX's original
+% \!\@makecol! to build the ship-out image of a \colpage.  The reason why we
+% need our own version is that a variation of \LaTeX, namely p\LaTeX{} for
+% Japanese, carelessly implements its own \!\@makecol! to make the resulting
+% \!\@outputbox! has a depth larger than \!\@maxdepth! if the \colpage{} has
+% \Mcfnote{}s whose last line is unusually deep.  To cope with the problem,
+% this macro at first invokes \!\@makecol!, and then reshape \!\@outputbox!
+% assigning $d=\!\@maxdepth!$ to \!\boxmaxdepth! to cap its depth, unless
+% this macro is used for the \lpage{} with $d=0$ because depth of the last
+% component of the \!\@outputbox! is incorporated in \!\@colht!.
+% 

+%    \begin{macrocode}
+%% Completing Column-Page
+
+\def\pcol@@makecol#1{\@makecol
+  \setbox\@outputbox\vbox to\@colht{\boxmaxdepth#1\unvbox\@outputbox}}
+%    \end{macrocode}
+% \end{macro}
+% 

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

+% \changes{v1.2-2}{2013/05/11}
+%	{Add save/discard of page-wise footnotes.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Remove unnecessary check of \cs{ifpcol@lastpage} on the
+%	 redefinition of \cs{@textbottom}.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Add a function to capture a broken spanning text, to combine it
+%	 with pre-spanning-text stuff, and to shift it left on
+%	 column-swapping.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add the addition of the element to $\pi^s(p)$ for a broken
+%	 spanning text.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add $\pi^m(p)\EQ\cs{pcol@mparbottom}$ to the argument of
+%	 \cs{pcol@defcurrpage}.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add \cs{@colht} and \cs{relax} as the first and third argument of
+%	 \cs{pcol@shrinkcolbyfn}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Move down the \cs{def}inition of \cs{pcol@currfoot} with $\bot$ to
+%	 place it just before the \cs{ifpcol@scfnote}/\cs{fi} construct to
+%	 make it clear how \cs{pcol@currfoot} is \cs{def}ined.}

+% 

+% The macro \!\pcol@makecol! is invoked solely from \!\pcol@output! to build
+% the shipping image of the \ccolpage{} which just has completed in
+% \!\@outputbox!.  This macro has two additional functions to its original
+% version \!\@makecol!\footnote{

+% 

+% Not \cs{pcol@@makecol} because the depth capping of \cs{@outputbox} is
+% done by \cs{pcol@opcol} when it saves the box into $\cc_c(\vb^b)$.}
+% 

+% invoked in this macro.
+% 
+% First, if $\cc_c(\tf)\neq\infty$ to mean the \colpage{} has \sync{}ation
+% points, \!\@makecol! is invoked with a special \!\def!inition of
+% \!\@textbottom! to put a vertical skip having $1/10000\,|fil|$ as its
+% stretch and shrink.  This modification is to nullify not only finite
+% stretches (as \!\raggedbottom! does) but also finite shrinks possibly
+% inserted just below the last \sync{}ation point to move up the first
+% visible item upward a little bit if active.  Therefore, \!\flushbottom!
+% setting is nullified for \colpage{}s having \sync{}ation points and a
+% small exceess from the bottom of a \colpage{} cannot be absorbed by
+% shrinks but visible at the bottom\footnote{

+% 

+% That is, the author gives higher priority to the perfect alignment of the
+% items following a \sync{}ation point.}.
+% 

+% Note that the original definition of \!\@textbottom! is saved in
+% \Midx{\!\pcol@textbottom!} before the invocation of \!\@makecol! and is
+% restored after that\footnote{

+% 

+% This save/restore cannot be done by a grouping because \!\@makecol! builds
+% \!\@outputbox! by local assignments.}.
+% 
+% Second, if $\CSIndex{pcol@sptext}=\true$ and $c=0$ to mean a \mctext{}
+% encounters a page break, we have the first half (or second or succeeding
+% part if the text lays across three or more pages) of the text in
+% \!\box!|255|.  Therefore, we add an element $\spt(H_n,h_n)$ to the tail of
+% the list of \mctext{}s $\pp^s(\ptop)=\!\pcol@sptextlist!$, where $H_n$ is
+% the height of \prespan{} in \!\pcol@prespan!\footnote{

+% 

+% Since we have a \sync{}ation point before a \mctext{} always, \prespan{}
+% or its sole contents \cs{vbox} has a vertical skip at its tail to make the
+% its depth 0 as discussed in \secref{sec:imp-sout-sync}.}
+% 

+% plus the total height of top floats calculated by \!\pcol@addflhd! with
+% $\cc_c(\tl)=\!\@toplist!$, and $h_n$ is the height-plus-depth of
+% \!\box!|255|.  Note that $H_n$ and $h_n$ are represented in the form of
+% integer and thus we produce them by expansions with \!\number!.
+% 
+% The addition, however, is not made if $h_n=0$ because painting its
+% \bground{} is harmful if an extension is specified to make the region
+% visible, while not painting or drawing a segment of \cseprule{} is very
+% natural.  Note that this $h_n=0$ case includes that in which \!\box!|255|
+% has nothing but its height-plus-depth is non-zero because of discarding
+% leading skips of the \mctext{} as pre-break skips.  This special case is
+% detected by decapsulating \!\box!|255| by \!\unvcopy!  and examining the
+% height-plus-depth of the result\footnote{

+% 

+% We cannot do
+% \cs{setbox}\cs{@cclv}\cs{vbox}\texttt{\Arg{\cs{unvbox}\cs{@cclv}}}
+% because it erases the effect of pre-break skip following some visible
+% material.}.
+% 

+% Also note that the list to be added is always for the \tpage{}, i.e.,
+% $\pp^s(\ptop)$ and thus we get and update it by \!\pcol@getcurrpinfo! and
+% \!\pcol@defcurrpage!, because the \mctext{} immediately follows a
+% \sync{}ation point in $\ptop$.  Then we let \!\box!|255| have the
+% \prespan{} followed by the \mctext{} being the original contents of
+% \!\box!|255|, which may be shifted left by
+% $\WT-w_c=\!\textwidth!-\!\columnwidth!$ by the macro
+% \!\pcol@shiftspanning! if \cswap{} is in effect so that its left edge is
+% aligned to that of the leftmost column, i.e., of the text area.
+% 
+% The third addition is for \Scfnote{}s.  If they are presented in
+% \!\footins!, we shrink \!\@colht! by its height plus depth
+% by \!\pcol@shrinkcolbyfn! and put the stretch and shrink factor of
+% \!\skip!\!\footins! at the bottom of \!\box!|255| by \!\pcol@unvbox@cclv!
+% to {\em remove} footnotes from the \colpage{} but keeping the
+% stretch\slash shrink contribution to the page breaking by their existence.
+% Then we save \!\footins! into a new \!\insert! to be referred to as
+% \!\pcol@currfoot!\footnote{

+% 

+% Not in \cs{pcol@footins} because it is destroyed in \cs{pcol@startpage}
+% just before saving operation into $\pp^f(p)$.}
+% 

+% by \!\pcol@savefootins! if $p=\ptop$ so that it is saved in $\pp^f(p)$ by
+% \!\pcol@startpage! afterward, or simply discard the contents of
+% \!\footins! otherwise because $\pp^f(p)$ has already been fixed.  Note
+% that these saving\slash discarding make \!\footins! void and thus
+% \!\@makecol! will not put footnotes.
+% 
+% On the other hand, if footnote typesetting is \mcfnote{}, \!\footins! is
+% kept unchanged so that its contents will be put by \!\@makecol! if it has
+% something.  As for \!\pcol@currfoot!, it should have its default value
+% $\!\voidb@x!=\bot$ assigned to it beforehand, so that, if $p=\ptop$,
+% \!\pcol@startpage! will make $\pp^f(p)=\bot$ unless \Scfnote{s} are given
+% in \!\footins!.
+% 

+%    \begin{macrocode}
+\def\pcol@makecol{\let\pcol@textbottom\@textbottom
+  \ifdim\pcol@textfloatsep=\maxdimen\else
+    \def\@textbottom{\vskip\z@\@plus.0001fil\@minus.0001fil}\fi
+  \ifpcol@sptext \ifnum\pcol@currcol=\z@
+    \pcol@getcurrpinfo\@tempcnta\@tempdima\@tempskipa
+    \setbox\@tempboxa\vbox{\unvcopy\@cclv}%
+    \@tempdimb\ht\@tempboxa \advance\@tempdimb\dp\@tempboxa
+    \ifdim\@tempdimb>\z@
+      \@tempdimb\ht\@cclv \advance\@tempdimb\dp\@cclv
+      \dimen@\ht\pcol@prespan \pcol@addflhd\@toplist\pcol@textfloatsep
+      \@cons\pcol@sptextlist{{\number\dimen@}{\number\@tempdimb}}%
+    \fi
+    \pcol@defcurrpage{\number\@tempcnta}\pcol@spanning\pcol@footins
+                     {\pcol@sptextlist}{\pcol@mparbottom}%
+    \setbox\@cclv\vbox{\unvbox\pcol@prespan \pcol@shiftspanning\@cclv
+                       \unvbox\@cclv}%
+  \fi\fi
+  \def\pcol@currfoot{\voidb@x}%
+  \ifpcol@scfnote \ifvoid\footins\else
+    \pcol@shrinkcolbyfn\@colht\footins\relax
+    \setbox\@cclv\vbox{\pcol@unvbox@cclv\footins}%
+    \ifnum\pcol@page=\pcol@toppage
+      \pcol@Log\pcol@makecol{save}\footins
+      \pcol@Fb
+      \pcol@savefootins\pcol@currfoot
+      \pcol@Fe{makecol(pagefn)}%
+    \else
+      \pcol@Log\pcol@makecol{discard}\footins
+      \setbox\@tempboxa\box\footins
+    \fi
+  \fi\fi
+  \pcol@Logstart\pcol@makecol
+  \ifvoid\footins\else \pcol@Log\@makecol{put}\footins \fi
+  \@makecol
+  \pcol@Logend\pcol@makecol
+  \let\@textbottom\pcol@textbottom}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \KeepSpace{1}
+% \begin{macro}{\@combinefloats}
+% \begin{macro}{\pcol@combinefloats}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for special float handling in a column-page with
+%	 synchronization points.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Remove the shrink of \cs{textfloatsep} because each column in the last
+%	 page is now made not taller than \cs{@colht} definitely by the
+%	 introduction of the pre-flushing column height check.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add the assignment of \cs{@maxdepth} to \cs{maxdepth} to nullify
+%	 the temproary setting done by \cs{@addtobot}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add special operations for columns having synchronization point to
+%	 move the infinite stretch and shrink to let it follow bottom floats
+%	 ratehr than preceding them.}

+% \begin{macro}{\pcol@@combinefloats}
+% \changes{v1.2-7}{2013/05/11}
+%	{Introduced to solve the \cs{output} request sneaking.}

+% 

+% The macro \!\pcol@combinefloats! being our own version of \!\@combinefloats!
+% is used in \LaTeX's \!\@makecol! because the original and our
+% own are made \!\let!-equal by \!\pcol@zparacol!, and also used in
+% \!\pcol@makenormalcol!  explicitly.  The customization is twofold for both
+% of top and bottom floats.
+% 
+% For the top floats, we invoke the original \!\@cflt! if
+% $\cc_c(\tf)=\infty$ to mean the \colpage{} to be shipped out does not have
+% \sync{}ation points, or otherwise our own \!\pcol@cflt! which we will
+% discuss shortly.  Prior to the invocation of \!\@cflt!, in addition, we
+% let $\!\maxdepth!=\!\@maxdepth!$ so that the macro refers to the value used
+% throughout a \env{paracol} environment instead of that modified by
+% \!\@addtobot! possibly affect the work in \!\@cflt! by the following
+% sequence.
+% 

+% \begin{eqnarray*}
+% \!\pcol@flushcolumn!(c)&\to&\!\pcol@trynextcolumn!\to\cdots\to\!\@addtobot!\\
+% &\to&\!\pcol@flushcolumn!(c{+}k)\to\!\pcol@@makecol!\to\!\@makecol!\\
+% &\to&\!\pcol@combinefloats!\to\!\@cflt!
+% \end{eqnarray*}
+%
+% For the bottom floats, we invoke the original \!\@cflb! always but, if
+% the \colpage{} has \sync{}ation points, we insert vertical skips of
+% $s=0\,|pt|\ |plus|\ 0.0001\,|fil|\ |minus|\ 0.0001\,|fil|$ and $-s$ before
+% and after the invocation respectively.  Since \!\@textbottom! is let have
+% the skip of $s$ by \!\pcol@makecol! for a \colpage{} having \sync{}ation
+% points and is inserted below bottom floats by \!\@makecol!\footnote{

+% 

+% The insertion point is common to \LaTeX{} and p\LaTeX{}.},
+% 

+% the effect of \!\@textbottom! is canceled by the skip of $-s$ but looks
+% moved above bottom floats.  Therefore, if the natural height of the
+% \colpage{} is smaller than \!\@colht!, bottom floats are flushed to the
+% page bottom as if \colpage{} itself is flushed by \!\newpage! etc.  On the
+% other hand, if the natural height is larger, more importantly, all shrinks
+% below the last \sync{}ation point is canceled by the infinite shrink in
+% $s$ above the bottom float but we should have sufficient space for shrinks
+% there thanks to \!\textfloatsep! to avoid the interference between the
+% bottom text and bottom floats.
+% 
+% In addition, if $\CSIndex{ifpcol@lastpage}=\true$ to mean the \colpage{} is
+% in the \lpage{}, we insert \!\textfloatsep! in \!\@outputbox! below the
+% bottom floats so that they are well separated from \postenv.  The switch
+% is also $\true$ in the invocation from \!\pcol@makenormalcol! for
+% \preenv{}, so that the bottom floats in it are well separated from the top
+% of multi-column stuff in the \spage.
+% 
+% On the other hand, the original \!\@combinefloats! saved in
+% \!\pcol@@combinefloats! by \!\pcol@zparacol! is used in \!\pcol@output! to
+% restore the original when it finds \!\output! request sneaking.
+% 

+%    \begin{macrocode}
+\def\pcol@combinefloats{%
+  \global\maxdepth\@maxdepth
+  \ifx\@toplist\@empty\else
+    \ifdim\pcol@textfloatsep=\maxdimen \@cflt \else \pcol@cflt \fi
+  \fi
+  \ifx\@botlist\@empty\else
+    \ifdim\pcol@textfloatsep=\maxdimen \@cflb
+    \else
+      \setbox\@outputbox\vbox{\unvbox\@outputbox
+        \vskip\z@\@plus.0001fil\@minus.0001fil}%
+      \@cflb
+      \setbox\@outputbox\vbox{\unvbox\@outputbox
+        \vskip\z@\@plus-.0001fil\@minus-.0001fil}%
+    \fi
+    \ifpcol@lastpage
+      \setbox\@outputbox\vbox{\box\@outputbox \vskip\textfloatsep}%
+    \fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 

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

+% \changes{v1.2-7}{2013/05/11}
+%	{Replace \cs{maxdepth} with \cs{@maxdepth}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
+%	 \cs{@outputbox} to obey the coding convention.}

+% 

+% The macro \!\pcol@cflt! is invoked solely from \!\pcol@combinefloats! if
+% the \colpage{} for which the macro combines the top floats has
+% \sync{}ation points.  The macro has the same structure as \LaTeX's version
+% \!\@cflt! but has three modifications.  The first one is that the floats
+% are packed in a \!\vbox! rather than listed in \!\@outputbox! to nullify
+% the stretch and shrink of \!\floatsep! to keep the \sync{}ation point from
+% moving by them\footnote{

+% 

+% Maybe unnecessary because of \!\@textbottom! inserted by \!\pcol@makecol!
+% but \ldots}.
+% 

+% The second is that we use \!\@maxdepth! instead of \!\maxdepth! to make it
+% clear we always use the value common throughout a \env{paracol}
+% environment.  The third is that the \!\textfloatsep! is replaced with
+% $\!\pcol@textfloatsep!=\cc_c(\tf)$ (definitely finite) which can have a
+% value different from \!\textfloatsep! when the float space is enlarged for
+% \sync{}ation.  If this enlargement is required, $\cc_c(\tf)$ is biased by
+% 10000\,|pt| and thus is assuredly\footnote{

+% 

+% Though not definitely in theoretical sense.}
+% 

+% larger than 5000\,|pt|.  If so, the insertion of \!\topfigrule! should be
+% inhibited because it has already been inserted by \!\pcol@synccolumn! or
+% there are no real floats but we only have the float for main vertical list
+% prior to the \sync{}ation point, or {\em\Uidx\mvlfloat} in short.
+% 

+%    \begin{macrocode}
+\def\pcol@cflt{%
+  \let\@elt\@comflelt
+  \setbox\@tempboxa\vbox{}%
+  \@toplist
+  \setbox\@outputbox\vbox{%
+    \boxmaxdepth\@maxdepth
+    \box\@tempboxa
+    \vskip-\floatsep
+    \ifdim\pcol@textfloatsep>5000\p@
+      \advance\pcol@textfloatsep-\@M\p@
+    \else
+      \topfigrule
+    \fi
+    \vskip\pcol@textfloatsep
+    \unvbox\@outputbox}%
+  \let\@elt\relax
+  \pcol@Fb
+  \xdef\@freelist{\@freelist\@toplist}%
+  \pcol@Fe{cflt}%
+  \global\let\@toplist\@empty}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@opcol}
+% \changes{v1.0}{2011/10/10}
+%	{Remove unnecessary assignment of \cs{@colht}.}

+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}

+% \changes{v1.2-1}{2013/05/11}
+%	{Add \cs{pcol@clearcst@unvbox} to add coloring \cs{special}s at the
+%	 top and bottom of the column-page to be shipped out, together with
+%	 the setting $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Rename \cs{pcol@outputpage} as \cs{pcol@outputcolumns}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
+%	 \cs{@currbox} to obey the coding convention.}

+% 

+% The macro \!\pcol@opcol! is invoked from \!\pcol@output! for the ordinary
+% completed \colpage{} built by \!\pcol@makecol!, or from the loop creating
+% \fcolumn{}s in \!\pcol@output! or \!\pcol@freshpage!.  At first it
+% saves the \colpage{} of column $c$ in \!\@outputbox!, which
+% \!\pcol@makecol! or \!\@tryfcolumn! just has built for an ordinary or
+% \fcolumn{} respectively, in an \!\insert! acquired from \!\@freelist! by
+% \!\@next!, and then adds it to the tail of $\S_c=|\pcol@shipped|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@shipped}
+% 

+% by \!\@cons!.  In this saving operation, we add the sequence of uncoloring
+% \!\special!s at the bottom to clear \colorstack{} by
+% \!\pcol@clearcst@unvbox! giving it \!\@outputbox! to be \!\unvbox!ed and
+% possibly coloring \!\special!s for the \colpage{}'s \colorctext{} saved in
+% $\csts$ at the top, so that the succeeding \colpage{} in printing order
+% starts with its own \colorctext.  For this addition, furthermore, we let
+% $\!\boxmaxdepth!=\!\@maxdepth!$ to keep the depth capping made in the box
+% builder from nullified\footnote{

+% 

+% Or to apply the capping dropped from p\LaTeX's \cs{@makecol}, or to do
+% nothing for the box made by \cs{@tryfcolumn} and thus being 0 deep.}.
+% 
+% Then if $c=0$, we fix the page number of the page $p$ having the
+% \colpage{} and let $\pp^p(q)$ have $\page(p)+(q-p)$ usually but possibly
+% $\page(p)+2(q-p)$ with \npaired{} \parapag{}ing, for all
+% $q\in[p{+1},\ptop]$ by \!\pcol@setpageno!.  After that, we invoke
+% \!\pcol@nextpage! to let $p=p'$ for the next \colpage{} of $c$, where
+% $p'=p+1$ usually but can be $p+k+1$ if we have consecutive $k$ \fpage{}s
+% from $p+1$.
+% 
+% Next, we check if the oldest page $\pbase$ is made ready to be shipped out
+% by the participation of the completed \colpage{} by \!\pcol@checkshipped!.
+% If so, we invoke \!\pcol@outputcolumns! giving argument 0 to ship out
+% $\pbase$ and its successor \fpage{}s.
+% 
+% Finally we set up the next page $p$ by \!\pcol@startpage! if $p>\ptop$
+% meaning it is new one, or by \!\pcol@getcurrpage! otherwise, and
+% reinitialize parameters for floats by \!\pcol@floatplacement! before
+% returning to the invoker.
+% 

+%    \begin{macrocode}
+\def\pcol@opcol{%
+  \pcol@Fb
+  \@next\@currbox\@freelist{\global\setbox\@currbox\vbox to\@colht{%
+      \boxmaxdepth\@maxdepth
+      \pcol@clearcst@unvbox\@outputbox}}\pcol@ovf
+  \pcol@Fe{opcol}%
+  \expandafter\@cons\csname pcol@shipped\number\pcol@currcol\endcsname\@currbox
+  \ifnum\pcol@currcol=\z@ \pcol@setpageno \fi
+  \pcol@nextpage
+  \pcol@checkshipped
+  \if@tempswa \pcol@outputcolumns\z@ \fi
+  \ifnum\pcol@page>\pcol@toppage \pcol@startpage
+  \else                          \pcol@getcurrpage
+  \fi
+  \pcol@floatplacement}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@setpageno}
+% \changes{v1.33-2}{2016/11/19}
+% 	{Add \cs{let}\cs{@elt}\cs{relax} before \cs{edef} of \cs{reserved@a}
+%	 for the sake of clarity.}

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

+% \changes{v1.2-2}{2013/05/11}
+%	{Completely recode reflecting the redesign of page context.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add an operation to increment $\string\mathit{page}(p)$ by two for
+%	 non-paired parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
+%	 invoker \cs{pcol@makecol}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^m(p)$.}

+% 

+% The macro \!\pcol@setpageno! is invoked from \!\pcol@opcol! when it
+% proceeses the \colpage{} of the first column $c=0$ to fix the page number
+% $\page(p)\gets\counter{page}=\!\c@page!$ of the page $p=\!\pcol@page!$
+% having the \colpage{}.  It is also invoked from \!\pcol@output@switch!
+% when it leaves from the first column to reflect a jump of \counter{page}
+% made in the column building.  In both cases, the macro lets $\pp^p(q)$
+% have $\page'(q)=\page(p)+(q-p)$, except for the case of \npaired{}
+% \parapag{}ing in which $\page'(q)=\page(p)+2(q-p)$ instead, for all
+% $q\in[p,\ptop]$.
+% 
+% Since we possibly have to update $\pp(q)$ such that $q\geq p$, at first we
+% temporarily let
+% $\Uidx\PPP=(\PP,\pp(\ptop))=\!\pcol@pages!\!\pcol@currpage!$ empty
+% after copying its original value into $\mathit{\Pi}'=\!\reserved@a!$.
+% Then we scan $\pi'(q)\in\mathit{\Pi}'$ for all $q\in[\pbase,\ptop]$ by
+% applying \!\pcol@setpnoelt! to each $\pi'(q)$ giving its five components
+% to the macro, so that the macro updates $\pp(q)$ by \!\pcol@defcurrpage!
+% letting $\pp^p(q)=\page'(q)$ if $q\geq p$, or equivalently $p-q\leq0$.
+% Note that we let \!\c@page!  have $\page'(q)$, but this assignment is
+% temporary and \!\c@page! will regain the value $\page(p)$ after
+% \!\pcol@setpageno! finishes.
+% 

+%    \begin{macrocode}
+\def\pcol@setpageno{\begingroup
+  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
+  \let\@elt\relax \edef\reserved@a{\pcol@pages\pcol@currpage}%
+  \global\let\pcol@pages\@empty \global\let\pcol@currpage\@empty
+  \let\@elt\pcol@setpnoelt \reserved@a
+  \endgroup}
+\def\pcol@setpnoelt#1#2#3#4#5{%
+  {\let\@elt\relax \xdef\pcol@pages{\pcol@pages\pcol@currpage}}%
+  \ifnum\@tempcnta>\z@ \gdef\pcol@currpage{\@elt{#1}#2#3{#4}{#5}}%
+  \else \pcol@defcurrpage{\number\c@page}{#2}{#3}{#4}{#5}%
+    \advance\c@page\@ne
+    \ifpcol@paired\else \advance\c@page\@ne \fi
+  \fi
+  \advance\@tempcnta\m@ne}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@defcurrpage}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced by the redesign of page context, partly replacing
+%	 \cs{pcol@setordpage} which once we call \cs{pcol@settextpage}.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
+%	 invoker \cs{pcol@makecol}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^m(p)$.}

+% 

+% The macro
+% $\!\pcol@defcurrpage!
+% \Arg{\pp^p(p)}\arg{\pp^i(p)}\arg{\pp^f(p)}\Arg{\pp^s(p)}\Arg{\pp^m(p)}$ 
+% is invoked from \!\pcol@makecol! to update $\pp^s(\ptop)$,
+% \!\pcol@setpnoelt! to update $\pp^p(p)$, \!\pcol@startpage! to initialize
+% a newly created page, \!\pcol@output@start! to initialize a \spage{},
+% \!\pcol@output@switch! to update $\pp^s(\ptop)$ and/or $\pp^f(\ptop)$, and
+% \!\pcol@setmpbelt! to update $\pp^m(p)$.  The macro \!\xdef!ines
+% \!\pcol@currpage! letting it have the \pctext{} $\pp(p)$ given by the
+% arguments.
+% 

+%    \begin{macrocode}
+\def\pcol@defcurrpage#1#2#3#4#5{{%
+  \let\@elt\relax \xdef\pcol@currpage{\@elt{#1}#2#3{#4}{#5}}}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@nextpage}
+% \changes{v1.2-7}{2013/05/11}
+%	{Remove unnecessary scan of $\pi(p_t)$.}

+% \begin{macro}{\pcol@nextpelt}
+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
+%	 invoker \cs{pcol@makecol}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^m(p)$.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Fix the bug that $\pi^h(q)$ is not referred correctly.}

+% 

+% The macro \!\pcol@nextpage! is invoked solely in \!\pcol@opcol! to let
+% $p$ be $p+k+1$ where $k$ is the number of \fpage{}s directly following
+% $p$, i.e., $k=\Abs{\Set{q>p}{p<\forall q'\leq q:\pp(q')^h<0}}$.  For
+% this update, the macro scans $\pp(q)\in\PP$ for all $q\In\pbase\ptop$
+% applying \!\pcol@nextpelt! to $\pp(q)$, to perform the following where
+% $p_0$ is $p$ before update and $f=\CSIndex{if@tempswa}$ being $\true$ at
+% initial, to let $p\gets p+k$, and then increments $p$ to have $p+k+1$.
+% $$
+% \<p,f\>\gets\cases{
+% 	\<p,f\>&	$q\leq p_0$\cr
+% 	\<p{+}1,f\>&	$q>p_0\;\land\;f\;\land\;\pp^i(q)\neq\bot\;\land\;
+%			\pp^h(q)<0$\cr
+%	\<p,\false\>&	otherwise}
+% $$
+% 

+%    \begin{macrocode}
+\def\pcol@nextpage{\begingroup
+  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
+  \@tempswatrue
+  \let\@elt\pcol@nextpelt \pcol@pages
+  \global\advance\pcol@page\@ne
+  \endgroup}
+\def\pcol@nextpelt#1#2#3#4#5{%
+  \ifnum\@tempcnta<\z@
+    \ifvoid#2\@tempswafalse
+    \else\ifdim\dimen#2<\z@
+      \if@tempswa \global\advance\pcol@page\@ne \fi
+    \else \@tempswafalse
+    \fi\fi
+  \fi
+  \advance\@tempcnta\m@ne}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@checkshipped}
+% The macro \!\pcol@checkshipped! is invoked solely in \!\pcol@opcol! to let
+% \CSIndex{if@tempswa} be $\true$ iff
+% $S_c=|\pcol@shipped|{\cdot}c\neq\emptyset$
+% 

+% \SpecialArrayIndex{c}{\pcol@shipped}
+% 

+% for all $c\In0\C$ to mean the oldest page $\pbase$ is ready to be shipped
+% out.
+% 

+%    \begin{macrocode}
+\def\pcol@checkshipped{\@tempswatrue
+  \@tempcnta\z@ \@whilenum\@tempcnta<\pcol@ncol\do{%
+    \expandafter\ifx\csname pcol@shipped\number\@tempcnta\endcsname\@empty
+      \@tempswafalse \fi
+   \advance\@tempcnta\@ne}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\pcol@getcurrpage}
+% \changes{v1.3-4}{2013/09/17}
+%	{Add a user \cs{pcol@addmarginpar}.}

+% \begin{macro}{\pcol@getpelt}
+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

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

+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \begin{macro}{\pcol@getcurrpinfo}
+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
+%	 invoker \cs{pcol@makecol}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^m(p)$.}

+% 

+% The macro \!\pcol@getcurrpage! is invoked in \!\pcol@opcol!,
+% \!\pcol@restartcolumn!, \!\pcol@addmarginpar!, \!\pcol@flushcolumn! and
+% \!\pcol@freshpage! to let;
+% 

+% \begin{eqnarray*}
+% &&\!\c@page!=\pp^p(p)\quad
+%   \!\@colht!=\pp^h(p)\quad
+%   \!\topskip!=\pp^t(p)\quad
+%   \CSIndex{ifpcol@nospan}=(\pp^i(p)=\bot)\\
+% &&\Midx{\!\pcol@spanning!}=\pp^i(p)\quad
+%   \Midx{\!\pcol@footins!}=\pp^f(p)\quad
+%   \Midx{\!\pcol@sptextlist!}=\pp^s(p)\\
+% &&\Midx{\!\pcol@mparbottom!}=\pp^m(p)
+% \end{eqnarray*}
+% 

+% for $p=\!\pcol@page!\in[p_b,p_t]$.  To do that, the macro scans all
+% $\pp(q)\in\PPP=(\PP,\pp(\ptop))$ applying \!\pcol@getpelt! to
+% $\pp(q)=
+% \Arg{\pp^p(q)}\arg{\pp^i(q)}\arg{\pp^f(q)}\Arg{\pp^s(q)}\Arg{\pp^m(q)}$
+% to invoke
+% $$
+% \!\pcol@getpinfo!
+% \Arg{\pp^p(q)}\arg{\pp^i(q)}\arg{\pp^f(q)}\Arg{\pp^s(q)}\Arg{\pp^m(q)}
+% \arg{pg}\arg{ch}\arg{ts}
+% $$
+% with the following arguments for \!\global! assignments, if $q=p$.
+% $$
+% \arg{pg}=\!\global!\!\c@page!\quad
+% \arg{ch}=\!\global!\!\@colht!\quad\arg{ts}=\!\global!\!\topskip!
+% $$
+% Then the macro \!\pcol@getpinfo! do the obvious assighments to
+% \!\pcol@spanning!, \!\pcol@footins!, \!\pcol@sptextlist!,
+% \!\pcol@mparbottom! and $\arg{pg}$, and the following
+% condintional assignments.
+% 

+% \begin{eqnarray*}
+% &&\<\arg{ch},\arg{ts},\CSIndex{ifpcol@nospan}\>=
+% \left\{\begin{array}{llll}
+%	\<\!\textheight!,&\!\pcol@topskip!,&\true\>&\quad\pp^i(q)=\bot\\
+%	\<\pp^h(q),&\pp^t(q),&\false\>&\quad\pp^i(q)\neq\bot\end{array}\right.
+% \end{eqnarray*}
+% 

+% \begin{Sloppy}{2800}\noindent
+% The other macro $\!\pcol@getcurrpinfo!\arg{pg}\arg{ch}\arg{ts}$ is invoked
+% in \!\pcol@makecol!, \!\pcol@startpage!, \!\pcol@output@switch!,
+% \!\pcol@sync!, \!\pcol@flushcolumn! and \!\pcol@make~flushedpage! do the
+% similar assignments using \!\pcol@getpinfo!, but it is not for $\pp(p)$
+% but for $\pp(\ptop)={}$\!\pcol@currpage!.  The macro \!\pcol@getpinfo!
+% also has a direct invoker \!\pcol@outputelt!.
+% \end{Sloppy}
+% 

+%    \begin{macrocode}
+\def\pcol@getcurrpage{\begingroup
+  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
+  \let\@elt\pcol@getpelt \pcol@pages\pcol@currpage
+  \endgroup}
+\def\pcol@getpelt#1#2#3#4#5{%
+  \ifnum\@tempcnta=\z@
+    \pcol@getpinfo{#1}#2#3{#4}{#5}%
+                  {\global\c@page}{\global\@colht}{\global\topskip}%
+  \fi
+  \advance\@tempcnta\m@ne}
+\def\pcol@getpinfo#1#2#3#4#5#6#7#8{\pcol@nospantrue
+  \gdef\pcol@spanning{#2}\gdef\pcol@footins{#3}\gdef\pcol@sptextlist{#4}%
+  \gdef\pcol@mparbottom{#5}%
+  #6#1\relax
+  \ifvoid#2\relax #7\textheight #8\pcol@topskip
+  \else #7\dimen#2\relax #8\skip#2\relax \pcol@nospanfalse
+  \fi}
+\def\pcol@getcurrpinfo{%
+  \edef\reserved@a{\expandafter\@cdr\pcol@currpage\@nil}%
+  \expandafter\pcol@getpinfo\reserved@a}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@floatplacement}
+% \changes{v1.0}{2011/10/10}
+%	{Add initialization of \cs{pcol@textfloatsep}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Remove clearing operation on \cs{@mparbottom} because it is no
+%	 longer in column-context.}

+% 

+% The macro \!\pcol@floatplacement! is invoked from \!\pcol@opcol!,
+% \!\pcol@output@start!, \!\pcol@flushcolumn!, \!\pcol@freshpage! and
+% \!\pcol@output@end! to reinitialize the parameters of \cwise{} float
+% placement at the beginning of a \colpage{} or that of \postenv.  The macro
+% lets \!\@textfloatsheight! be 0 and then invokes \!\@floatplacement!, as
+% \!\@opcol! does its tail\footnote{

+% 

+% But $\!\@mparbottom!=0$ is not done because it is meaningless now.}.
+% 

+% In addition, the macro lets \!\pcol@textfloatsep! be \!\maxdimen! to mean
+% the new \colpage{} does not have \sync{}ation point at initial.
+% 

+%    \begin{macrocode}
+\def\pcol@floatplacement{%
+  \global\@textfloatsheight\z@ \global\pcol@textfloatsep\maxdimen
+  \@floatplacement}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Starting New Page}
+% \label{sec:imp-startpage}
+% 
+% \begin{macro}{\pcol@startpage}
+% \changes{v1.0}{2011/10/10}
+%	{Add assignment of \cs{pcol@firstprevdepth} to be \cs{relax}.}

+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}

+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@settextpage} as \cs{pcol@setordpage}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Duplicate \cs{stepcounter} of \cs{c@page} if non-paired
+%	 parallel-paging is in effect.} 
+% \changes{v1.3-3}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^s(p)$.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^m(p)$.}

+% \changes{v1.32-3}{2015/10/10}
+% 	{Add $\hbox{\cs{f@depth}}\EQ0$ to override
+%	 $\hbox{\cs{f@depth}}\EQ\hbox{\texttt{1sp}}$ done by
+%	 \cs{@dblfloatplacement}.}
+% \changes{v1.32-3}{2015/10/10}
+% 	{Modify the code to apply \cs{@sdblcolelt} to \cs{@dbldeferlist} so
+%	 as to work with both 2015 (or newer) and 2014 (or older) versions
+%	 of \LaTeX.}
+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+% The macro \!\pcol@startpage! is invoked from \!\pcol@opcol! with
+% $\!\pcol@currpage!=\pp(p{-}1)$ to start a new page $p=\!\pcol@page!$, or
+% from \!\pcol@output@start! with a too large \preenv{} or
+% \!\pcol@freshpage! with $\!\pcol@currpage!=|{}|$ and $\!\c@page!=\page(p)$
+% to start a new page $p=0$.
+% 
+% First, we let $\!\pcol@firstprevdepth!=\!\relax!$ to mean we have (had)
+% left from the \spage{} so that \!\pcol@output@end! will be informed of
+% that.  Next we let $\ptop=p$ and then, if invoked from \!\pcol@opcol!,
+% obtain $\pp^p(p{-}1)$ by \!\pcol@getcurrpinfo! to have $\page(p{-}1)$ in
+% \!\c@page!, and let $\PP\gets\PPP=(\PP,\pp(p{-}1))$ with
+% $\pp^f(p{-}1)=\!\pcol@currfoot!$ into which \!\pcol@makecol! saved
+% \Scfnote{}s if any.  Next we lets $\!\c@page!=\page(p{-}1)+1$ unless
+% \npaired{} \parapag{}ing is in effect or in other words if
+% $\CSIndex{ifpcol@paired}=\true$, or $\!\c@page!=\page(p{-}1)+2$ otherwise,
+% by \!\stepcounter!.  Then we let $\!\@colht!=\!\textheight!$ as the base
+% value without \spanning, and $\!\topskip!=\!\pcol@topskip!$ because the
+% new page is the second or succeeding one built in \env{paracol}
+% environment.
+% 

+%    \begin{macrocode}
+%% Starting New Page
+
+\def\pcol@startpage{%
+  \global\let\pcol@firstprevdepth\relax
+  \global\pcol@toppage\pcol@page
+  \ifx\pcol@currpage\@empty\else
+    \pcol@getcurrpinfo{\global\c@page}\@tempdima\@tempskipa
+    \@cons\pcol@pages
+      {{\number\c@page}\pcol@spanning\pcol@currfoot
+       {\pcol@sptextlist}{\pcol@mparbottom}}%
+    \stepcounter{page}\ifpcol@paired\else \stepcounter{page}\fi
+  \fi
+  \global\@colht\textheight
+  \global\topskip\pcol@topskip
+%    \end{macrocode}
+% 
+% Then, we build \fpage{}s if any as follows.  First we invoke
+% \!\@dblfloatplacement! to reinitialize the parameters for \pwise{} float
+% placement.  In addition, we let $\!\f@depth!=0$ to nullify the
+% setting $\!\f@depth!=|1sp|$ possiblly done by \!\@dblfloatplacement! as
+% discussed in the item-(\ref{item:ovv-float-@dblfloatplacement}) of
+% \secref{sec:imp-ovv-float}.  Then we repeat \!\@tryfcolumn!  giving it
+% \!\@dbldeferlist!  having \pwise{} floats not contributed to previous
+% pages yet, while $\CSIndex{if@fcolmade}=\true$ meaning it builds \fpage{}s
+% in \!\@outputbox!.  For each \fpage{}, we acquire an \!\insert!  from
+% \!\@freelist! by \!\@next! for $\pp^i(\ptop)$ to let it have the
+% followings to represent the \fpage{}.
+% 

+% \begin{eqnarray*}
+% \pp^p(\ptop)&=&\!\c@page!\quad
+% \pp^b(\ptop)=\!\@outputbox!\quad
+% \pp^h(\ptop)=-\!\maxdimen!\quad
+% \pp^t(\ptop)=\!\pcol@topskip!\\
+% \pp^f(\ptop)&=&\bot\quad
+% \pp^s(\ptop)=\emptyset\quad
+% \pp^m(\ptop)=\emptyset
+% \end{eqnarray*}
+% 

+% We also increment $p$ and $\ptop$, and also \!\c@page! by one or two
+% according to \CSIndex{ifpcol@paired} by \!\stepcounter!, to let them have
+% the values for the page following the \fpage{}s.
+% 

+%    \begin{macrocode}
+  \@dblfloatplacement \let\f@depth\z@
+  \@tryfcolumn\@dbldeferlist
+  \@whilesw\if@fcolmade\fi{%
+    \pcol@Fb
+    \@next\@currbox\@freelist{%
+      \global\setbox\@currbox\box\@outputbox}\pcol@ovf
+    \pcol@Fe{startpage(fcol)}%
+    \global\dimen\@currbox-\maxdimen
+    \global\skip\@currbox\pcol@topskip
+    \@cons\pcol@pages{{\number\c@page}\@currbox\voidb@x{}{}}%
+    \stepcounter{page}\ifpcol@paired\else \stepcounter{page}\fi
+    \global\advance\pcol@page\@ne \global\pcol@toppage\pcol@page
+    \@tryfcolumn\@dbldeferlist}%
+%    \end{macrocode}
+% 
+% Next, we copy \!\@dbldeferlist! containing \pwise{} floats which
+% could not be included in \fpage{}s to \!\reserved@b!, clear the list, and
+% then scan the copied list by applying \!\@sdblcolelt! to each list
+% element to invoke \!\@addtodblcol! for adding the element to \!\@dbltoplist!
+% or keeping it in \!\@dbldeferlist! or \!\@deferlist! depending on \LaTeX's
+% version, as \LaTeX's \!\@startdblcolumn!  does.  In addition, as discussed
+% in item-(\ref{item:ovv-float-@addtodblcol}) of
+% \secref{sec:imp-ovv-float}, we also clear \!\@deferlist! after saving it in
+% \!\reserved@c! prior to the scan, and then after the scan we concatenate
+% \!\@dbldeferlist! and \!\@deferlist! to let the former have the result and
+% restore \!\@deferlist! from \!\reserved@c!.
+% 
+% Then If this scan results in empty \!\@dbltoplist! to mean the new page
+% does not have any \spanning, we invoke \!\pcol@defcurrpage! with
+% $\pp^i(\ptop)=\pp^f(\ptop)=\bot$ and $\pp^s(\ptop)=\pp^m(\ptop)=\emptyset$
+% so that $\pp(\ptop)$ reprsents a page perfectly empty.
+% 

+%    \begin{macrocode}
+  \begingroup
+    \let\reserved@b\@dbldeferlist \let\reserved@c\@deferlist
+    \global\let\@dbldeferlist\@empty \global\let\@deferlist\@empty
+    \let\@elt\@sdblcolelt
+    \reserved@b
+    \let\@elt\relax \xdef\@dbldeferlist{\@dbldeferlist\@deferlist}%
+    \global\let\@deferlist\reserved@c
+  \endgroup
+  \ifx\@dbltoplist\@empty
+    \pcol@defcurrpage{\number\c@page}\voidb@x\voidb@x{}{}%
+%    \end{macrocode}
+% 
+% Otherwise, i.e., \!\@dbltoplist! is not empty, we scan all elements in it
+% by letting $\!\@elt!=\!\@comdblflelt!$ to have all \pwise{} floats in
+% \!\@tempboxa!.  Then, after returning all elements to \!\@freelist!, we
+% acquire an \!\insert! from \!\@freelist! to be $\pp^i(\ptop)$ by \!\@next!
+% and store the contents of \!\@tempboxa! in $\pp^b(\ptop)$ after removing
+% the last vertical skip \!\dblfloatsep! and then adding \!\dblfigrule! and
+% the vertical skip \!\dbltextfloatsep!.  The other elements of $\pp(\ptop)$
+% are set as follows to represent the page with \spanning{} which makes the
+% height of each column \!\@colht! shrunk from its initial value
+% \!\textheight!  by the series of \!\@addtodblcol!.
+% 

+% \begin{eqnarray*}
+% \pp^p(\ptop)&=&\!\c@page!=\page(\ptop)\quad
+% \pp^h(\ptop)=\!\@colht!\quad
+% \pp^t(\ptop)=\!\pcol@topskip!\quad
+% \pp^f(\ptop)=\bot\\
+% \pp^s(\ptop)&=&\emptyset\quad
+% \pp^m(\ptop)=\emptyset\quad
+% \end{eqnarray*}
+% 
+% Finally, regardless of the existence of the \pwise{} floats, we let
+% $\!\pcol@footins!=\bot$ to mean the \tpage{} does not have any \Scfnote{}s,
+% so far if footnote typesetting is \scfnote, or never otherwise.
+% 

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

+% \changes{v1.3-2}{2013/09/17}
+%	{Rename \cs{pcol@outputpage} as \cs{pcol@outputcolumns}.}

+% 

+% The macro \!\pcol@outputcolumns!$\arg{all}$ is invoked from \!\pcol@opcol!
+% with $\arg{all}=0$ to ship out the page $\pbase$ and \fpage{}s following
+% it if any, or \!\pcol@sync! with $\arg{all}=1$ to ship out all pages in
+% $\PP$.  It copies $\PP=\!\pcol@pages!$ into $\mathit{\Pi}'=\!\reserved@b!$
+% and clear $\PP$ once to remove pages shipped out from it.  Then, after
+% initializing $f_o=\CSIndex{if@tempswa}=\true$ to ship out (the first)
+% ordinary page and $f_f=\CSIndex{ifpcol@outputflt}=\true$ to ship out
+% \fpage{}s (following the first page), it scans all
+% $\pp(q)\in\mathit{\Pi}'$ applying $\!\pcol@outputelt!\arg{all}$ to
+% $\pp(q)$ to ship it out or keep it in $\PP$.
+% 

+%    \begin{macrocode}
+%% Shipping Page Out
+
+\def\pcol@outputcolumns#1{\begingroup
+  \def\@elt{\pcol@outputelt#1}\@tempswatrue \pcol@outputflttrue
+  \let\reserved@b\pcol@pages \gdef\pcol@pages{}%
+  \reserved@b
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@outputelt}
+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^s(p)$.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise reflecting the new page context element $\pi^m(p)$.}

+% 

+% The macro $\!\pcol@outputelt!
+% \arg{all}\Arg{\pp^p(q)}\arg{\pp^i(q)}\arg{\pp^f(q)}
+% \Arg{\pp^s(q)}\Arg{\pp^m(q)}$ ships out the ordinary or \fpage{} $q$ if
+% $f_o=\true$ or $f_f=\true$ respectively.  After initializing
+% \!\@outputbox! to be $\bot$, we retrive the page $q$'s information by
+% \!\pcol@getpinfo! to have $\page(q)$ in \!\c@page! locally, \!\textheight!
+% or $\pp^h(q)$ in $h=\!\@tempdima!$,
+% $f_{\it{}ns}=\CSIndex{ifpcol@nospan}=(\pp^i(q)=\bot)$, and
+% $\!\pcol@footins!={\pp^f(q)}$.
+% 

+%    \begin{macrocode}
+\def\pcol@outputelt#1#2#3#4#5#6{%
+  \setbox\@outputbox\box\voidb@x
+  \pcol@getpinfo{#2}#3#4{#5}{#6}\c@page\@tempdima\@tempskipa
+%    \end{macrocode}
+% 
+% Then, we do one of the followings according to $h$ and $f_o$.
+% 

+% \begin{itemize}
+% \item $h<0$\\
+% It means $q$ is a \fpage{}.  If $f_f=\true$, we let \!\@outputbox! have
+% $\pp^b(q)$ to be shipped out, paint its \bground{} with $\bgc_{\{F,f\}}$
+% by \!\pcol@bg@paintbox! letting the basic height \!\pcol@bg@floatheight!
+% of the paining region 
+% $\bgr_{\{F,f\}}$ be
+% $\HT=\!\pcol@bg@textheight!=\!\textheight!+\!\maxdepth!$, and return
+% $\!\insert!{\cdot}\pp^i(q)$ to \!\@freelist! by \!\@cons! because it is no
+% longer necessary.  Then if $\CL<\C$ to mean \parapag{}ing is in effect, we
+% let \!\pcol@rightpage! be an empty box but paint its \bground{} too, because
+% the right counterpart of left parallel float page should be always blank.
+% Note that we temporarily increment $\page(q)$ by one for \npaired{} right
+% \parapag{}ee so that the paiting macro performs page-parity dependent
+% operations correctly.
+% 

+% \Index{parallel-paging}

+% \Index{float page}

+% 
+% On the other hand if $f_f=\false$, we simply return $\pp(q)$ back to $\PP$.
+% \end{itemize}
+% 

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

+% \changes{v1.3-3}{2013/09/17}
+%	{Add painting of page-wise float page.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add building a empty right parallel float page.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \ifdim\@tempdima<\z@
+    \ifpcol@outputflt
+      \def\pcol@bg@floatheight{\pcol@bg@textheight}%
+      \setbox\@outputbox\vbox to\textheight{%
+        \pcol@bg@paintbox{Ff}\unvbox\pcol@spanning}%
+      \pcol@Fb
+      \@cons\@freelist\pcol@spanning
+      \pcol@Fe{outputelt(spanning)}%
+      \ifnum\pcol@ncolleft<\pcol@ncol
+        \setbox\pcol@rightpage\vbox to\textheight{%
+          \ifpcol@paired\else \advance\c@page\@ne \fi
+          \pcol@bg@paintbox{Ff}\vfil}%
+      \fi
+    \else
+      \@cons\pcol@pages{{#2}#3#4{#5}{#6}}%
+    \fi
+%    \end{macrocode}
+% 

+% \begin{itemize}
+% \item $h\geq0\;\land\;f_o=\true$\\
+% It means $q$ is a non-\fpage{} to be shipped out.  If $\arg{all}=0$, we
+% let $f_o=\false$ to keep succeeding non-\fpage{}s from being shipped out.
+% Then we build the ship-out image of the right \parapag{}e $q$ in
+% \!\pcol@rightpage! by \!\pcol@ioutputelt! giving it the box and the column
+% range $\LBRP\CL\C$ if $\CL<\C$ to mean \parapag{}ing, and then that of the
+% left \parapag{}e in \!\@outputbox! by \!\pcol@ioutputelt! again but giving
+% it $\LBRP0\CL$ and \!\@outputbox!.  Note that the right-first left-second
+% order is essential, because in the process to build right \parapag{}e we
+% have to examine the existence of $\pp^i(q)$ and $\pp^f(q)$ and then refer
+% to their height and depth to make the region corresponding to them blank,
+% while the boxes of these \!\insert!s are made void in the building process
+% of the left \parapag{}e obviously.
+% 
+% Then after the ship-out image building, we \!\global!ly let
+% $\CSIndex{ifpcol@firstpage}=\false$ to tell \!\pcol@ioutputelt! and
+% \!\pcol@makeflushedpage! that the pages they build are no longer first of
+% a \env{paracol} environment and thus $\pp^i(q)$ should have \pwise{}
+% floats rather than \preenv{} hereafter.
+% \end{itemize}
+% 

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

+% \changes{v1.1}{2012/05/11}
+% 	{Use $\cs{pcol@columnwidth}{\cdot}c$ instead of \cs{columnwidth} as
+%	 the width of $c$'s \cs{hbox}.}

+% \changes{v1.2-4}{2013/05/11}
+%	{Add column-swapping for even pages if specified.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add ship-out of page-wise footnote.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Move the core of ship-out image building to \cs{pcol@ioutputelt} for
+% 	 parallel pageing.}

+% 

+%    \begin{macrocode}
+  \else\if@tempswa
+    \ifnum#1=\z@ \@tempswafalse \fi
+    \ifnum\pcol@ncolleft<\pcol@ncol
+      \pcol@Logstart{\pcol@outputelt{right}}%
+      \pcol@ioutputelt\pcol@ncolleft\pcol@ncol\pcol@rightpage
+      \pcol@Logend{\pcol@outputelt{right}}%
+    \fi
+    \pcol@Logstart{\pcol@outputelt{left}}%
+    \pcol@ioutputelt\z@\pcol@ncolleft\@outputbox
+    \pcol@Logend{\pcol@outputelt{left}}%
+    \global\pcol@firstpagefalse
+%    \end{macrocode}
+% 

+% \begin{itemize}
+% \item $h\geq0\;\land\;f_o=\false$\\
+% It means $q$ is a non-\fpage{} to be kept.  Therefore, we let
+% $f_f=\false$ to keep \fpage{}s following it from being shipped out.  Then
+% we return $\pp(q)$ to $\PP$ by \!\@cons!.
+% \end{itemize}
+% 

+%    \begin{macrocode}
+  \else
+    \pcol@outputfltfalse
+    \@cons\pcol@pages{{#2}#3#4{#5}{#6}}%
+  \fi\fi
+%    \end{macrocode}
+% 
+% Finally, if $\!\@outputbox!\neq\bot$ to mean $\pp(q)$ is to be
+% shipped out, we invoke \!\@outputpage! to do it and increment $\pbase$ to
+% let it has $q+1$.  Note that since we have let $\!\c@page!=\page(q)$, the
+% direct and indirect references to it in \!\@outputpage! are correctly done.
+% Also note that the \!\global! increment of it by \!\stepcounter! in
+% \!\@outputpage! will be overriden by the \!\global! assignment to it done
+% by \!\pcol@startpage! or \!\pcol@getcurrpage! invoked from \!\pcol@opcol!
+% if $\arg{all}=0$, or by \!\pcol@getcurrpinfo! invoked from \!\pcol@sync!
+% otherwise.
+% 

+%    \begin{macrocode}
+  \ifvoid\@outputbox\else
+    \global\advance\pcol@basepage\@ne \@outputpage
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@ioutputelt}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add column-separating rule drawing and background painting.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add a logic to cope with non-uniform column-separating gaps.}

+% 

+% The macro $\!\pcol@ioutputelt!\<\Cfrom\>\<\Cto\>\arg{b}$ is invoked solely
+% in \!\pcol@outputelt! but can be done twice with
+% $(\Cfrom,\Cto,b)=(\CL,\C,\!\pcol@rightpage!)$ if \parapag{}ing is in
+% effect and with $(\Cfrom,\Cto,b)=(0,\CL,\!\@outputbox!)$ always, to build
+% the ship-out image of the right or left \parapag{}e $q$ in the box $b$
+% respectively.
+% 
+% After opening a \!\vbox! of \!\textheight! tall for $b$, at first we
+% increment $\page(q)$ by one for right \parapag{}e if it is \npaired, so
+% that painting macros perform page-parity dependent operations correctly.
+% 
+% Next, we put materials to be shipped out in the box $b$ as follows.
+% First, if $\pp^f(q)\neq\bot$ to mean the page $q$ has \Scfnote{}, we paint
+% their \bground{} with $\bgc_{\{N,n\}}$ by \!\pcol@bg@paintbox! letting the
+% basic height \!\pcol@bg@footnoteheight! of the paining region
+% $\bgr_{\{N,n\}}$ be the height-plus-depth of $\pp^f(q)$.
+% We do the painting at this earliest stage of the image building in order
+% to use the left-top corner of the text area where we are now at as the
+% origin for painting, and to let the region may be overlaid by those of
+% columns and \csepgap{}s.  We also let $h=\pp^h(q)=\!\@tempdima!$ shrunk by
+% the height-plus-depth by \!\pcol@shrinkcolbyfn!.
+% 

+%    \begin{macrocode}
+\def\pcol@ioutputelt#1#2#3{\setbox#3\vbox to\textheight{%
+  \ifpcol@paired\else\ifnum#1=\z@\else \advance\c@page\@ne \fi\fi
+  \ifvoid\pcol@footins\else
+    \def\pcol@bg@footnoteheight{\@elt{\ht\pcol@footins}\@elt{\dp\pcol@footins}}%
+    \pcol@bg@paintbox{Nn}%
+    \pcol@shrinkcolbyfn\@tempdima\pcol@footins\relax
+  \fi
+%    \end{macrocode}
+%
+% Second, if $f_{\it ns}=\false$ to mean $\pp(q)$ has \spanning{} in
+% $\pp^b(q)$, we do one of the followings.
+% 

+% \begin{itemize}
+% \item
+% If $\Cfrom=0$ to mean the target is the left \parapag{}e, $\pp^b(q)$ is
+% put by \!\unvbox!, painting its \bground{} with $\bgc_{\{F,f\}}$ by
+% \!\pcol@bg@paintbox! letting the basic height \!\pcol@bg@floatheight!  of
+% the paining region $\bgr_{\{F,f\}}$ be the height-plus-depth of $\pp^b(q)$
+% if $q$ is not the first page and thus $\pp^b(q)$ has \pwise{} floats.  We
+% also return the \!\insert!  $\pp^i(q)$ to \!\@freelist! by \!\@cons!.
+% 
+% \item
+% If $\Cfrom\neq0$ to mean right \parapag{}e and $q$ is the first page,
+% \!\pcol@rightpage! has \preenv{} in the right \parapag{}e.  Therefore, we
+% simply put the box but making its height and depth equal to those of
+% $\pp^b(q)$, without painting because the box has already been painted, and
+% with \!\nointerlineskip! to prevent baseline-skip insertion below the box.
+% 
+% \item
+% Otherwise, i.e., $\Cfrom\neq0$ and $q$ is not the first page, we put an
+% empty box whose height and depth equal to those of $\pp^b(q)$ by
+% \!\pcol@phantom!, with painting as done for floats in the left \parapag{}e
+% and with \!\nointerlineskip!.
+% \end{itemize}
+% 

+% Note that after putting \spanning{} and/or painting the \bground{}, we
+% temporarily increment \!\topmargin! by the height-plus-depth of
+% $\pp^b(q)$, so that painting macros for columns, \csepgap{}s and
+% \mctext{}s assume the top edge of column area as that of text area when
+% they extend the top edges of their regions upward to the page top.
+% 

+% \Index{extension of background painting region}

+% 

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \ifpcol@nospan\else
+    \def\pcol@bg@floatheight{%
+      \@elt{\ht\pcol@spanning}\@elt{\dp\pcol@spanning}}%
+    \@tempdimb\ht\pcol@spanning \advance\@tempdimb\dp\pcol@spanning
+    \ifnum#1=\z@
+      \ifpcol@firstpage\else \pcol@bg@paintbox{Ff}\fi
+      \pcol@Fb
+      \@cons\@freelist\pcol@spanning \unvbox\pcol@spanning
+      \pcol@Fe{ioutputelt(spanning)}%
+    \else\ifpcol@firstpage
+      \ht\pcol@rightpage\ht\pcol@spanning
+      \dp\pcol@rightpage\dp\pcol@spanning
+      \box\pcol@rightpage \nointerlineskip
+    \else
+      \pcol@bg@paintbox{Ff}\pcol@phantom\pcol@spanning \nointerlineskip
+    \fi\fi
+    \advance\topmargin\@tempdimb
+  \fi
+%    \end{macrocode}
+%
+% Third, we invoke \!\pcol@buildcolseprule! giving it $h$ being $\pp^h(q)$
+% but possibly shrunk by \Scfnote{}s, the column range $\LBRP\Cfrom\Cto$,
+% and \!\@maxdepth! to mean $q$ is non-\lpage, to draw a \cseprule{}
+% possibly broken by the speces for \mctext{}s in the box \!\pcol@tempboxa!
+% and to paint the \bground{}s of columns, \csepgap{}s and \mctext{} in the
+% box \!\@tempboxa! which we put into $b$ immediately.
+% 
+% Fourth, we put a \!\hbox! of \!\textwidth! wide having \!\hbox!es
+% of $\w_c=|\pcol@columnwidth|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}
+% 

+% wide containing $\sigma_c$ followed by \!\hss! for all $c\In\Cfrom\Cto$,
+% where $\sigma_c=\!\box!{\cdot}s_c(q)$ being the first element removed from
+% $\S_c$ by \!\@next! and then returned to \!\@freelist! by \!\@cons! if it
+% is not $\bot$, or \!\voidb@x!  otherwise.  We sepearate \!\hbox!es of
+% $\sigma_c$ by making each \!\hbox! preceded by \Midx{\!\pcol@@hfil!} being
+% \!\relax! for the first one and the macro \!\pcol@hfil! for others giving
+% it an argument $c^g=\!\pcol@colsepid!\in\{c,c{-}1\}$ which we discuss
+% shortly to put a gap of $\gap_{c^g}=|\pcol@columnsep|{\cdot}c^g$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% wide optionally having a \cseprule{} and being painted.
+% 
+% Note that the scanning order of $c\In\Cfrom\Cto$ is usually ascending of
+% course, but is descending if \cswap{} is specified and $\page(q)\bmod2=0$.
+% For this ordering, we invoke
+% $\!\pcol@swapcolumn!\arg{c'}\arg{c}\<\Cfrom\>\<\Cto\>$ to have $c$ for
+% the $(c'-\Cfrom)$-th iteration of the scanning where $c'=\!\@tempcnta!$
+% and $c=\!\@tempcntb!$.  Another operation done by the macro is to let
+% $c^g=c-1$ if swapped or $c^g=c$ otherwise, because if swapped the
+% column-$c$ is followed by the gap which follows $c-1$ if not swapped.
+% 

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \pcol@buildcolseprule\@tempdima#1#2\@maxdepth \unvbox\@tempboxa
+  \hb@xt@\textwidth{%
+    \let\pcol@@hfil\relax
+    \@tempcnta#1\relax \@whilenum\@tempcnta<#2\do{%
+      \pcol@swapcolumn\@tempcnta\@tempcntb#1#2\relax
+      \expandafter\@next\expandafter\@currbox
+        \csname pcol@shipped\number\@tempcntb\endcsname
+        \relax{\let\@currbox\voidb@x}%
+      \ifvoid\@currbox\else
+        \pcol@Fb
+        \@cons\@freelist\@currbox
+        \pcol@Fe{ioutputelt(page)}%
+      \fi
+      \expandafter\@tempdima
+        \csname pcol@columnwidth\number\@tempcntb \endcsname
+      \pcol@@hfil \hb@xt@\@tempdima{\box\@currbox\hss}%
+      \edef\pcol@@hfil{\noexpand\pcol@hfil{\pcol@colsepid}}%
+     \advance\@tempcnta\@ne}}%
+%    \end{macrocode}
+%
+% Fifth, if $\pp^f(q)\neq\bot$ to mean the page $q$ has \Scfnote{}s, we put
+% them at the bottom of \!\@outputbox! by \!\pcol@putfootins!, and return
+% $\pp^f(q)$ to \!\@freelist!, if $\Cfrom=0$ meaning left \parapag{}e.
+% Otherwise for the right \parapag{}e, we simply put an empty box whose
+% height and depth equal to those of $\pp^f(q)$ by \!\pcol@phantom!,
+% preceded by a vertical skip of $\!\skip!{\cdot}\pp^f(q)$ and then
+% \!\nointerlineskip! to inhibit baseline skip insertion above the box, and
+% followed by null \!\vskip! as done in \!\pcol@putfootins!.
+% 
+% Sixth and finally\footnote{

+% 

+% Not necessary to be finally, but we placed this assignment at the end of
+% the box to make it clear the depth capping is only for the box.},
+% 

+% we let $\!\boxmaxdepth!=\!\@maxdepth!$ to cap the depth of $b$ which we
+% are now closing, as done for each \colpage{} and as expected to be applied
+% to \Scfnote{}s.
+% 

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \ifvoid\pcol@footins\else
+    \ifnum#1=\z@
+      \pcol@Log\pcol@outputelt{output}\pcol@footins
+      \pcol@putfootins\pcol@footins
+      \pcol@Fb
+      \@cons\@freelist\pcol@footins
+      \pcol@Fe{ioutputelt(footins)}%
+    \else
+      \vskip\skip\pcol@footins \nointerlineskip
+      \pcol@phantom\pcol@footins \vskip\z@
+    \fi
+  \fi
+  \boxmaxdepth\@maxdepth}}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@phantom}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for parallel-paging.}

+% 

+% The macro \!\pcol@phantom!$\<b\>$ is used in \!\pcol@ioutputelt!,
+% \!\pcol@makeflushedpage! and \!\pcol@output@end! to put an empty box, whose
+% height and depth are equal to that of the argument box $b$ being a kind of
+% \pwstuff, into \!\pcol@rightpage! for the right \parapag{}e whose left
+% counterpart has $b$ in it.  That is, the macro is used to make a region
+% corresponding to $b$ blank.  To put the empty box, we locally let
+% \!\@tempboxa! have it setting its height and depth to those of $b$ and
+% then put it.
+% 

+%    \begin{macrocode}
+\def\pcol@phantom#1{{%
+  \setbox\@tempboxa\vbox{}\ht\@tempboxa\ht#1\dp\@tempboxa\dp#1\box\@tempboxa}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@buildcolseprule}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for column-separating rule drawing and background
+%	 painting for columns, column-separating gaps and spanning texts.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced for non-uniform column-separating gaps.}

+% \changes{v1.34}{2018/05/07}
+% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}

+% \begin{macro}{\pcol@buildcselt@S}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background under-painting for spanning texts.}

+% \begin{macro}{\pcol@buildcselt}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for column-separating rule drawing and background
+%	 painting for columns, column-separating gaps and spanning texts.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced for non-uniform column-separating gaps.}

+% \changes{v1.34}{2018/05/07}
+% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}

+% 

+% The macro $\!\pcol@buildcolseprule!\<H_{n+1}\>\<\Cfrom\>\<\Cto\>\<d\>$ is
+% used in \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and
+% \!\pcol@iflushfloats!  to build a box containing \cseprule{} possibly
+% broken by \mctext{}s and to paint \bground{}s of columns and \csepgap{}s
+% for $c\In\Cfrom\Cto$ and \mctext{}s in the \lpage{} ($d=0$) or non-last
+% page ($d=\!\@maxdepth!$) $p$ having \colpage{}s of $H_{n+1}$ tall where
+% $n=\Abs{\pp^s(p)}$.
+% 
+% For initializing the drawing and painting process, we let
+% $\!\@tempdimb!=H_0+h_0=0$,
+% $(\!\pcol@bg@from!,\!\pcol@bg@to!)=(\CBfrom,\CBto)=(\Cfrom,\Cto)$, and
+% make boxes $b_r=\!\pcol@tempboxa!$ for the rule and $b_b=\!\@tempboxa!$ for
+% the \bground{} empty.  Then we apply
+% \!\pcol@buildcselt@S!$\<H_i\>\<h_i\>$ to each element $\spt(H_i,h_i)$ of
+% $\pp^s(p)$ to under-paint the \bground{} of each \mctext{} by
+% \!\pcol@bg@paintbox! defining its region $\bgr_S(i)$ by letting their top
+% edge positions $y_0=\!\pcol@bg@spanningtop!=H_i$, and height
+% $y_1-y_0=\!\pcol@bg@spanningheight!=h_i$ if $H_i+h_i<H_{n+1}$ to mean the
+% \mctext{} is non-last, or $(H_{n+1}-H_i)+d$ if last to fill the narrow
+% strip of $d=\!\@maxdepth!$ tall below the text for non-\lpage{}s.
+% 
+% Then we scan $\pp^s(p)$ again but applying
+% $\!\pcol@buildcselt!\~\<H_i\>\<h_i\>$ to each element $\spt(H_i,h_i)$ to
+% do the followings.
+% 

+% \begin{enumerate}
+% \item
+% To $b_r$, add a vertical rule whose height is $H'_i=H_i-(H_{i-1}+h_{i-1})$
+% and width is \!\columnseprule! if $H'_i>0$, and then a vertical skip of
+% $h_i$, as the rule segment between $(i{-}1)$-th and $i$-th \mctext{}s.
+% Note that $H_i$ and $h_i$ are represented in the form of integers and thus
+% we need |sp| to use them as dimensions.
+% 
+% \item
+% To $b_b$, add painted \bground{}s for all columns $c\In\Cfrom\Cto$ and
+% \csepgap{}s $c\In\Cfrom{\Cto{-}1}$ by \!\pcol@bg@paintcolumns! defining
+% their regions $\bgr_{\{c,g\}}^c(i)$ by letting common top edge position
+% $y_0=\!\pcol@bg@columntop!=H_{i-1}+h_{i-1}$ and common height
+% $y_1-y_0=\!\pcol@bg@columnheight!=H'_i$, if $H'_i>0$.  Also add painted
+% \bground{} for the $i$-th \mctext{} by \!\pcol@bg@paintbox! as we did for
+% under-painting but this time the region is $\bgr_s(i)$.
+% 
+% \item
+% Let $\!\@tempdimb!=H_i+h_i$ for the next element $\spt(H_{i+1},h_{i+1})$.
+% \end{enumerate}
+% 

+% Then if $H'_{n+1}>0$, we add the last rule segment of $H'_{n+1}$ tall to
+% $b_r$, and add painted \bground{}s for columns and \csepgap{}s as done in
+% the step\Tie2 above but letting $y_1-y_0=H'_{n+1}+d$ to let the common
+% bottom edge of the their regions reach the bottom of text area for
+% non-\lpage{}s.
+% 
+%    \begin{macrocode}
+\def\pcol@buildcolseprule#1#2#3#4{%
+  \@tempdima#1\relax \dimen@#4\relax
+  \let\pcol@bg@from#2\relax \let\pcol@bg@to#3\relax
+  \setbox\pcol@tempboxa\vbox{}\setbox\@tempboxa\vbox{}%
+  \let\@elt\pcol@buildcselt@S \pcol@sptextlist
+  \@tempdimb\z@ \let\@elt\pcol@buildcselt \pcol@sptextlist
+  \let\@elt\relax \advance\@tempdima-\@tempdimb
+  \ifdim\@tempdima>\z@
+    \setbox\pcol@tempboxa\vbox{\unvbox\pcol@tempboxa
+      \hrule\@height\@tempdima\@width\columnseprule}%
+    \setbox\@tempboxa\vbox{\unvbox\@tempboxa
+      \let\@elt\relax
+      \edef\pcol@bg@columntop{\number\@tempdimb sp}%
+      \edef\pcol@bg@columnheight{%
+        \@elt{\number\@tempdima sp}\@elt{\number\dimen@ sp}}%
+      \pcol@bg@paintcolumns}%
+  \fi}
+\def\pcol@buildcselt@S#1#2{%
+  \setbox\@tempboxa\vbox{\unvbox\@tempboxa
+    \let\@elt\relax
+    \def\pcol@bg@spanningtop{\@elt{#1sp}}%
+    \advance\@tempdima-#1sp\relax \advance\@tempdima-#2sp\relax
+    \advance\dimen@\@tempdima
+    \edef\pcol@bg@spanningheight{\@elt{#2sp}%
+      \ifdim\@tempdima>\z@\else \@elt{\number\dimen@ sp}\fi}%
+    \pcol@bg@paintbox{S}}}
+\def\pcol@buildcselt#1#2{%
+  \@tempdimc#1sp \advance\@tempdimc-\@tempdimb
+  \setbox\pcol@tempboxa\vbox{\unvbox\pcol@tempboxa
+    \ifdim\@tempdimc>\z@ \hrule\@height\@tempdimc\@width\columnseprule \fi
+    \vskip#2sp}%
+  \setbox\@tempboxa\vbox{\unvbox\@tempboxa
+    \let\@elt\relax
+    \edef\pcol@bg@columntop{\number\@tempdimb sp}%
+    \edef\pcol@bg@columnheight{\@elt{\number\@tempdimc sp}}%
+    \ifdim\@tempdimc>\z@ \pcol@bg@paintcolumns \fi
+    \def\pcol@bg@spanningtop{\@elt{#1sp}}%
+    \advance\@tempdima-#1sp\relax \advance\@tempdima-#2sp\relax
+    \advance\dimen@\@tempdima
+    \edef\pcol@bg@spanningheight{\@elt{#2sp}%
+      \ifdim\@tempdima>\z@\else \@elt{\number\dimen@ sp}\fi}%
+    \pcol@bg@paintbox{s}}%
+  \@tempdimb#1sp \advance\@tempdimb#2sp\relax}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@hfil}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for column-separating rule drawing.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced for non-uniform column-separating gaps.}

+% \changes{v1.34}{2018/05/07}
+% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}

+% 

+% The macro $\!\pcol@hfil!\<c\>$ is used in \!\pcol@ioutputelt!,
+% \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! to separate column
+% $c{+}1$ and $c$ or $c$ and $c{+}1$ according as the columns are
+% swapped or not in the page the caller macros are building.
+% 

+% \Index{column-swapping}

+% 

+% If $\!\columnseprule!=r>0$, the macro puts the followings; a horizontal
+% space of $\gap_{c}/2=|\pcol@columnsep|{\cdot}c/2$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% followed by a skip $-r/2$ to nullify the width of the rule; the rule in
+% \!\pcol@tempboxa! which \!\pcol@buildcolseprule! built, with color
+% $|\pcol@colseprulecolor|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% or \!\pcol@colseprulecolor! according as the former is defined or not,
+% i.e., \!\colseprulecolor!\oarg{mode}\ARg{color}$|[|c|]|$ is declared or
+% not; and $\gap_c/2$ again but preceded by $-r/2$.  On the other hand if
+% $r=0$, we simply put a space of $\gap_c$.  Note that the skips of
+% $\gap_c/2$ and $\gap_c$ are accompanied by 1\,|fil| inifinit stretch to
+% avoid underfull when $\sum_{c=\Cfrom}^{\Cto-2}(\w_c+\gap_c)+\w_{\Cto-1}<\WT$
+% where $(\Cfrom,\Cto)=\{(0,\CL),(\CL,C)\}$, due to arithmetic errors in
+% calculations of $\w_c$ and $\gap_c$\footnote{

+% 

+% It is assured the sum of $w_c$ and $\gap_c$ cannot exceed $\WT$ even with
+% arithmetic errors and thus overfull never occurs.}. 
+% 

+%    \begin{macrocode}
+\def\pcol@hfil#1{{%
+  \@tempdima\csname pcol@columnsep#1\endcsname\relax
+  \ifdim\columnseprule>\z@
+    \hskip.5\@tempdima\@plus1fil\relax
+    \hskip-.5\columnseprule
+    \@ifundefined{pcol@colseprulecolor#1}%
+      {\pcol@colseprulecolor}{\@nameuse{pcol@colseprulecolor#1}}%
+    \copy\pcol@tempboxa \hskip-.5\columnseprule
+    \hskip.5\@tempdima\@plus1fil\relax
+  \else \hskip\@tempdima\@plus1fil\relax
+  \fi}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@@outputpage}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced keep the original definition of \cs{@outputpage}.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced keep the original definition of \cs{@outputpage}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced keep the original definition of \cs{@outputpage}.}

+% \begin{macro}{\@outputpage}
+% \changes{v1.3-2}{2013/09/17}
+%	{Redefined for parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Redefined for background painting.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Redefined for marginal note placement.}

+% \changes{v1.34}{2018/05/07}
+% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}

+% 

+% The macro \!\@outputpage!, being our own version of \LaTeX's one kept in
+% \!\pcol@@outputpage!, ships out a page $p$ or \parapag{}e pair in $p$.
+% The reason why we redefine this macro is that we need a few special
+% operations for \parapag{}ing and \bgpaint{} {\em outside} of \env{paracol}
+% environments.  Therefore, the macro is not only used in our own macros
+% \!\pcol@outputelt!, \!\pcol@output@start!, \!\pcol@output@flush!,
+% \!\pcol@output@clear!, \!\pcol@flushfloats! and \!\pcol@output@end!, but
+% also in \LaTeX's \!\@opcol! and \!\@doclearpage!\footnote{

+% 

+% And possibly in \CSIndex{@outputdblcol} if double-column typesetting is
+% done outside \env{paracol}.}
+% 

+% invoked from our own or \LaTeX's \!\output! routine.
+% 
+% First we calculate $H'_M=\!\topmargin!+\!\headheight!+\!\headsep!$ to place
+% the origin of \bgpaint{} at the top edge of text area in what \LaTeX{}
+% assumes as a page, i.e., shifted 1\,inch down from the real page.  Then if
+% $\CSIndex{ifpcol@output}=\true$ to mean this macro is used in a
+% \env{paracol} environment, we build the painted \bground{}s of left and
+% right \parapag{}es in $\!\pcol@tempboxa!=b_l$ and $\!\@tempboxa!=b_r$ by
+% putting a vertical skip of $H'_M$, and invoking \!\pcol@bg@paintpage!
+% with the setting $(\!\pcol@bg@from!,\!\pcol@bg@to!)=(\CBfrom,\CBto)$ be
+% $(0,\CL)$ and $(\CL,\C)$ respectively.  Note that \!\pcol@bg@paintpage!
+% paints \bground{}s of regions $\bgr_a^{[c]}$ for all
+% $a\in\{T,B,L,R,C,S,t,b,l,r\}$ and $c\In\CBfrom\CBto$, and for $b_r$ we
+% temporarily increment $\page(p)$ by one if \npaired{} \parapag{}ing is in
+% effect.
+% 
+% Otherwise, i.e., if $\CSIndex{ifpcol@output}=\false$ indicating outside
+% use, we build the painted \bground{}s in $b_l$ and $b_r$ similarly but
+% with the following differences;  \bgpaint{} is done if
+% $\CSIndex{ifpcol@havelastpage}=\true$ to mean the page to be shipped has
+% the \lpage{} of closed \env{paracol} as its part and
+% $\!\set@color!\neq\!\relax!$ to mean some coloring package is loaded;
+% page \bground{} painting is done by \!\pcol@bg@@paintpage! because
+% \!\pcol@bg@paintpage! is not available outside \env{paracol} environments;
+% the \bground{} of \postenv{} is painted by \!\pcol@bg@@paintbox! for the
+% region $\bgr_{\{P,p\}}=[(0,\WT)(\HB,\HT)]$ where
+% $\HB=\!\pcol@bg@preposttop!
+% \in\{\!\pcol@bg@preposttop@left!,\!\pcol@bg@preposttop@right!\}$
+% having the bottom edge of the last 
+% \env{paracol} environment (having right \parapag{}e for $b_r$).  In
+% addition, we examine if $\!\pcol@rightpage!\neq\bot$ to mean the right
+% \parapag{}e was built by \!\pcol@output@end! when the last \env{paracol}
+% environment was closed and, if so, make the box \!\textheight! tall adding
+% \!\vfil! to its bottom.
+% 
+% Then regardless of \CSIndex{ifpcol@output}, we do the followings; let the
+% height and depth of $b_l$ and $b_r$ be 0 because they cannot occupy any
+% real spaces in the ship-out image; temporarily let
+% $\CSIndex{ifpcol@swapcolumn}=\false$ if $\page(p)$ is odd, $\CL=\C$ to
+% mean \parapag{}ing is not in effect\footnote{

+% 

+% Since the assignments of $\CL$ and $\C$ in \CSIndex{pcol@zparacol} are
+% \CSIndex{global} and they are not nodified anywhere else, examining their
+% equality outside \env{paracol} environments is safe and meaningful.},
+% 

+% \parapag{}ing is done in \npaired{} mode\footnote{

+% 

+% We need this examination because $\CSIndex{ifpcol@swapcolumn}=\false$ for
+% \npaired{} \parapag{}ing is made locally by \!\pcol@zparacol!.},
+% 

+% or we are outside \env{paracol} environments and the page does not have
+% anything produced in environments.  That is, we let
+% $\CSIndex{ifpcol@swapcolumn}=\true$ if the page has something produced by
+% a \env{paracol} environment, \cswap{} and \parapag{}ing are specified for
+% the (last) environment\footnote{

+% 

+% Column-swapping may be enabled {\em after} the last \env{paracol}
+% environment was closed but we consider the enablement is effective for the
+% page having the environment.},
+% 

+% and the page number is even.  Note that a page may have two or more
+% (\lpage{}s of) \env{paracol} environements whose \parapag{}ing style can
+% be inconsistent including the case some of them are not \parapag{}ed.  If
+% this inconsistency happens the page is shipped out following the style of
+% the last environment.  Also note that even if the last environment is not
+% \parapag{}ed, the right \parapag{}e kept in \!\pcol@rightpage! is assuredly
+% shipped out.
+% 
+% Then if \cswap{} is in effect, we ship out the right \parapag{}e at first
+% by \!\pcol@outputpage@r! and then the left one by \!\pcol@outputpage@l! to
+% swap the left and right.  Otherwise, the ship-out order is normal and thus
+% the invocation order is \!\pcol@outputpage@l!  then \!\pcol@outputpage@r!.
+% Note that if \npaired{} \parapag{}ing is in effect, the page number to
+% given to \!\pcol@outputpage@r! as its argument is $\page(p)+1$ if it is
+% the second one, i.e., not swapped, while the argument in other cases and
+% of \!\pcol@outputpage@l! are always $\page(p)$.  Then finally, we
+% \!\global!ly let $\CSIndex{ifpcol@havelastpage}=\false$ because so far the
+% next page does not have \env{paracol}'s \lpage{} especially when we are
+% outside it, let \!\pcol@bg@preposttop@left! and
+% \!\pcol@bg@preposttop@right! have 0 because, if we are outside, the next
+% \preenv{} should start from the top of a page, and let
+% $\mpbout=\!\pcol@mparbottom@out!$ be $\mpboutz=\!\pcol@mparbottom@zero!$
+% because so far we have no marginal notes given in \env{paracol}
+% environments\footnote{

+% 

+% This assignment in a \env{paracol} environment is meaningless because
+% $\mpbout$ is meaningless too, but not harmful.}.
+% 

+%    \begin{macrocode}
+\let\pcol@@outputpage\@outputpage
+\def\@outputpage{\begingroup
+  \@tempdima\topmargin \advance\@tempdima\headheight \advance\@tempdima\headsep
+  \ifpcol@output
+    \setbox\pcol@tempboxa\vtop{\vskip\@tempdima \global\pcol@bg@paintedfalse
+     \let\pcol@bg@from\z@ \let\pcol@bg@to\pcol@ncolleft
+     \pcol@bg@paintpage}%
+    \ifpcol@bg@painted \@tempswatrue \else \@tempswafalse \fi
+    \setbox\@tempboxa\vtop{\vskip\@tempdima \global\pcol@bg@paintedfalse
+      \ifpcol@paired\else \advance\c@page\@ne \fi
+      \let\pcol@bg@from\pcol@ncolleft \let\pcol@bg@to\pcol@ncol
+      \pcol@bg@paintpage}%
+  \else
+    \def\reserved@a{\vskip\@tempdima \global\pcol@bg@paintedfalse
+      \ifpcol@havelastpage \ifx\set@color\relax\else
+        \pcol@bg@@paintpage \pcol@bg@@paintbox{Pp}%
+      \fi\fi}%
+    \setbox\pcol@tempboxa\vbox{%
+      \let\pcol@bg@preposttop\pcol@bg@preposttop@left
+      \let\pcol@bg@from\z@ \let\pcol@bg@to\pcol@ncolleft \reserved@a}%
+    \ifpcol@bg@painted \@tempswatrue \else \@tempswafalse \fi
+    \setbox\@tempboxa\vbox{\ifpcol@paired\else \advance\c@page\@ne \fi
+      \let\pcol@bg@preposttop\pcol@bg@preposttop@right
+      \let\pcol@bg@from\pcol@ncolleft \let\pcol@bg@to\pcol@ncol
+      \reserved@a}%
+    \ifvoid\pcol@rightpage\else
+      \pcol@Logstart{\@outputpage{rightset}}%
+      \setbox\pcol@rightpage\vbox to\textheight{\unvbox\pcol@rightpage \vfil}%
+      \pcol@Logend{\@outputpage{rightset}}%
+    \fi
+  \fi
+  \ht\pcol@tempboxa\z@ \dp\pcol@tempboxa\z@
+  \ht\@tempboxa\z@ \dp\@tempboxa\z@
+  \ifodd\c@page                                 \pcol@swapcolumnfalse \fi
+  \ifnum\pcol@ncolleft<\pcol@ncol\else          \pcol@swapcolumnfalse \fi
+  \ifpcol@output\else \ifpcol@havelastpage\else \pcol@swapcolumnfalse \fi\fi
+  \@tempcnta\c@page
+  \ifpcol@paired\else \advance\@tempcnta\@ne    \pcol@swapcolumnfalse \fi
+  \ifpcol@swapcolumn \pcol@outputpage@r\c@page \pcol@outputpage@l\@tempcnta
+  \else              \pcol@outputpage@l\c@page \pcol@outputpage@r\@tempcnta
+  \fi
+  \global\pcol@havelastpagefalse \gdef\pcol@bg@preposttop@left{0pt}%
+  \global\let\pcol@bg@preposttop@right\pcol@bg@preposttop@left
+  \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@outputpage@l}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for shipping out left parallel-pages.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for column-separating rule drawing and background
+%	 painting in left parallel-pages.}

+% \changes{v1.34}{2018/05/07}
+% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}

+% \begin{macro}{\pcol@outputpage@r}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for shipping out right parallel-pages.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for column-separating rule drawing and background
+%	 painting in right parallel-pages.}

+% \begin{macro}{\pcol@outputpage@ev}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@outputpage@l!\arg{page}$, used solely in our own
+% version of \!\@outputpage!, at first lets \!\c@page! have $\arg{page}$
+% which definitely has the value that \!\c@page! had when we start
+% \!\@outputpage!.  That is, even when this macro is invoked after
+% \!\pcol@outputpage@r! due to swapped \parapag{}ing,
+% 

+% \Index{column-swapping}
+% 

+% this assignment cancels the increment of \!\c@page! done in \LaTeX's
+% \!\@outputpage! or in other word \!\pcol@@outputpage! because in this case
+% \parapag{}es are \paired{}.  Then we make \!\@themargin! \!\let!-equal to
+% \!\evensidemargin! if two-side typesetting is in effect and \!\c@page! is
+% even, or to \!\oddsidemargin! otherwise for the reference in
+% \!\pcol@outputpage@ev! as shown shortly.
+% 
+% Next, if \bgpaint{} took place in \!\@outputpage!, we let \!\everyvbox!
+% have the macro invocation $\!\pcol@outputpage@ev!\<b_l\>$ to be expanded
+% to the following sequence so that they are the leading materials in the
+% \!\vbox! to be \!\shipout!; examination if the document is processed by a
+% Japanese \LaTeX{} named p\LaTeX{} and then, if so, a control sequence
+% \!\yoko! to put materials naturally; the painted \bground{} $b_l$ shifted
+% right by \!\@themargin!; \!\nointerlineskip!  to inhibit \!\baselineskip!
+% insertion after $b_l$; emptying \!\everyvbox! to ensure nothing will be
+% inserted into internal \!\vbox!es; and the assignment of \!\yoko! to
+% \!\let! it be \!\relax! if necessary.  This trick with \!\everyvbox! is
+% necessary\footnote{

+% 

+% Unless we rewrite \CSIndex{@outputpage}.}
+% 

+% because $b_l$ should be put {\em before} \!\pcol@@outputpage! puts the
+% page header, or the header would be overlaid by regions, e.g.,
+% $\bgr_{\{t,T\}}$ in natural cases.
+% 
+% The tricky elements to handle \!\yoko! in the sequence is necessary for
+% p\LaTeX{} whose \!\@outputpage! has \!\yoko! as the first element of the
+% \!\vbox! to be \!\shipout!, because \!\yoko! must be the first element of
+% a box but our \!\everyvbox! to put \bground{} would make it non-first.
+% That is by the tricky elements, the \!\vbox! should have \!\yoko! as the
+% first element from \!\everyvbox! and then that put by p\LaTeX's
+% \!\@outputpage! is nullified by \!\let!\!\yoko!\!\relax! in the
+% \!\everyvbox! just for the \!\vbox! to be shipped out.  On the other hand
+% in ordinary \LaTeX, \!\yoko! does not appear in the \!\vbox! or is
+% modified.  The examination of the use of p\LaTeX{} is also trickily done
+% by comparing the expansion results of \!\meaning!\!\yoko! and
+% \!\string!\!\yoko!.  Since the former results in the tokens ``\!\yoko!''
+% which \!\string!\!\yoko!  gives us iff \!\yoko! is a primitive of
+% underlying \TeX{} being p\TeX{} if so, the comparison should give us
+% equality iff p\LaTeX{} is in use\footnote{

+% 

+% Unless some other \TeX{} has a primitive named \CSIndex{yoko}.  This
+% examination is more strict than that with \CSIndex{pfmtname} for
+% \CSIndex{ifpcol@bfbottom}.}.
+% 
+% Then we invoke \!\pcol@@outputpage! being (p)\LaTeX's original version of
+% \!\@outputpage! to ship out \!\@outputbox! finally.
+% 
+% The macro \!\pcol@outputpage@r!$\arg{page}$ performs similar operations but
+% it does them only when $\!\pcol@rightpage!\neq\bot$ to mean we are in an
+% \env{paracol} environment with \parapag{}ing or outside it but in the page
+% in which it resides.  Other differences are as follows; $\arg{page}$ can
+% be $\page(p)+1$ for \npaired{} right \parapag{}es; \!\@outputbox! is
+% locally made \!\let!-equal to \!\pcol@rightpage! prior to the invocation
+% of \!\pcol@@outputpage!; and $b_r$ is given to \!\pcol@outputpage@ev! as
+% its argument.
+% 

+%    \begin{macrocode}
+\def\pcol@outputpage@l#1{%
+  \pcol@Logstart{\@outputpage{left}}%
+  \global\c@page#1\relax
+  \let\@themargin\oddsidemargin
+  \if@twoside\ifodd\c@page\else \let\@themargin\evensidemargin \fi\fi
+  \if@tempswa \everyvbox{\pcol@outputpage@ev\pcol@tempboxa}\fi
+  \pcol@@outputpage
+  \pcol@Logend{\@outputpage{left}}}
+\def\pcol@outputpage@r#1{%
+  \begingroup
+  \ifvoid\pcol@rightpage\else
+    \global\c@page#1\relax
+    \let\@outputbox\pcol@rightpage
+    \pcol@Logstart{\@outputpage{right}}%
+    \let\@themargin\oddsidemargin
+    \if@twoside\ifodd\c@page\else \let\@themargin\evensidemargin \fi\fi
+    \ifpcol@bg@painted \everyvbox{\pcol@outputpage@ev\@tempboxa}\fi
+    \pcol@@outputpage
+    \pcol@Logend{\@outputpage{right}}%
+  \fi
+  \endgroup}
+\def\pcol@outputpage@ev#1{%
+  \edef\reserved@a{\meaning\yoko}\edef\reserved@b{\string\yoko}%
+  \ifx\reserved@a\reserved@b \yoko\fi
+  \moveright\@themargin\box#1\nointerlineskip \everyvbox{}%
+  \ifx\reserved@a\reserved@b \let\yoko\relax \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% 
+% \section{Starting New Column-Page}
+% \label{sec:imp-startcolumn}
+% 
+% \begin{macro}{\pcol@startcolumn}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add \cs{@colht} and \cs{@tempdimb} as the first and third argument of
+%	 \cs{pcol@shrinkcolbyfn}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Fix the memory leak caused by mistakingly preserving $\pi^f(p)$
+%	 when $p\EQ p_t$.}
+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+% The macro $\!\pcol@startcolumn!\arg{f}$ is invoked from \!\pcol@output!
+% with $f=1$ and \!\pcol@freshpage! with $f=0$ to start a new \colpage.
+% This macro has two additional functions to \LaTeX's \!\@startcolumn!, one
+% for \Scfnote{}s and the other for coloring.
+% 
+% First, if the page $p$ in which the new \colpage{} resides has \Scfnote{}s
+% in $\pp^f(p)=\!\pcol@footins!$ because the column is not the leading one,
+% 

+% \Index{leading column}

+% 

+% we temporarily shrink \!\@colht! and \!\@colroom! by the space required to
+% put $\pp^f(p)$ by \!\pcol@shrinkcolbyfn! during the trial of deferred
+% float placement, remembering the existence of the footnotes by letting
+% $\!\@tempdimb!=-\!\skip!\!\pcol@footins!$ which should be 0 otherwise.
+% This shrinkage is essentially required when $p<\ptop$ because $\pp^f(p)$
+% has been fixed to be a part of $p$ and thus deferred floats cannot push
+% footnotes down to succeeding pages.  In the case of $p=\ptop$, the
+% shrinkage is also desirable to avoid unnecessary pushing down of footnotes
+% which \TeX{} has decided to be in $p$.
+% 
+% Then after trying put deferred floats in the \colpage{} by \!\@tryfcolumn!
+% and \!\pcol@trynextcolumn! as done in \LaTeX's \!\@startcolumn!, we
+% \!\insert! $\pp^f(p)$, if it is has some footnoes, by letting \!\footins!
+% have it by \!\pcol@getcurrfoot! so that \TeX{} will be aware of the
+% footnotes when it examines the page break of the \colpage{}.  That is, if
+% $p<\ptop$ the \!\insert!ion is to keep the vertical space for $\pp^f(p)$ in
+% the building process of the \colpage{} in $p$ because any \Scfnote{s}
+% cannot be added to $p$ any more, and thus $\pp^f(p)$ is preserved until
+% the page $p$ is shipped out.  On the other hand if $p=\ptop$, \Scfnote{s}
+% in $p$ can grow further and thus \!\insert!ed footnotes will be captured
+% again by \!\pcol@output@switch! or \!\pcol@startpage!.  Therefore, if
+% $p=\ptop$, we release $\pp^f(p)$ to \!\@freelist!.
+% 
+% Then if $p=\ptop$, we also \!\insert! deferred footnotes in $\df$ until
+% their total height reaches \!\@colht! by \!\pcol@deferredfootins! if $f=1$
+% to mean this macro is invoked from \!\pcol@output!\footnote{

+% 

+% The \cs{insert}ion of $\pp^f(p)$ also requiers $f=1$ but this examination
+% is redundant because $\pp^f(p)=\bot$ definately if $f=0$.}.
+% 

+% Note that the deferred footnote \!\insert!ion in the case of $f=0$ will
+% be done afterward when \!\pcol@freshpage! does \!\pcol@restartcolumn! at
+% its tail.  Also note that \!\pcol@deferredfootins! examines if
+% $\!\@tempdimb!=0$ to mean $\pp^f(p)=\bot$ and thus \!\skip!\!\footins!
+% should be taken into account in its extraction of the footnotes from $\df$.
+% 
+% Then after restoring \!\@colht! and canceling the temporary shrinkage of
+% \!\@colroom!, we invoke \!\pcol@savecolorstack! to save \colpage{}'s
+% \colorctext{} into $\csts$ so that coloring \!\special!s to reestablish
+% $\csts$ will be put at its top if it has something when we leave it.
+% 

+%    \begin{macrocode}
+%% Starting New Column Page
+
+\def\pcol@startcolumn#1{%
+  \@tempdima\@colht \@tempdimb\z@
+  \ifvoid\pcol@footins\else
+    \pcol@shrinkcolbyfn\@colht\pcol@footins\@tempdimb
+  \fi
+  \global\@colroom\@colht
+  \@tryfcolumn\@deferlist
+  \if@fcolmade\else
+    \pcol@trynextcolumn
+    \ifpcol@scfnote \ifnum#1>\z@
+      \ifvoid\pcol@footins\else
+        \edef\pcol@currfoot{\pcol@footins}%
+        \pcol@getcurrfoot\copy
+        \pcol@Log\pcol@startcolumn{insert}\footins
+        \insert\footins{\unvbox\footins}%
+        \ifnum\pcol@page=\pcol@toppage
+          \pcol@Fb
+          \@cons\@freelist\pcol@footins
+          \pcol@Fe{startcolumn(pagefn)}%
+        \fi
+      \fi
+      \ifnum\pcol@page=\pcol@toppage
+        \pcol@deferredfootins\pcol@startcolumn \fi
+    \fi\fi
+  \fi
+  \advance\@tempdima-\@colht
+  \global\advance\@colroom\@tempdima
+  \global\advance\@colht\@tempdima
+  \pcol@savecolorstack}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@trynextcolumn}
+% \changes{v1.2-2}{2013/05/11}
+%	{No change in the code itself but its explanation is modified
+%	 according to the drastic redesign of \cs{pcol@startcolumn}.}

+% 

+% The macro \!\pcol@trynextcolumn! is invoked from \!\pcol@startcolumn! and
+% \!\pcol@flush~column! to try to move deferred floats in \!\@deferlist!
+% into \!\@toplist! or \!\@botlist!.  The body of this macro is perfectly
+% equivalent to the \cs{else} part of \CSIndex{if@fcolmade} in \LaTeX's
+% \!\@startcolumn!.
+% 

+%    \begin{macrocode}
+\def\pcol@trynextcolumn{\begingroup
+  \let\reserved@b\@deferlist
+  \global\let\@deferlist\@empty
+  \let\@elt\@scolelt
+  \reserved@b
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Background Painting}
+% \label{sec:imp-bgpaint}
+% 
+% \begin{macro}{\pcol@bg@from}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@to}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

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

+%    \begin{macrocode}
+%% Background Painting
+
+\let\pcol@bg@to\pcol@ncol
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \KeepSpace{4}
+% \begin{macro}{\pcol@bg@paintpage}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@paintpage}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@paintcolumns}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@paintcolumns}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@paintbox}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@paintbox}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

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

+% \begin{quote}\raggedright
+% \!\pcol@outputelt!\Tie(|Ff|),
+% \!\pcol@ioutputelt!\Tie(|Nn|, |Ff|),
+% \!\pcol@buildcselt!\Tie(|Ss|),
+% \!\pcol@output@start!\Tie(|Pp|),
+% \!\pcol@output@clear!\Tie(|Ff|),
+% \!\pcol@makeflushedpage!\Tie(|Ff|),
+% \!\pcol@imakeflushedpage!\Tie(|Nn|),
+% \!\pcol@output@end!\Tie(|Nn|).
+% \end{quote}
+% 

+% The macro \!\@outputpage! also uses the function but \!\pcol@bg@@paintbox!
+% explicitly with $A=|Pp|$.  Therefore \!\pcol@bg@@paintbox! invokes
+% \!\pcol@bg@paint@i! with \!\pcol@bg@paint@ii!  giving it $A_b=A$ and
+% $A_g=A_c=\emptyset$.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@@paintpage{%
+  \pcol@bg@paint@i{%
+    \pcol@bg@paint@ii{TBLR}{G}{C}\pcol@bg@paint@ii{tblr}{}{}}}
+\def\pcol@bg@@paintcolumns{\pcol@bg@paint@i{\pcol@bg@paint@ii{}{g}{c}}}
+\def\pcol@bg@@paintbox#1{\pcol@bg@paint@i{\pcol@bg@paint@ii{#1}{}{}}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@bg@paint@i}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@bg@paint@i!\Arg{body}$ is used in
+% \!\pcol@bg@@paintpage!, \!\pcol@bg@@paint~columns! and
+% \!\pcol@bg@@paintbox! to paint \bground{}s by a sequence of
+% \!\pcol@bg@paint@ii! specified in $\arg{body}$.  The painted \bground{} is
+% built in \!\@tempboxa! being a \!\vtop! having a null \!\vskip! as its
+% first element so that everything put in the box is below its reference
+% point at its top.  Then, before invoking \!\pcol@bg@paint@ii! in
+% $\arg{body}$, we do the followings;  \!\global!ly let
+% $\CSIndex{ifpcol@bg@painted}=\false$ to indicate so far any painted
+% \bground{} are produced;  make \!\pcol@bg@leftmargin! \!\let!-equal
+% to \!\pcol@lrmargin! to use this \!\dimen! register locally with the
+% more appropriate alias;  negate \!\pagerim! locally to calculate $\HT$
+% easily;  decrement $\CBto$ by one locally for the column scanning loop for
+% $c\In\CBfrom{\CBto{-}1}$ in \!\pcol@bg@paint@ii!;  and \!\offinterlineskip!
+% to inhbit inter-line \!\baselineskip! insertion in the box.  Then after
+% the invocation of the sequence of \!\pcol@bg@paint@ii! in $\arg{body}$ and
+% closing the box, we let the height, depth and width of the box be 0 so
+% that it does not occupy any real space in the outer box in which the box
+% is put.  Finally, if $\CSIndex{ifpcol@bg@painted}=\true$ meaning that some
+% painted \bground{}s are built in the box, we put the box into the outer
+% box surrounding it by \!\nointerlineskip! to inhibit inter-line
+% \!\baselineskip! insertion before and after it.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@paint@i#1{%
+  \setbox\@tempboxa\vtop{\vskip\z@
+    \global\pcol@bg@paintedfalse
+    \let\pcol@bg@leftmargin\pcol@lrmargin
+    \pagerim-\pagerim \advance\pcol@bg@to\m@ne
+    \offinterlineskip #1}%
+  \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa\z@
+  \ifpcol@bg@painted \nointerlineskip \box\@tempboxa \nointerlineskip \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@bg@paint@ii}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@bg@paint@ii!\Arg{A_b}\Arg{A_g}\Arg{A_c}$ appears only
+% in the argument of \!\pcol@bg@paint@i! used in
+% \!\pcol@bg@@paintpage!, \!\pcol@bg@@paintcolumns! and
+% \!\pcol@bg@@paintbox! to paint \bground{}s of regions $\bgr_a$ for
+% $a\in{}A_b\subseteq\{T,B,L,R,S,F,N,P,t,b,l,r,s,f,n,p\}$, $\bgr_a^c$ for
+% $a\in{}A_g\subseteq\{G,g\}$ and $c\In\CBfrom{\Cto{-}1}$, and $\bgr_a^c$ for
+% $a\in A_c\subseteq\{C,c\}$ and $c\In\CBfrom\CBto$.
+% 
+% First we invoke \!\pcol@bg@swappage! with \CSIndex{ifpcol@bg@swap} to
+% let \!\pcol@bg@left~margin! and \CSIndex{ifpcol@bg@@swap} have values
+% accorging to \CSIndex{ifpcol@bg@swap}, \CSIndex{if@twoside} and the parity
+% of $\page(p)$.  Then we invoke $\!\pcol@bg@paintregion!\arg{a}\arg{c}$ for
+% all $a\in A_b$ and $c=-1$ to paint the \bground{} of $\bgr_a$.  Second, we
+% invoke \!\pcol@bg@swappage! again but with \CSIndex{ifpcol@swapcolumn}
+% instead of \CSIndex{ifpcol@bg@swap}, and \!\pcol@bg@paintregion! as well
+% but for $a\in\{A_g,A_c\}$ and $c\In\CBfrom{\CBto{-}1}$.  Third and
+% finally, we make yet another invocation of \!\pcol@bg@paintregion! for
+% $a\in A_c$ and $c=\CBto-1$.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@paint@ii#1#2#3{%
+  \pcol@bg@swappage\ifpcol@bg@swap\fi
+  \@tfor\reserved@b:=#1\do{\pcol@bg@paintregion\reserved@b\m@ne}%
+  \pcol@bg@swappage\ifpcol@swapcolumn\fi
+  \@tfor\reserved@b:=#2#3\do{%
+    \pcol@currcol\pcol@bg@from \@whilenum\pcol@currcol<\pcol@bg@to\do{%
+      \pcol@bg@paintregion\reserved@b\pcol@currcol
+     \advance\pcol@currcol\@ne}}%
+  \@tfor\reserved@b:=#3\do{\pcol@bg@paintregion\reserved@b\pcol@currcol}}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@bg@swappage}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@bg@swappage!\arg{if}\cs{fi}$ is used solely in
+% \!\pcol@bg@paint@ii! but twice with $\arg{if}=\CSIndex{ifpcol@bg@swap}$
+% and then with $\arg{if}=\CSIndex{ifpcol@swapcolumn}$, to let
+% \!\pcol@bg@leftmargin! and \CSIndex{ifpcol@bg@@swap} have values for
+% \mirror{}ing according to the truth values of $\arg{if}$ and
+% \CSIndex{if@twoside} and the parity of $\page(p)$ of the page $p$ for
+% which \bgpaint{} is taking place.  That is, they are let have the values
+% as follows.
+% 

+% \begin{eqnarray*}
+% W&=&\cases{\CSIndex{oddsidemargin}&
+%              $\page(p)\bmod2=1\;\lor\CSIndex{if@twoside}=\false$\cr
+%            \CSIndex{evensidemargin}&
+%              $\page(p)\bmod2=0\;\land\CSIndex{if@twoside}=\true$}\\
+% \rlap{$\displaystyle(\!\pcol@bg@leftmargin!,\CSIndex{ifpcol@bg@@swap})$}
+%   \phantom{W}\\
+% &=&\cases{(W,\;\false)&$\page(p)\bmod2=1\lor\;\arg{if}=\false$\cr
+%           (\WP-(W+\WT+2\,|in|),\;\true)&
+%             $\page(p)\bmod2=\land\;\arg{if}=\true$}
+% \end{eqnarray*}
+% 

+% Note that $\WP-(W+\WT+2\,|in|)$ means the right margin width minus 1\,|in|
+% with given left margin width $W$, and thus
+% $\WM=\!\pcol@bg@leftmargin!+1\,|in|$ gives us the right margin width we
+% need in \mirror{}ed \bgpaint.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@swappage#1#2{%
+  \pcol@bg@leftmargin\oddsidemargin \pcol@bg@@swapfalse
+  \ifodd\c@page\else
+    \if@twoside \pcol@bg@leftmargin\evensidemargin \fi
+    #1% \ifpcol@{bg@swap,swapcolumn}
+    \pcol@bg@@swaptrue
+    \advance\pcol@bg@leftmargin\textwidth \advance\pcol@bg@leftmargin2in
+    \advance\pcol@bg@leftmargin-\paperwidth
+    \pcol@bg@leftmargin-\pcol@bg@leftmargin
+    #2% \fi
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@bg@paintregion}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@paintregion@i}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@bg@paintregion!\arg{a}\arg{c}$ is used only in
+% $\!\pcol@bg@paint@ii!\Arg{A_b}\Arg{A_g}\Arg{A_c}$ but as many times as
+% $\Abs{A_b}+\Abs{A_g}(\CBto-\CBfrom-1)+\Abs{A_c}(\CBto-\CBfrom)$ to paint
+% \bground{} region $\bgr_a^{[c]}$ specified by $|\pcol@bg@@|{\cdot}a$
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@@}

+% 

+% with color $\bgc_a^c=|\pcol@bg@color@|{\cdot}a{\cdot}|@|{\cdot}c$
+% 

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% 

+% or, if it is undefined, $\bgc_a=|\pcol@bg@color@|{\cdot}a$.
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+%
+% If $\bgr_a^c$ or $\bgr_a$ is defined, the painted \bground{} is built in
+% \!\@tempboxa! with \!\vtop! having null vertical skip at its top and by
+% $\!\pcol@bg@paintregion@i!\Arg{F_x}\Arg{F_y}\Arg{F_w}\Arg{F_h}$ where
+% the arguments are defined in the body of the macro $|\pcol@bg@@|{\cdot}a$
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@@}

+% 

+% and thus we need triple \!\expandafter! to give them to the macro.  Prior
+% to the invocatoin of the macro, we let $\!\reserved@a!=a'$ have
+% $a{\cdot}|@|{\cdot}c$ if $\bgc_a^c$ is defined for $a\in\{G,C,g,c\}$, or
+% $a$ otherwise definitely for $a\notin\{G,C,g,c\}$.
+% 
+% Then \!\pcol@bg@paintregion@i! calculates $x_0=\!\@tempdima!$,
+% $y_0=\!\@tempdimb!$, $x_1=\!\@tempdimc!$ and $y_1=\!\dimen@!$ of the
+% region $\bgr_a^{[c]}$ by $\!\pcol@bg@calculate!\arg{z}\arg{z_0}\Arg{F}$
+% giving it
+% $(z,z_0,F)\in\{(x_0,0,F_x),(y_0,0,F_y),(x_1,x_0,F_w),(y_1,y_0,F_h)\}$,
+% where $(x_0,y_0)$ and $(x_1,y_1)$ is the left-top and right-bottom corner
+% of the painting region in the text-area coordinate, i.e., left-right and
+% top-down coordinate whose origin is at the left-top corner of the leftmost
+% column.  Next we modify $\{x,y\}_{\{0,1\}}$ for \bgext{} by
+% $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ with $(z,s,d)\in
+% \{(x_0,\hbox{`|-|'},|l|),(y_0,\hbox{`|-|'},|t|),
+% (x_1,\emptyset,|r|),\~(y_1,\emptyset,|b|)\}$.
+% 
+% Now we have $[(x_0,y_0)(x_1,y_1)]$ and thus, if not \mirror{}ed, we place
+% $\bgr_a^{[c]}$ at $(x_0,y_0)$ by a vertical skip of $y_0$ and shifting a
+% \!\hbox! for the region right by $x_0$ by \!\moveright!, and paint the box
+% putting a \!\vrule! of $(x_1-x_0)$ wide and $(y_1-y_0)$ tall, letting
+% \!\current@color! have $\bgc_r^{[c]}=|\pcol@bg@colr|{\cdot}a'$ and then
+% invoking \!\pcol@set@color! being the orinigal definition of
+% \!\set@color!.
+% 

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% 

+% On the other hand if \mirror{}ing is to be done, the region should be
+% $[(\WT{-}x_1,y_0)(\WT{-}x_0,y_1)]$ and thus the shift amount for
+% \!\moveright! of the \!\hbox! is $(\WT-x_1)$.
+% 
+% Then after \!\pcol@bg@paintregion@i! finshes its work,
+% \!\pcol@bg@paintregion! lets the switch
+% \CSIndex{ifpcol@bg@painted}${}=\true$ because we painted $\bgr_a^{[c]}$,
+% lets the height, depth and width of \!\@tempboxa!  be 0 to make it a
+% phantom, and then put it into the outside box opened by
+% \!\pcol@bg@paint@i!.  On the other hand, if neither $\bgc_r^c$ nor
+% $\bgc_r$ defined to mean the \bgpaint{} of the region is not specified, we
+% do nothing.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@paintregion#1#2{%
+  \@ifundefined{pcol@bg@color@#1@\number#2}%
+    {\def\reserved@a{#1}}{\edef\reserved@a{#1@\number#2}}%
+  \@ifundefined{pcol@bg@color@\reserved@a}\relax
+    {\setbox\@tempboxa\vtop{\vskip\z@
+       \expandafter\expandafter\expandafter
+         \pcol@bg@paintregion@i\csname pcol@bg@@#1\endcsname}%
+     \global\pcol@bg@paintedtrue
+     \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa\z@ \box\@tempboxa}}
+\def\pcol@bg@paintregion@i#1#2#3#4{%
+  \pcol@bg@calculate\@tempdima\z@{#1}%
+  \pcol@bg@calculate\@tempdimb\z@{#2}%
+  \pcol@bg@calculate\@tempdimc\@tempdima{#3}%
+  \pcol@bg@calculate\dimen@\@tempdimb{#4}%
+  \pcol@bg@addext\@tempdima{-}{l}\pcol@bg@addext\@tempdimc{}{r}%
+  \pcol@bg@addext\@tempdimb{-}{t}\pcol@bg@addext\dimen@{}{b}%
+  \vskip\@tempdimb
+  \ifpcol@bg@@swap
+    \advance\@tempdima-\@tempdimc \@tempdima-\@tempdima
+    \advance\@tempdimc-\textwidth \@tempdimc-\@tempdimc
+    \moveright\@tempdimc\hbox{%
+      \advance\dimen@-\@tempdimb
+      \edef\current@color{\@nameuse{pcol@bg@color@\reserved@a}}\pcol@set@color
+      \vrule\@width\@tempdima\@height\dimen@}%
+  \else
+    \moveright\@tempdima\hbox{%
+      \advance\@tempdimc-\@tempdima \advance\dimen@-\@tempdimb
+      \edef\current@color{\@nameuse{pcol@bg@color@\reserved@a}}\pcol@set@color
+      \vrule\@width\@tempdimc\@height\dimen@}%
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \KeepSpace{3}
+% \begin{macro}{\pcol@bg@calculate}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@advance}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@negative}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@nadvance}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@dimen}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@bg@calculate!\arg{z}\arg{z_0}\arg{F}$ is used in
+% \!\pcol@bg@paintregion@i! and \!\pcol@bg@addext! to accumulate dimensional
+% values specified in $F$ into a \!\dimen! register $z$ with initial value
+% $z_0$.  The specificatoin $F$ is a sequence of $\!\@elt!\Arg{f}$ to add $f$
+% to $z$, $\!\pcol@bg@negative!\Arg{F^-}$ to subtract the amount specified
+% by $F^-$ from $z$, or macros expanded to either of them.
+% 
+% The macro makes \!\pcol@bg@dimen! \!\let!-equal to $z$ and \!\@elt! to
+% \!\pcol@bg@advance!, lets $z=z_0$, and then does what is specified in $F$\@.
+% Therefore, $\!\@elt!\arg{f}$ appearing directly or indirectly in $F$ does
+% $\!\advance!\arg{z}\arg{f}$ for the accumulation.  On the other hand,
+% \!\pcol@bg@negative! makes \!\@elt! \!\let!-equal to \!\pcol@bg@nadvance!
+% to let $\!\@elt!\arg{f}$ do $\!\advance!\arg{z}{-}\arg{f}$ for
+% subtraction, does $F^-$, and then remake $\!\@elt!=\!\pcol@bg@advance!$.
+% Note that $f$ may be expanded to a negative amount having `|-|' its
+% beginning to results in $\!\@elt!\arg{f}$ expanded to
+% $\!\advance!\arg{z}{-}{-}\arg{f'}$ with some positive amount $f'$, but
+% this double negation is legitimate in \TeX{} and is equivalent to
+% $\!\advance!\arg{z}\arg{f'}$.  The macro \!\pcol@bg@negative! is used in
+% the following macros.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@bg@ext@inf@l!,
+% \!\pcol@bg@ext@inf@r!,
+% \!\pcol@bg@ext@inf@t!,
+% \!\pcol@bg@@t!,
+% \!\pcol@bg@@b!,
+% \!\pcol@bg@@l!,
+% \!\pcol@bg@@r!,
+% \!\pcol@bg@@n!,
+% \!\pcol@bg@@p!.
+% \end{quote}
+% 

+%    \begin{macrocode}
+\def\pcol@bg@calculate#1#2#3{\let\pcol@bg@dimen#1\relax
+  \let\@elt\pcol@bg@advance \pcol@bg@dimen#2\relax #3}
+\def\pcol@bg@negative#1{\let\@elt\pcol@bg@nadvance #1\relax
+  \let\@elt\pcol@bg@advance}
+\def\pcol@bg@advance#1{\advance\pcol@bg@dimen#1\relax}
+\def\pcol@bg@nadvance#1{\advance\pcol@bg@dimen-#1\relax}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{3}
+% \begin{macro}{\pcol@bg@addext}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@ext@inf@l}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@ext@inf@r}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@ext@inf@t}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@ext@inf@b}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The macro $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ is used only in
+% \!\pcol@bg@paintregion@i! but four times with $(z,s,d)\in
+% \{(x_0,\hbox{`|-|'},|l|),(y_0,\hbox{`|-|'},|t|),
+% (x_1,\emptyset,|r|),\~(y_1,\emptyset,|b|)\}$, to perform \bgext{} on a
+% \!\dimen! register $z$.
+% 
+% First the macro gets $e=|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'
+% \in e_a^{[c]}(\{x,y\}^{\{{+},{-}\}})$
+% 

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}

+%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}

+% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% 

+% where $a'=\!\reserved@a!\~\in\{a{\cdot}|@|{\cdot}c,a\}$.  Then if
+% $e<9000\PT$ being a finite \bgext, we let $z\gets z\pm e$
+% according to $s$, i.e. $+$ if $s=\emptyset$ while $-$ if $s={}$`|-|'.
+% Otherwise, i.e., $e\geq9000\PT$ for a infinite \bgext, let $e'$
+% be the value shown below by invoking $|\pcol@bg@ext@inf@|{\cdot}d$
+% 

+% \SpecialArrayMainIndex{d}{\pcol@bg@ext@inf@}
+% $$
+% e'=\cases{-(\WM-\WR)&$d=|l|$\cr
+%           \WP-(\WM-\WR)&$d=|r|$\cr
+% 	    -(\HM-\HR)&$d=|t|$\cr
+% 	    \HP-(\HM-\HR)&$d=|b|$\cr}
+% $$
+% where $\WM-\WR$ is specified by \!\pcol@bg@pageleft! and $\HM-\HR$ by
+% \!\pcol@bg@pagetop!.  Then we let $z=e'\pm(e-10000\PT)$ according to $s$
+% again, i.e., move $z$ {\em inside\/} by $(10000\PT-e)$ from $e'$.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@addext#1#2#3{%
+  \dimen@ii\@nameuse{pcol@bg@ext@#3@\reserved@a}\relax
+  \ifdim\dimen@ii<9000\p@\relax \advance#1#2\dimen@ii
+  \else
+    \pcol@bg@calculate#1\z@{\@nameuse{pcol@bg@ext@inf@#3}}%
+    \advance\dimen@ii-\@M\p@ \advance#1#2\dimen@ii
+  \fi}
+\def\pcol@bg@ext@inf@l{\pcol@bg@negative\pcol@bg@pageleft}
+\def\pcol@bg@ext@inf@r{\pcol@bg@negative\pcol@bg@pageleft
+  \pcol@bg@paperwidth}
+\def\pcol@bg@ext@inf@t{\pcol@bg@negative\pcol@bg@pagetop}
+\def\pcol@bg@ext@inf@b{\pcol@bg@negative\pcol@bg@pagetop
+  \pcol@bg@paperheight}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{7}
+% \begin{macro}{\pcol@bg@paperwidth}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@paperheight}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@pageleft}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@pagetop}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@textheight}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@columnleft}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@columnright}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@columnwidth}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@columnsep}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% The following macros specify the whole or a part of
+% $F\in\{F_x,F_y,F_w,F_h\}$ being the body of $|\pcol@bg@@|{\cdot}a$ for
+% \bgpaint{} regions $\bgr_a^{[c]}$.
+% 

+% \begin{eqnarray*}
+% \!\pcol@bg@paperwidth!&=&	\WP-2\WR=\!\paperwidth!-2\!\pagerim!
+% 	\quad(t,T,b,B,r,R)\\
+% \!\pcol@bg@paperheight!&=&	\HP-2\HR=\!\paperheight!-2\!\pagerim!
+% 	\quad(b,B)\\
+% \!\pcol@bg@pageleft!&=&	\WM-\WR=
+% 				(\!\pcol@bg@leftmargin!+1\,|in|)-\!\pagerim!\\
+% &	\rlap{$(t,T,b,B,l,L,r,R)$}\\
+% \!\pcol@bg@pagetop!&=&	\HM-\WR\\
+% 	&=&(\!\topmargin!+\!\headheight!+\!\headsep!+1\,|in|)-\!\pagerim!\\
+% &	\rlap{$(t,T,b,B)$}\\
+% \!\pcol@bg@textheight!&=&	\HT=\!\textheight!+\!\@maxdepth!\\
+% &	\rlap{$(b,B,l,L,r,R,C,G,n,N,p,P)$}\\
+% \!\pcol@bg@columnleft!&=&	\W_c=\sum_{d=\CBfrom}^{c-1}(w_c+g_c)
+% 	\quad(c,C)\\
+% \!\pcol@bg@columnright!&=&	\W_c+w_c=
+% 				\!\pcol@bg@columnleft!+\!\pcol@bg@columnwidth!\\
+% &	\rlap{$(g,G)$}\\
+% \!\pcol@bg@columnwidth!&=&	w_c=|\pcol@columnwidth|{\cdot}c
+% 	\quad(c,C)\\
+% \!\pcol@bg@columnsep!&=&	g_c=|\pcol@columnsep|{\cdot}c
+% 	\quad(g,G)
+% \end{eqnarray*}
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% Note that \!\pagerim! in $F$ means $-\!\pagerim!$ because its sign is
+% reversed by \!\pcol@bg@paint@i!.  The macros are used in
+% $|\pcol@bg@@|{\cdot}a$
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@@}

+% 

+% whose region identifier $a$ is shown in paretheses above, but besides them
+% \!\pcol@bg@paperwidth! is also used in \!\pcol@bg@ext@inf@r!,
+% \!\pcol@bg@paperheight! in \!\pcol@bg@ext@inf@b!, \!\pcol@bg@pageleft! in
+% \!\pcol@bg@ext@inf@l! and \!\pcol@bg@ext@inf@r!, and \!\pcol@bg@pagetop!
+% in \!\pcol@bg@ext@inf@t!  and \!\pcol@bg@ext@inf@b!.  Also note that
+% \!\pcol@bg@textheight! is used in \!\pcol@output@clear! while it is
+% temporarily redefined in \!\pcol@output@start! and \!\pcol@output@end!.
+% 
+%    \begin{macrocode}
+\def\pcol@bg@paperwidth{\@elt\paperwidth \@elt{2\pagerim}}
+\def\pcol@bg@paperheight{\@elt\paperheight \@elt{2\pagerim}}
+\def\pcol@bg@pageleft{\@elt{1in}\@elt\pcol@bg@leftmargin \@elt\pagerim}
+\def\pcol@bg@pagetop{\@elt{1in}\@elt\topmargin \@elt\headheight \@elt\headsep
+  \@elt\pagerim}
+\def\pcol@bg@textheight{\@elt\textheight \@elt\@maxdepth}
+\def\pcol@bg@columnleft{%
+  \@tempcnta\pcol@bg@from \@whilenum\@tempcnta<\pcol@currcol\do{%
+    \@elt{\@nameuse{pcol@columnwidth\number\@tempcnta}}%
+    \@elt{\@nameuse{pcol@columnsep\number\@tempcnta}}%
+   \advance\@tempcnta\@ne}}
+\def\pcol@bg@columnright{\pcol@bg@columnleft \pcol@bg@columnwidth}
+\def\pcol@bg@columnwidth{\@elt{\@nameuse{pcol@columnwidth\number\pcol@currcol}}}
+\def\pcol@bg@columnsep{\@elt{\@nameuse{pcol@columnsep\number\pcol@currcol}}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \KeepSpace{7}
+% \begin{macro}{\pcol@bg@preposttop}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@preposttop@left}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@preposttop@right}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@columntop}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@columnheight}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@floatheight}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@footnoteheight}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@spanningtop}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@spanningheight}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for background painting.}

+% 

+% Besides the macros shown above, $|\pcol@bg@@|{\cdot}a$ uses the following
+% macros defined by macros using \!\pcol@bg@paintpage!,
+% \!\pcol@bg@paintcolumns! or \!\pcol@bg@paintbox!.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@bg@preposttop! being \!\pcol@bg@preposttop@left! or
+% \!\pcol@bg@preposttop@right! for $a\in\{p,P\}$ by \!\@outputpage! and
+% \!\pcol@output@end!, the latter of which may define only the left one if
+% the closing environment is not \parapag{}ed.  That is, both of left and
+% right macros are usually equivalent, but the right one can be smaller than
+% the left if we have two or more (\lpage{}s of) \env{paracol} environments
+% in a page and the closing environment is not \parapag{}ed while some
+% others are.  In such case, \!\@outputpage! or \!\pcol@output@start!,
+% another macro referring to them, must paint the region below
+% \!\pcol@bg@preposttop@right! in the right page as a part of \preenv{} or
+% \postenv{} by \!\let!ting \!\pcol@bg@preposttop! be
+% \!\pcol@bg@preposttop@left! and \!\pcol@bg@preposttop@right! for the left
+% and right \parapag{}es respectively.  Both macros have common initial
+% value 0.
+% 
+% \item
+% \!\pcol@bg@columntop! and \!\pcol@bg@columnheight! for $a\in\{c,g\}$ by
+% \!\pcol@build~colseprule! and \!\pcol@buildcselt!.
+% 
+% \item
+% \!\pcol@bg@spanningtop! and \!\pcol@bg@spanningheight! for $a\in\{s,S\}$ by
+% \!\pcol@buildcselt!.
+% 
+% \item
+% \!\pcol@bg@floatheight! for $a\in\{f,F\}$ by \!\pcol@outputelt!,
+% \!\pcol@ioutputelt!, \!\pcol@output@clear! and \!\pcol@makeflushedpage!
+% 
+% \item
+% \!\pcol@bg@footnoteheight! for $a\in\{n,N\}$ by \!\pcol@ioutputelt!,
+% \!\pcol@imakeflushed~page! and \!\pcol@output@end!.
+% \end{itemize}
+% 
+%    \begin{macrocode}
+\def\pcol@bg@preposttop@left{0pt}
+\let\pcol@bg@preposttop@right\pcol@bg@preposttop@left
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{18}
+% \begin{macro}{\pcol@bg@@c}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@C}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@g}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@G}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@s}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@S}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@t}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@T}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@b}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@B}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@l}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@L}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@r}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@R}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@f}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@F}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@n}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@N}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@p}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% \begin{macro}{\pcol@bg@@P}
+% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}

+% 

+% The macros $|\pcol@bg@@|{\cdot}a$
+% 

+% \SpecialArrayMainIndex{a}{\pcol@bg@@}

+% 

+% define arguments $F_x$, $F_y$, $F_w$ and $F_h$ to be passed to
+% \!\pcol@bg@paintregion@i! in their bodies to calculate $(x_0,y_0)$ and
+% $(x_1{-}x_0,y_1{-}y_0)$ for regions $\bgr_a^{[c]}$ as shown below in the
+% form of $(x_0,y_0)+(x_1{-}x_0,y_1{-}y_0)$ (to have $(x_1,y_1)$), where
+% $H^c=\!\pcol@bg@columntop!$, $h^c=\!\pcol@bg@columnheight!$,
+% $H^s=\!\pcol@bg@spanningtop!$, $h^s=\!\pcol@bg@spanningheight!$,
+% $h^f=\!\pcol@bg@floatheight!$, $h^n=\!\pcol@bg@footnoteheight!$ and
+% $H^p=\!\pcol@bg@preposttop!$ calculated by macros which invoke \bgpaint{}
+% macros, while $s^n=\!\skip!\!\footins!$.
+% 

+% \begin{eqnarray*}
+% \bgr_c^c&\;:\;&(\W_c\;,\;H^c)\ +\ (w_c\;,\;h^c)\\
+% \bgr_C^c&:&(\W_c\;,\;0)\ +\ (w_c\;,\;\HT)\\
+% \bgr_g^c&:&((\W_c+w_c)\;,\;H^c)\ +\ (g_c\;,\;h^c)\\
+% \bgr_G^c&:&((\W_c+w_c)\;,\;0)\ +\ (g_c\;,\;\HT)\\
+% \bgr_{\{s,S\}}&:&(0\;,\;H^s)\ +\ (\WT\;,\;h^s)\\
+% \bgr_{\{t,T\}}&:&(-(\WM-\WR)\;,\;-(\HM-\HR))\ +\ ((\WP-2\WR)\;,\;\HM-\HR)\\
+% \bgr_{\{b,B\}}&:&(-(\WM-\WR)\;,\;\HT)\ +\ 
+%                  ((\WP-2\WR)\;,\;(\HP-2\HR)-((\HM-\HR)+\HT))\\
+% \bgr_{\{l,L\}}&:&(-(\WM-\WR)\;,\;0)\ +\ ((\WM-\WR)\;,\;\HT)\\
+% \bgr_{\{r,R\}}&:&(\WT\;,\;0)\ +\ ((\WP-2\WR)-((\WM-\WR)+\WT)\;,\;\HT)\\
+% \bgr_{\{f,F\}}&:&(0\;,\;0)\ +\ (\WT\;,\;h^f)\\
+% \bgr_{\{n,N\}}&:&(0\;,\;\HT-(h^n+s^n))\ +\ (\WT\;,\;h^n+s^n)\\
+% \bgr_{\{p,P\}}&:&(0\;,\;H^p)\ +\ (\WT\;,\;\HT-H^p)
+% \end{eqnarray*}
+% 

+%    \begin{macrocode}
+\def\pcol@bg@@c{%
+  {\pcol@bg@columnleft}%
+  {\@elt\pcol@bg@columntop}%
+  {\pcol@bg@columnwidth}%
+  {\pcol@bg@columnheight}}
+\def\pcol@bg@@C{%
+  {\pcol@bg@columnleft}%
+  {}%
+  {\pcol@bg@columnwidth}%
+  {\pcol@bg@textheight}}
+\def\pcol@bg@@g{%
+  {\pcol@bg@columnright}%
+  {\@elt\pcol@bg@columntop}%
+  {\pcol@bg@columnsep}%
+  {\pcol@bg@columnheight}}
+\def\pcol@bg@@G{%
+  {\pcol@bg@columnright}%
+  {}%
+  {\pcol@bg@columnsep}%
+  {\pcol@bg@textheight}}
+\def\pcol@bg@@s{%
+  {}%
+  {\pcol@bg@spanningtop}%
+  {\@elt\textwidth}%
+  {\pcol@bg@spanningheight}}
+\def\pcol@bg@@t{%
+  {\pcol@bg@negative\pcol@bg@pageleft}%
+  {\pcol@bg@negative\pcol@bg@pagetop}%
+  {\pcol@bg@paperwidth}%
+  {\pcol@bg@pagetop}}
+\def\pcol@bg@@b{%
+  {\pcol@bg@negative\pcol@bg@pageleft}%
+  {\pcol@bg@textheight}%
+  {\pcol@bg@paperwidth}%
+  {\pcol@bg@paperheight
+    \pcol@bg@negative{\pcol@bg@pagetop \pcol@bg@textheight}}}
+\def\pcol@bg@@l{%
+  {\pcol@bg@negative\pcol@bg@pageleft}%
+  {}%
+  {\pcol@bg@pageleft}%
+  {\pcol@bg@textheight}}
+\def\pcol@bg@@r{%
+  {\@elt\textwidth}%
+  {}%
+  {\pcol@bg@paperwidth
+    \pcol@bg@negative{\pcol@bg@pageleft \@elt\textwidth}}%
+  {\pcol@bg@textheight}}
+\def\pcol@bg@@f{%
+  {}%
+  {}%
+  {\@elt\textwidth}%
+  {\pcol@bg@floatheight}}
+\def\pcol@bg@@n{%
+  {}%
+  {\pcol@bg@textheight
+    \pcol@bg@negative{\pcol@bg@footnoteheight \@elt{\skip\footins}}}%
+  {\@elt\textwidth}%
+  {\pcol@bg@footnoteheight \@elt{\skip\footins}}}
+\def\pcol@bg@@p{%
+  {}%
+  {\@elt\pcol@bg@preposttop}%
+  {\@elt\textwidth}%
+  {\pcol@bg@textheight \pcol@bg@negative{\@elt\pcol@bg@preposttop}}}
+\let\pcol@bg@@S\pcol@bg@@s
+\let\pcol@bg@@T\pcol@bg@@t
+\let\pcol@bg@@B\pcol@bg@@b
+\let\pcol@bg@@L\pcol@bg@@l
+\let\pcol@bg@@R\pcol@bg@@r
+\let\pcol@bg@@F\pcol@bg@@f
+\let\pcol@bg@@N\pcol@bg@@n
+\let\pcol@bg@@P\pcol@bg@@p
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \KeepSpace{10}
+% \section{Special Output Routines}
+% \label{sec:imp-sout}
+% 
+% \subsection{Dispatcher}
+% \label{sec:imp-sout-disp}
+% 
+% \changes{v1.22}{2013/06/30}
+%	{\cs{pcol@op@cpush} was introduced for output request to push color
+%	 stack but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@cpush} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+%	{\cs{pcol@op@cpop} was introduced for output request to pop color
+%	 stack but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@cpop} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+%	{\cs{pcol@op@cset} was introduced for output request to set
+%	 $\gamma_0^c$ but removed in v1.34}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@cpop} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% 
+% \begin{macro}{\pcol@op@start}
+% \begin{macro}{\pcol@op@switch}
+% \begin{macro}{\pcol@op@flush}
+% \begin{macro}{\pcol@op@clear}
+% \begin{macro}{\pcol@op@end}
+% 

+% The macro $|\pcol@op@|{\cdot}f$ where $f\in
+% F=\{|start|,|switch|,|flush|,|clear|,|end|\}$ has
+% our own \!\outputpenalty! code less than $-10000$ to invoke the
+% corresponding macro $|\pcol@output@|{\cdot}f$.  The code macros are given
+% to \!\pcol@invokeoutput! as its argument by \!\pcol@zparacol! ($f=|start|$),
+% \!\pcol@switchcol! ($f=|switch|$), \!\pcol@visitallcols! ($f=|switch|$),
+% \!\pcol@com@flushpage! ($f=|flush|$), \!\pcol@com@clearpage!
+% ($f=|clear|$), \!\pcol@flushclear! ($f=|switch|$), and \!\endparacol!
+% ($f=|end|$) to set one of them into \!\outputpenalty!, so that the other
+% user \!\pcol@specialoutput! examines which special function is invoked.

+% 

+% \SpecialIndex{\pcol@output@start}

+% \SpecialIndex{\pcol@output@switch}

+% \SpecialIndex{\pcol@output@flush}

+% \SpecialIndex{\pcol@output@clear}

+% \SpecialIndex{\pcol@output@end}

+% 

+%    \begin{macrocode}
+%% Special Output Routines: Dispatcher
+
+\def\pcol@op@start{-10010}
+\def\pcol@op@switch{-10011}
+\def\pcol@op@flush{-10012}
+\def\pcol@op@clear{-10013}
+\def\pcol@op@end{-10014}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@op@mcpush} was introduced for coloring specified in math
+%	 mode but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@mcpush} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@op@mcpush@pone} was introduced for coloring specified in
+%	 math mode but removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@mcpush@pone} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@op@mcpop} was introduced for coloring specified in math
+%	 mode but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@mcpop} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@op@mcpop@pone} was introduced for coloring specified in
+%	 math mode but removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@op@mcpop@pone} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

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

+% \changes{v1.2-2}{2013/05/11}
+%	{Add footnote logging if $\cs{outputpenalty}\EQ-10004$.}

+% \changes{v1.22}{2013/06/30}
+%	{Add the invocation of \cs{pcol@output@}${\cdot}f$ for
+%	 $f\in\{\string\texttt{cpush},\string\texttt{cpop},
+% 	 \string\texttt{cset}\}$}
+% \changes{v1.24}{2013/07/27}
+%	{Add examination with $P_{\string\rm{push}}$ and $P_{\string\rm{pop}}$
+%	 and invocation of \cs{pcol@output@mcpush} and
+%	 \cs{pcol@output@mcpop}.}
 
+% \changes{v1.34}{2018/05/07}
+%	{Remove examinations related to $f\in\{{\tt cpush},{\tt cpop},{\tt
+%	 mcpush},{\tt mcpop}\}$.}

+% 

+% The macro \!\pcol@specialoutput! is invoked solely in \!\pcol@output! to
+% invoke our own or \LaTeX's special output routine.  It examines if
+% $P=\!\outputpenalty!\in\Set{\cs{pcol@op@}{\cdot}f}{f\in F}$ and then, if
+% so, before invoking $|\pcol@output@|{\cdot}f$, we rebuild \!\@holdpg!
+% removing \!\lastbox! and the last vertical skip as done in \LaTeX's
+% \!\@specialoutput!.  We also let $\!\outputpenalty!=-10000$\footnote{

+% 

+% It can be any value larger than -10004.}
+% 

+% so that \!\vsize! is correctly set to \!\@colroom! in the second half of
+% \!\pcol@output! after this macro finishes.
+% 
+% \hfuzz9pt
+% Otherwise, i.e., if $P\notin\Set{\cs{pcol@op@}{\cdot}f}{f\in{}F}$,
+% we simply invokes \LaTeX's \!\@specialoutput!\footnote{

+% 

+% With footnote logging if $\cs{outputpenalty}=-10004$.}.
+% 

+%    \begin{macrocode}
+\def\pcol@specialoutput{%
+  \ifnum\outputpenalty=\pcol@op@start\relax
+    \let\reserved@a\pcol@output@start
+  \else\ifnum\outputpenalty=\pcol@op@switch\relax
+    \let\reserved@a\pcol@output@switch
+  \else\ifnum\outputpenalty=\pcol@op@flush\relax
+    \let\reserved@a\pcol@output@flush
+  \else\ifnum\outputpenalty=\pcol@op@clear\relax
+    \let\reserved@a\pcol@output@clear
+  \else\ifnum\outputpenalty=\pcol@op@end\relax
+    \let\reserved@a\pcol@output@end
+  \else \let\reserved@a\@specialoutput
+  \fi\fi\fi\fi\fi
+  \ifnum\outputpenalty=-\@Miv\relax
+    \ifvoid\footins\else \pcol@Log\dummy{dummy}\footins \fi
+  \fi
+  \ifx\reserved@a\@specialoutput\else
+    \global\setbox\@holdpg\vbox{\unvbox\@holdpg \unvbox\@cclv
+      \setbox\@tempboxa\lastbox \unskip}%
+    \outputpenalty-\@M
+  \fi
+  \reserved@a}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \subsection{Building Starting Page} \label{sec:imp-sout-start}
+% 
+% \begin{macro}{\pcol@output@start}
+% \changes{v1.0}{2011/10/10}
+% 	{Change the order of operations.}

+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}

+% \changes{v1.0}{2011/10/10}
+%	{Add special operation in case of too small room for column-pages.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add initialization of $\string\mathit{\string\Phi}$ and
+%	 page-wise footnote output operations, and revise reflecting
+%	 the redesign of page context.}
 
+% \changes{v1.2-7}{2013/05/11}
+%	{Add \cs{pcol@outputtrue} to solve the \cs{output} request sneaking.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Include the effect of the separation of pre-environment bottom
+%	 floats and columns in the starting page into the check of too large
+%	 pre-envronment stuff.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Change the page builder for too tall pre-environment stuff from
+%	 \cs{pcol@makenormalcol} to \cs{@makecol} because the page should be
+%	 built by the ordinary mechanism.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Let $\cs{ifpcol@output}\EQ\string\mathit{false}$ temporarily before
+%	 the invocation of \cs{@outputpage} for too tall pre-environment
+%	 stuff because the page is considered as outside
+%	 \string\texttt{paracol} envrionments.}

+% \changes{v1.32-3}{2015/10/10}
+% 	{Add depth clearing of imported deferred floats in case that some of
+%	 them has \texttt{1sp}.}

+% \changes{v1.35-4}{2018/12/31}
+% 	{Add \cs{belowfootnoteskip} to $H_f$ being the space for the
+%	 non-merged pre-environment footnotes.}

+% 

+% The macro \!\pcol@output@start! is invoked solely from
+% \!\pcol@specialoutput! to process the special \!\output! request made in
+% \!\pcol@zparacol! and to build the {\em\Uidx\spage} from which parallel
+% columns start possibly with the stuff preceding \beginparacol{}, or
+% {\em\Uidx\preenv} in short.  First, we turn
+% $\CSIndex{ifpcol@output}=\true$ so that \!\output!  requests for page
+% breaks are processed by our own macros such as \!\pcol@makecol! hereafter.
+% Then we let $p=\pbase={\ptop}=0$ and $\PP=\emptyset$ because we have
+% nothing for $q<\ptop=0$.  We also move \!\@deferlist! to \!\@dbldeferlist!
+% and then let \!\@deferlist! be empty because all \cwise{} dererred floats
+% become \pwise{}.  In this float importation, as discussed in
+% item-(\ref{item:ovv-float-@output@start}) of
+% \secref{sec:imp-ovv-float}, we force all floats in the list have
+% depth 0 to ensure no one has |1sp| to conform our own and old-fashioned
+% \pwise{} float placement mechanism\footnote{

+% 

+% Though having \texttt{1sp} is almost imposiible.}.
+% 

+% We then and let $\df=\bot$ because we don't have any deferred footnotes.
+% 
+% Next we caculate $H=H_r-(H_m+H_f+H_b)$ where $H_r=\!\@colroom!$; $H_m$ is
+% the height-plus-depth of the main vertical list in \!\@holdpg!; $H_f$ is
+% the sum of \!\skip!\!\footins!, the height-plus-depth of \!\footins! and
+% \!\belowfootnoteskip!, if \!\footins! is not $\bot$ or 0 otherwise; and
+% $H_b=\!\textfloatsep!$ if the \preenv{} has bottom floats or 0 otherwise.
+% That is, $H$ is the room for each of \colpage{} in the \spage.  Then we
+% examine if $H<1.5\times\!\baselineskip!$ to mean \!\pcol@output!  would
+% force a page break with warning.  If so, we assume we have a page break
+% before \beginparacol{} to ship out \preenv{} to avoid the warning.
+% Therefore, we invoke \LaTeX's \!\@makecol!\footnote{

+% 

+% \Sloppy{2500}%
+% We can be unaware of our customization for \sync{}ation in
+% \CSIndex{pcol@combinefloats} because \CSIndex{pcol@textfloatsep} is
+% made $\infty$ by \CSIndex{pcol@zparacol}.}
+% 

+% giving it \!\@holdpg!  through \!\@cclv! to build the ship-out image in
+% \!\@outputbox!.  Then the box is passed to \!\@outputbox! for which we
+% temporarily let $\CSIndex{ifpcol@output}=\false$ because the page is
+% assumed to be outside the \env{paracol} environment having just started.
+% 
+% After that we invoke \!\pcol@startpage! to let it produce $\pp(\ptop)$ for
+% the \spage{} $\ptop=0$ letting $\!\pcol@currpage!$ be empty so that the
+% macro will not refer to it.  The page $\pp(0)$ is usually empty but can
+% have non-empty $\pp^i(0)$ with imported deferred floats which are now
+% \pwise.  Moreover, we can have two or more pages if deferred \pwise{}
+% floats produce \fpage{s}.  However, we can be unaware of these effects of
+% floats because the resulting $\PP^+$ with them is correct of course.
+% 
+% Then let $\!\topskip!=\!\pcol@topskip!$ being the value at \beginparacol,
+% and $\cs{ifpcol@}\~|firstpage|={\false}$, because we have the \spage{}
+% without \preenv{} and thus the first item of each column will be at its
+% top.
+% 

+% \CSINDEX{ifpcol@firstpage}
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Building First Page
+
+\def\pcol@output@start{%
+  \global\pcol@outputtrue
+  \global\pcol@page\z@ \global\pcol@toppage\z@ \global\pcol@basepage\z@
+  \global\let\pcol@pages\@empty
+  \global\let\@dbldeferlist\@deferlist \global\let\@deferlist\@empty
+  {\def\@elt##1{\global\dp##1\z@}\@dbldeferlist}%
+  \setbox\z@\box\pcol@topfnotes
+  \@tempdima\@colroom
+  \advance\@tempdima-\ht\@holdpg \advance\@tempdima-\dp\@holdpg
+  \ifvoid\footins\else
+    \advance\@tempdima-\skip\footins
+    \advance\@tempdima-\ht\footins \advance\@tempdima-\dp\footins
+    \advance\@tempdima-\belowfootnoteskip
+  \fi
+  \ifx\@botlist\@empty\else \advance\@tempdima-\textfloatsep \fi
+  \ifdim\@tempdima<1.5\baselineskip
+    \setbox\@cclv\box\@holdpg \@makecol
+    \pcol@outputfalse \@outputpage \pcol@outputtrue
+    \global\let\pcol@currpage\@empty \pcol@startpage
+    \global\topskip\pcol@topskip \global\pcol@firstpagefalse
+%    \end{macrocode}
+% 
+% Otherwise, i.e., if $H\geq1.5\times\!\baselineskip!$, we invoke
+% \!\pcol@makenormalcol! to make the \preenv{} as the \spanning{} of the
+% \spage.  The macro is different from \!\@makecol! as follows;  the height
+% of resulting \!\@outputbox! is natural rather than \!\textheight!;
+% \Mgfnote{}s is excluded if any; and the skip of \!\textfloatsep! is added
+% below the bottom floats also if any,
+% 
+% Then we let $h$ be the height-plus-depth of \!\@outputbox! being the
+% \spanning{} and shrink \!\@colht! by $h$.  Next if
+% $h>\HB=\!\pcol@bg@preposttop!
+% \in\{\!\pcol@bg@preposttop@left!,\~\!\pcol@bg@preposttop@right!\}$, being
+% the bottom of the previous \env{paracol} environment (having right
+% \parapag{}e) or 0 if the curret page does not have it, to mean we have
+% ordinary single-columned stuff in \preenv{}, we paint its \bground{} by
+% \!\pcol@bg@paintbox! temporarily letting $\!\pcol@bg@textheight!=h$ so
+% that $y_0=\HB$ and $y_1=h$ for $\bgr_{\{p,P\}}$.  This \bgpaint{} is not
+% only for $\pp^b(0)$ which we acquire from from \!\@freelist! by \!\@next!
+% and let have the \spanning, but also for \!\pcol@rightpage! if $\CL<\C$ to
+% mean \parapag{}ing for which we temporarily increment \!\c@page! by one if
+% \npaired.
+% 
+% We also let $\pp^h(0)$ be the shrunk \!\@colht!, and $\pp^t(0)$ be
+% \!\topskip! if $h=0$ assuming that the page does
+% not have any \spanning{}\footnote{

+% 

+% Checking the emptiness by \cs{pcol@ifempty} does not work well for the
+% very first page of a document because it has a \cs{write} as the very
+% first item.}
+% 

+% to typeset \colpage{}s from the top of the page, or otherwise be 0
+% together with \!\topskip! to inhibit the ordinary \!\topskip! insertion.
+% 
+% As for $\pp^m(0)$, we define it as follows, referring to
+% $\mpbout=\!\pcol@mparbottom@out!=\{\mpb_L^l,\mpb_L^r,\mpb_R^l,\mpb_R^r\}$,
+% where $\mpb_X^x$ has exactly one element $\mpar(h,t)$ which may be the
+% position of last marginal notes in the last \env{paracol} environment in
+% the page we are working on, or $\mpb_X^x=\{\mpar(0,0)\}$ if such marginal
+% note or the environment itself does not exist in the page.  On the other
+% hand, $B=\!\@mparbottom!$ may have non-zero for the bottom edge of the
+% last marginal note in \preenv{} including the last \env{paracol}
+% environment if any.  Therefore, what we need to do is to let
+% $\mpb_L^x=\{\mpar(0,B)\}$ to reflect the marginal node whose bottom is at
+% $B$ and which can be different from what $\mpb_L^x$ had, where $x$ is the
+% target margin in the \preenv{} determined by \CSIndex{if@mparswitch}, the
+% parity of $\page(0)$ and \CSIndex{if@reversemargin}.
+% 
+% The replacement is done by \!\pcol@do@mpbout! which invokes
+% $\!\pcol@do@mpbout@whole!\arg{m_L^l}\~\arg{m_L^r}\arg{\mpb_R^l}\arg{\mpb_R^r}$
+% where $m_L^x\in\{M_L^x,\,\!\pcol@do@mpbout@elem!\arg{M_L^x}\}$ whose choice
+% is made according that $x\in\{l,r\}$ is the target margin (latter) or not
+% (former).  Therefore, prior to the invocation of \!\pcol@do@mpbout!, we
+% \!\def!fine \!\pcol@do@mpbout@whole! so that it \!\xdef!ines
+% $\mpbout=\!\pcol@mparbottom@out!$ with its four arguments, and
+% \!\pcol@do@mpbout@elem! to let it be expanded to
+% $\!\@elt!\Arg{0}\Arg{B}=\mpar(0,B)$.  After that, we also invoke
+% \!\pcol@bias@mpbout! giving it $-h$ to replace $\mpar(t,b)$ being the sole
+% element of each $\mpb_{\{L,R\}}^{\{l,r\}}$ in the resulting $\mpbout$ with
+% $\mpar(t-h,b-h)$ to have what we give to $\pp^m(0)$.  This replacement
+% transforms the coordinates for text area to that for columns, and makes it
+% possible for the first marginal note in each margin in the \env{paracol}
+% environment we now start to exploit the space for \preenv{} even if it is
+% tall extraordinarily.
+% 
+% Then we let $\pp(0)$ have $\pp^i(0)$ and $\pp^m(0)$ shown above, and
+% $\pp^p(0)=\!\c@page!$, $\pp^f(0)=\bot$ and $\pp^s(0)=\emptyset$ by
+% \!\pcol@defcurrpage!, and let $\CSIndex{ifpcol@firstpage}=\true$ because
+% $\pp^b(0)$ has \preenv.
+% 

+% \changes{v1.3-6}{2013/09/17}
+%	{Delete the argument of \cs{pcol@makenormalcol} because now it is
+%	 not used too tall pre-environment stuff.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add background painting of pre-environment stuff.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add initialization of $\pi^m(0)$.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \else
+    \pcol@makenormalcol
+    \@tempdima\ht\@outputbox \advance\@tempdima\dp\@outputbox
+    \global\advance\@colht-\@tempdima
+    \def\reserved@a{%
+      \ifdim\pcol@bg@preposttop=\@tempdima\else
+        \edef\pcol@bg@textheight{\@elt{\number\@tempdima sp}}%
+        \pcol@bg@paintbox{Pp}%
+      \fi}
+    \ifnum\pcol@ncolleft<\pcol@ncol
+      \global\setbox\pcol@rightpage\vbox{%
+        \ifpcol@paired\else \advance\c@page\@ne \fi
+        \let\pcol@bg@preposttop\pcol@bg@preposttop@right
+        \reserved@a \unvbox\pcol@rightpage}%
+    \fi
+    \pcol@Fb
+    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
+      \let\pcol@bg@preposttop\pcol@bg@preposttop@left
+      \reserved@a \unvbox\@outputbox}}\pcol@ovf
+    \pcol@Fe{output@start(preenv)}%
+    \global\dimen\@currbox\@colht
+    \ifdim\@tempdima=\z@ \@tempskipa\topskip \else \@tempskipa\z@ \fi
+    \global\skip\@currbox\@tempskipa \global\topskip\@tempskipa
+    \def\pcol@do@mpbout@whole##1##2##3##4{%
+      \xdef\pcol@mparbottom@out{{##1}{##2}{##3}{##4}}}%
+    \def\pcol@do@mpbout@elem\@elt##1##2{\@elt{0}{\number\@mparbottom}}%
+    \pcol@do@mpbout
+    \pcol@bias@mpbout{-\@tempdima}%
+    \pcol@defcurrpage{\number\c@page}\@currbox\voidb@x{}{\pcol@mparbottom@out}%
+    \global\pcol@firstpagetrue
+  \fi
+%    \end{macrocode}
+% 
+% Then regardless of $H$, we do the followings for all columns $c\In0\C$ to
+% build $\cc_c$, after initializing \!\@colroom! to be \!\@colht!, and
+% invoking \!\pcol@floatplacement! to reinitialize the parameters of
+% \cwise{} float placement.
+% 
+% First, if we have let $\!\topskip!=0$ with the \preenv,
+% we let $\cc_c(\vb^b)$ have an invisible \!\hrule! whose
+% height and depth are 0 as the very first vertical item of the \colpage.
+% When we visit the column $c$ for the first time afterward, we will
+% \!\unvbox! the box to let \TeX's page builder have $\!\topskip!=0$ and the
+% invisible rule.  Then the first vertical item of the \colpage{} is added
+% but it is recognized as non-first by \TeX's page builder and thus it
+% inserts \!\baselineskip! referring to \!\prevdepth! as the depth of the
+% last item.  The important issue is that the \!\prevdepth! to be referred
+% is assured having its value at \beginparacol, which is usually the depth
+% of the last item of \spanning, by the following mechanism: (1)
+% \!\pcol@invokeoutput! invoked in \!\pcol@zparacol! saves \!\prevdepth! in
+% \!\pcol@prevdepth! before the \!\output! request for
+% \!\pcol@output@start!; (2) \!\pcol@prevdepth! is saved in $\cc_c(\pd)$ by
+% \!\pcol@setcurrcolnf!  invoked from \!\pcol@output@start! as discussed
+% afterward; (3) when the column $c$ is visited for the first time, the
+% special output routine \!\pcol@output@start! itself ($c=0$) or
+% \!\pcol@output@switch! ($c>0$) restores \!\pcol@prevdepth! from
+% $\cc_c(\pd)$ by \!\pcol@getcurrcol!; (4) \!\pcol@invokeoutput!  which made
+% the \!\output! request for (3) lets \!\prevdepth! have the value of
+% \!\pcol@prevdepth! after the request.  Therefore, the baseline progress
+% from the last line of the \spanning{} to the first line of each
+% \colpage{} should be very natural as we see in the third and fourth lines
+% of \secref{sec:man-close} of Part \ref{part:man}.
+% 
+% Then we invoke \!\pcol@setcurrcolnf! to save the following values for
+% $\cc_c(e)$ ($e\neq\vb$); $\cc_c(\ft)=\!\voidb@x!$ because $c$ does not
+% have \Mcfnote{}s so far;  $\cc_c(\pd)=\!\prevdepth!$ as discussed above;
+% $\cc_c(\tl)=\cc_c(\ml)=\cc_c(\bl)=\emptyset$ because
+% \!\pcol@makenormalcol! and \!\@combinefloats! invoked from it emptied
+% them; $\cc_c(\dl)=\emptyset$ as discussed above;
+% $\cc_c(\tn)=\!\c@topnumber!$, $\cc_c(\bn)=\!\c@botnumber!$ and
+% $\cc_c(\tn)=\!\c@totalnumber!$ as initialized by \!\@floatplacement!
+% invoked from \!\pcol@floatplacement!;
+% $\cc_c(\tr)=\!\topfraction!\times\!\@colht!$ and
+% $\cc_c(\br)=\!\bottomfraction!\times\!\@colht!$ as initialized by
+% \!\@floatplacement!; $\cc_c(\sw)$ is defined by \CSIndex{if@nobreak} and
+% \cs{if@after}\~|indent|
+% 

+% \expandafter\SpecialIndex\csname if@afterindent\endcsname
+% 

+% at the time of \beginparacol; and
+% $\cc_c(\ep)=\!\everypar!$ at the time of \beginparacol.  We also let
+% $\cc_c(\vb^p)=0$ because $p=0$ and $\cc_c(\vb^r)=\!\@colroom!$ defined
+% above.  In addition, we let $\S_c=\emptyset$ because we don't have any
+% \colpage{} having been completed.
+% 
+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% We also examine if $\Celtshadow^c=\cs{pcol@columncolor}\cdot c$ is defined
+% and, if so, acquire an \!\insert! from \!\@freelist! to let
+% $\Celt^c=\cs{pcol@columncolor@box}\cdot c$ have the coloring \!\special!
+% for the color defined in $\Celtshadow^c$ by invoking \!\pcol@set@color!
+% being the origina \!\set@color! with nullification of \!\aftergroup!.
+% Otherwise, we let $\Celt^c=\bot$ .
+% 

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

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.34}{2018/05/07}
+%	{Add initialization of
+%	 $\gamma_0^c\EQ\cs{pcol@columncolor@box}\cdot c$.} 

+% 

+%    \begin{macrocode}
+  \global\@colroom\@colht \pcol@floatplacement
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \pcol@Fb
+    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
+      \ifdim\topskip=\z@ \hrule\@height\z@\@width\z@ \fi}}\pcol@ovf
+    \pcol@Fe{output@start(col)}%
+    \pcol@setcurrcolnf
+    \global\count\@currbox\z@
+    \global\dimen\@currbox\@colroom
+    \expandafter\gdef\csname pcol@shipped\number\pcol@currcol\endcsname{}%
+    \pcol@ifccdefined
+      {\@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
+        \def\current@color{\pcol@ccuse{}}\let\aftergroup\@gobble
+        \pcol@set@color}}\pcol@ovf}%
+      {\def\@currbox{\voidb@x}}%
+    \pcol@ccxdef{\@currbox}%
+   \advance\pcol@currcol\@ne}%
+%    \end{macrocode}
+%

+% \changes{v1.2-1}{2013/05/11}
+%	{Add emptying \cs{pcol@colorstack} and the invocation of
+%	 \cs{pcol@savecolorstack} at the beginnig of the first
+%	 column-page to be built.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add insertion of \cs{footins} having footnotes to be merged if it
+%	 is not void.}

+% \changes{v1.22}{2013/06/30}
+%	{Move emptying \cs{pcol@colorstack} to \cs{pcol@zparacol}.}
+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.35-1}{2018/12/31}
+% 	{Add \cs{interlinepenalty} insertion for the first column to avoid
+%	 vertical overfull due to the first item taller than the column
+%	 room.}
 
+% 

+% Finally, we let $c=\!\pcol@currcol!=0$ for the first column, and regain the
+% parameters in $\cc_0$ by \!\pcol@getcurrcol!.  Then before putting
+% $\cc_0(\vb^b)$ to the main vertical list by \!\unvbox! returning
+% $\cc_0(\vb)$ to \!\@freelist! by \!\@cons! because it has become useless
+% so far, we save the \colorctext{} just with $\Celt^c$ into $\csts$ by
+% \!\pcol@savecolorstack! because $\CST$ is emptied by \!\pcol@zparacol!.
+% Then we \!\insert! \!\footins! through itself to the main vertical list if
+% it is not $\bot$ and thus has footnotes to be \mgfnote{}.  This
+% \!\insert!ion is different from other footnote \!\insert!ion because
+% \!\footins! is not \!\unvbox!ed but is put as a whole and is followed by
+% \!\penalty!\!\interlinepenalty!, so that footnotes will not be broken by
+% \TeX's page builder to prevent the reconnection of a broken footnote with
+% innapropriate glue discarding, which we will discuss in
+% \secref{sec:imp-fnote}.  We also add a penalty 10000 or
+% \!\interlinepenalty! according to $\CSIndex{if@nobreak}=\true$ or not to
+% allow the first column to start from a new page when its first item is
+% taller than the room in the \spage{}.
+% 

+%    \begin{macrocode}
+  \global\pcol@currcol\z@
+  \pcol@getcurrcol
+  \pcol@savecolorstack
+  \pcol@Fb
+  \@cons\@freelist\@currbox \unvbox\@currbox
+  \pcol@Fe{output@start(col)}%
+  \ifvoid\footins\else
+    \pcol@Log\pcol@output@start{insert}\footins
+    \insert\footins{\box\footins\penalty\interlinepenalty}%
+  \fi
+  \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@makenormalcol}
+% \changes{v1.2-2}{2013/05/11}
+%	{Replace the building operation of \cs{@outputbox} with footnotes
+%	 with the invocation of \cs{pcol@combinefootins} and add the
+%	 examination of \cs{ifpcol@mgfnote}.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Turn \cs{ifpcol@lastpage} be $\string\true$ temporarily for
+%	 \cs{pcol@combinefloats} to separate bottom floats in 
+%	 pre-environment stuff and the multi-column stuff in
+%	 \string\texttt{paracol} environment by \cs{textfloatsep}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Completely redesigined to use \cs{@makecol} if pre-environment
+%	 stuff has bottom floats.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+% The macro \!\pcol@makenormalcol! is invoked solely from
+% \!\pcol@output@start! to let \!\@output~box! have the \preenv{} as
+% \spanning{} of the \spage.  The operations this macro performs are very
+% similar to those of \!\@makecol!, which in fact is used in this macro
+% itself, but has the following differences.
+% 

+% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
+% \item
+% If $\CSIndex{ifpcol@mgfnote}=\true$, we exclude footnotes in \!\footins!
+% from \!\@outputbox!, because they are \mgfnote{} with \Scfnote{}s given in
+% columns, by saving it into \!\@tempboxa! during the building process and
+% restoring it from the box register.
+% 
+% \item
+% If \preenv{} does not have bottom floats, we build \!\@outputbox! by
+% ourselves without relying on \!\@makecol! because the skips put into the
+% bottom (or near it) by the macro is harmful to making \preenv{} and
+% parallel columns naturally connected.  Therfore, we move
+% \!\@holdpg! to \!\@outputbox! adding \!\footins! to its tail if any by
+% \!\pcol@combinefootins!, and then combine top floats if any by
+% \!\pcol@combinefloats!\footnote{

+% 

+% Since we do not have bottom floats, the order of materials in the
+% resulting \!\@outputbox! being top floats, main text and footnotes should
+% be consistent with other pages with any \LaTeX{} including p\LaTeX.}.
+% 

+% In addition, we clear \!\@midlist! and retuns its contents to
+% \!\@freelist! as \!\@makecol! does.
+% 
+% \item
+% If \preenv{} has bottom floats, on the other hand, we use \!\@makecol! to
+% build \preenv{} in \!\@outputbox! moving \!\@holdpg! into \!\box!|255|
+% prior to the invocation\footnote{

+% 

+% Therefore the order of footnotes and bottom floats is consistent with
+% other pages and columns, i.e., footnote-first in the native \LaTeX{} while
+% float-first in p\LaTeX{}, for example.}.
+% 

+% Also before invocation in addition, we temporarily let
+% $\CSIndex{ifpcol@lastpage}=\true$ to let
+% $\!\@combinefloats!=\!\pcol@combinefloats!$ used in \!\@makecol!  put a
+% vertical skip of \!\textfloatsep! below the bottom floats so that the
+% floats are well seperated from the top of multi-column stuff in the
+% \spage.  We also nullify \!\@textbottom! by making it \!\let!-equal to
+% \!\relax! because it is unncessary to put an infinitely stretchable skip
+% at the bottom\footnote{

+% 

+% Even if unharmful.},
+% 

+% and let $\!\vbadness!=10000$ to avoid an inevitable underfull message
+% because \!\@makecol! lets \!\@outputbox! as tall as \!\textheight!.
+% 
+% \item
+% In both cases but especially that with bottom floats, resulting
+% \!\@outputbox! is decapsulated by \!\unvbox! to make its height {\em
+% natural}.
+% \end{enumerate}
+% 

+% Note that the special function for \sync{}ed \colpage{} in
+% \!\pcol@combinefloats! used directly or indirectly in this macro, on the
+% other hand, is not active in the invocation because \!\pcol@zparacol!
+% initialized $\!\pcol@textfloatsep!=\infty$ to mean we have no \sync{}ation
+% points.  Also
+% note that bottom floats and non-\mgfnote{} footnotes are put in
+% \!\@outputbox! and thus they will not appear at the bottom of the page
+% but above the \colpage{}s in the page\footnote{

+% 

+% We could put them at the bottom by keeping them somewhere and insert them
+% in \!\pcol@outputcolumns!, but it will cause another problem that the
+% numbers of the figures and footnotes are smaller than those in \colpage{}s
+% which are above them.}.
+% 

+%    \begin{macrocode}
+\def\pcol@makenormalcol{%
+  \ifpcol@mgfnote \setbox\@tempboxa\box\footins \fi
+  \begingroup
+  \ifx\@botlist\@empty
+    \ifvoid\footins \setbox\@outputbox\box\@holdpg
+    \else           \pcol@combinefootins\@holdpg\footins
+    \fi
+    \pcol@Fb
+    \let\@elt\relax \xdef\@freelist{\@freelist\@midlist}%
+    \pcol@Fe{makenormalcol}%
+    \global\let\@midlist\@empty
+    \pcol@combinefloats
+  \else
+    \pcol@lastpagetrue
+    \setbox\@cclv\box\@holdpg \let\@textbottom\relax \vbadness\@M
+    \@makecol
+  \fi
+  \global\setbox\@outputbox\vbox{\unvbox\@outputbox}%
+  \endgroup
+  \ifpcol@mgfnote \setbox\footins\box\@tempboxa \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \subsection{Column-Switching}
+% \label{sec:imp-sout-switch}
+% 
+% \begin{macro}{\pcol@output@switch}
+% \changes{v1.2-1}{2013/05/11}
+%	{Add \cs{pcol@clearcst@unvbox} to add coloring \cs{special}s at the
+%	 top and bottom of the column-page to be saved.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Add the capture of a spanning text when it is closed.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add $\pi^s(p)\EQ\cs{pcol@sptextlist}$ to the argument of
+%	 \cs{pcol@defcurrpage}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add $\pi^m(p)\EQ\cs{pcol@mparbottom}$ to the argument of
+%	 \cs{pcol@defcurrpage}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Let \cs{dimen@} have the height of \cs{pcol@prespan} if it is not
+%	 $\bot$, or 0 if $\bot$ for the sake of clarity.}

+% 

+% The macro \!\pcol@output@switch! is invoked from
+% \!\pcol@specialoutput! to process the special \!\output! request made in
+% \!\pcol@switchcol!, \!\pcol@visitallcols! and \!\pcol@flushclear!, for a
+% \cswitch{} from $c=\!\pcol@currcol!$ to $d=\!\pcol@nextcol!$ which can be
+% $c$.  The macro is also invoked from \!\pcol@makeflushedpage!  to \sync{}e
+% and to flush all \ccolpage{}s but staying in $c$.
+% 
+% First, we examine if the \cswitch{} is to close a \mctext, i.e.,
+% $\CSIndex{ifpcol@sptext}={\true}$ and $c=0$, and if so we do the
+% following; let $h_p$ be the height of \!\pcol@prespan! having \prespan{}
+% if it is not $\bot$, or 0 if $\bot$ to mean we have had a page break in
+% the \mctext; add $h_p$ to \!\@colroom! which we temporarily shrank when
+% the \mctext{} starts; add an elemnent $\spt(H,h)$ to the tail of
+% $\pp^s(\ptop)=\!\pcol@sptextlist!$ by \!\pcol@getcurrpage! and
+% \!\pcol@defcurrpage!, where $H$ is $h_p$ plus the total height of top
+% floats measured by \!\pcol@addflhd!, and $h$ is the height-plus-depth of
+% \!\@holdpg! having (a part of) \mctext, represented in the form of
+% integers and thus expanded with \!\number!; shift \!\@holdpg! left by
+% \!\pcol@shiftspanning! if the column-0 is not the leftmost due to \cswap;
+% and then put \prespan{} and (maybe shifted) \!\@holdpg! into \!\@holdpg!
+% itself so as to let \!\@holdpg! have everything in the \colpage{} 0 as
+% usual.
+% 
+% Note that it can be $\!\pcol@prespan!=\bot$ if \mctext{} had a page break
+% (or multiple ones) in it as shown above.  This empty \prespan{}, however,
+% does not always means that we have no top floats because the page break in
+% the \mctext{} can produce a \colpage{} with top floats which are deferred
+% from the previous page(s), or though unlikely the \mctext{} itself has
+% float environments.  Therefore, the measurement of the total height of top
+% floats are always necessary.  Also note that we perform these operations
+% at the first \cswitch{} for \cscan{}ing from $c=0$ with
+% $\CSIndex{ifpcol@sptext}=\true$, i.e., prior to the \sync{}ation itself
+% which takes place afterword, as explained shortly.
+% 
+% Then regardless of the operations above, we acquire an \!\insert! from
+% \!\@freelist! by \!\@next! for $\cc_c(\vb)$ to store the \ccolpage{} in
+% (maybe modified) \!\@holdpg! by \!\pcol@clearcst@unvbox! to add uncoloring
+% \!\special!s to rewind the \colorstack{} $\CST^c$ at the bottom and
+% possibly coloring ones to establish that saved in $\csts$ at the top as
+% the \colorctext{} for the \colpage{} when it has the first item.
+% 
+% Then if $\!\footins!\neq\bot$, we perform one of the followings.
+% 

+% \begin{itemize}
+% \item
+% If \Scfnote{} typesetting is in effect and $p=\ptop$, we save \!\footins!
+% into $\pp^f(p)$ by the sequence of \!\pcol@getcurrpinfo! to get $\pp(p)$,
+% \!\pcol@savefootins! to move it in $\pp^f(p)$, and \!\pcol@defcurrpage! to
+% update $\pp(p)$ with $\pp^f(p)$.
+% 
+% \item
+% If \Scfnote{} typesetting is in effect but $p<\ptop$, we simply discard
+% the contents of \!\footins!  by making it $\bot$, because \!\footins!
+% should have $\pp^f(p)$ which has been already fixed.
+% 
+% \item
+% If \Mcfnote{} typesettinng is in effect, by \!\pcol@savefootins! we save
+% \!\footins! into \!\pcol@currfoot!, which should be $\bot$ in other cases,
+% so that it will be saved into $\cc_c(\ft)$ by \!\pcol@setcurrcol!
+% afterward.
+% \end{itemize}
+% %
+% Then if $c=0$, we invoke \!\pcol@setpageno! to reflect the jump of
+% \!\c@page! made in the building process of the \colpage{} to $\pp(q)$ for
+% all $q\in[p,\ptop]$.  After that, we save $c$'s \cctext{} into $\cc_c$ by
+% \!\pcol@setcurrcol! and let $\cc_c(\vb^p)=p$ and
+% $\cc_c(\vb^r)=\!\@colroom!$.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Column-Switching
+
+\def\pcol@output@switch{%
+  \ifpcol@sptext\ifnum\pcol@currcol=\z@
+    \ifvoid\pcol@prespan \dimen@\z@ \else \dimen@\ht\pcol@prespan \fi
+    \global\advance\@colroom\dimen@
+    \pcol@addflhd\@toplist\pcol@textfloatsep
+    \pcol@getcurrpinfo\@tempcnta\@tempdima\@tempskipa
+    \@tempdimb\ht\@holdpg \advance\@tempdimb\dp\@holdpg
+    \@cons\pcol@sptextlist{{\number\dimen@}{\number\@tempdimb}}%
+    \pcol@defcurrpage{\number\@tempcnta}\pcol@spanning\pcol@footins
+                     {\pcol@sptextlist}{\pcol@mparbottom}%
+    \pcol@shiftspanning\@holdpg
+    \setbox\@holdpg\vbox{\unvbox\pcol@prespan \unvbox\@holdpg}%
+  \fi\fi
+  \pcol@Fb
+  \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{
+    \pcol@clearcst@unvbox\@holdpg}}\pcol@ovf
+  \pcol@Fe{output@switch}%
+  \def\pcol@currfoot{\voidb@x}%
+  \ifvoid\footins\else
+    \ifpcol@scfnote
+      \ifnum\pcol@page=\pcol@toppage
+        \pcol@getcurrpinfo\@tempcnta\@tempdima\@tempskipa
+        \pcol@Log\pcol@output@switch{save}\footins
+        \pcol@Fb
+        \pcol@savefootins\pcol@footins
+        \pcol@Fe{output@switch(pagefn)}%
+        \pcol@defcurrpage{\number\@tempcnta}\pcol@spanning\pcol@footins
+                         {\pcol@sptextlist}{\pcol@mparbottom}%
+      \else
+        \pcol@Log\pcol@output@switch{discard}\footins
+        \setbox\@tempboxa\box\footins
+      \fi
+    \else
+      \pcol@Log\pcol@output@switch{save}\footins
+      \pcol@Fb
+      \pcol@savefootins\pcol@currfoot
+      \pcol@Fe{output@switch(colfn)}%
+    \fi
+  \fi
+  \ifnum\pcol@currcol=\z@ \pcol@setpageno \fi
+  \pcol@setcurrcol
+  \global\count\@currbox\pcol@page
+  \global\dimen\@currbox\@colroom
+%    \end{macrocode}
+% 
+% Next, we examine if $\CSIndex{ifpcol@sptext}=\true$ and $c=0$ again, and
+% if so we {\em broadcast} \CSIndex{if@nobreak} and
+% \CSIndex{if@afterindent}, or in other words $\cc_c(\sw)$, and tokens in
+% $\!\everypar!=\cc_c(\ep)$, to pretend all columns follow the \mctext.
+% That is, for each column $e$, we restore its \cctext{} from $\cc_e$ by
+% \!\pcol@getcurrcol!, let \CSIndex{if@nobreak} and \CSIndex{if@afterindent}
+% have the values for $c$ ($\in\{0,\C{-}1\}$) and $\!\everypar!=\cc_c(\ep)$,
+% and then save the context to $\cc_e$ by \!\pcol@setcurrcol! so that
+% $\cc_e(\sw)=\cc_c(\sw)$ and $\cc_e(\ep)=\cc_c(\ep)$.  After that, we
+% \!\global!ly turn $\CSIndex{ifpcol@sptext}=\false$ to give it the default
+% state.
+% 
+% Note that this broadcast is essential when the \mctext{} has sectioning
+% commands to have consistent settings of the page break inhibition, the
+% skip above the another sectioning command following them, and the
+% indentation of the first paragraph, for all columns.  On the other hand,
+% broadcasting of \!\everypar! is natural even when it does not have
+% sectioning commands because all columns may be considered following the
+% \mctext.  Also note that, as mentioned in the explanation of the first
+% examination at the beginning of this macro, we perform these operations at
+% the first \cswitch{} for \cscan{}ning from $c=0$ with
+% $\CSIndex{ifpcol@sptext}=\true$ prior to the \sync{ation} following the
+% \mctext.  This means, if $\CSIndex{if@nobreak}={\true}$,
+% $\!\penalty!=10000$ is inserted at the top and bottom end of the space for
+% \mctext{} in the columns such that $c\neq0$, the former by this \cscan{}
+% and the latter by the \cswitch{} to $c$ made after the synchronization.
+% Therefore, if our \sync{ation} mechanism and \TeX's page builder once
+% agreed both end can be in a page, both end will not chosen as page
+% break points\footnote{

+% 

+% As for $c=0$, its top end of \mctext{} is a feasible break point to make
+% the penalty insertion asymmetric.  Therefore, we need to reinvestigate if
+% the condition of the broadcast is really appropriate, and, if
+% inappropriate, have to go back to the old implementation in which
+% \cs{ifpcol@sync} is included in the condition.  Otherwise, if proved
+% appropriate, we will have to consider to make the penalty insertion
+% symmetric by adding \cs{nobreak} at the top of \mctext{} in $c=0$.}.
+% 

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

+% \changes{v1.2-7}{2013/05/11}
+%	{Modify broadcasting of $\kappa_c(\sigma)$ so that \cs{@afterindent}
+%	 is broadcasted with \cs{@nobreak}.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Rename \cs{ifpcol@mctext} as \cs{ifpcol@sptext}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Modify the condition of broadcasting $\kappa_0(\sigma)$ and
+%	 $\kappa_0(\varepsilon)$ accompanied with \cs{ifpcol@sptext} from
+%	 \cs{ifpcol@sync} to $c\EQ0$ so that the broadcast is made in the
+%	 first column-switching in column-scanning.}

+% 

+%    \begin{macrocode}
+  \let\reserved@a\@nobreakfalse \let\reserved@b\@afterindentfalse
+  \ifpcol@sptext\ifnum\pcol@currcol=\z@
+    \if@nobreak \let\reserved@a\@nobreaktrue \fi
+    \if@afterindent \let\reserved@b\@afterindenttrue \fi
+    \@temptokena\everypar
+    \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+      \pcol@getcurrcol \reserved@a \reserved@b \everypar\@temptokena
+      \pcol@setcurrcol
+     \advance\pcol@currcol\@ne}%
+    \global\pcol@sptextfalse
+  \fi\fi
+%    \end{macrocode}
+% 

+% \changes{v1.2-2}{2013/05/11}
+%	{Add the case
+%	 $\cs{ifpcol@clear}\EQ\cs{ifpcol@sync}\EQ\string\mathit{true}$ for
+%	 the invocation of \cs{pcol@restartcolumn} for pre-flushing column
+%	 height check.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Modify the code structure to let
+%	 $\cs{if@tempswa}\EQ\string\mathit{true}$ according to the
+%	 modification of the broadcast of $\kappa_0(\sigma)$ and
+%	 $\kappa_0(\varepsilon)$.}

+% 
+% Finally we invoke \!\pcol@sync! for the \sync{}ation if
+% \CSIndex{ifpcol@sync} or \CSIndex{ifpcol@clear} is $\true$, and then
+% \!\pcol@restartcolumn! to restart the \ccolpage{} $d$ if
+% $\CSIndex{ifpcol@clear}={}\false$ to mean ordinary (but possibly
+% \sync{}ed) \cswitch{} or $\CSIndex{ifpcol@clear}={}\true$ but
+% $\CSIndex{ifpcol@sync}={}\true$ too to mean pre-flushing column height
+% check, before finishing \!\output!  routine letting
+% $\CSIndex{ifpcol@sync}=\false$ for next \cswitch.
+% 

+%    \begin{macrocode}
+  \@tempswafalse \ifpcol@sync \@tempswatrue \fi \ifpcol@clear \@tempswatrue \fi
+  \if@tempswa \pcol@sync \fi
+  \@tempswatrue
+  \ifpcol@clear \ifpcol@sync\else \@tempswafalse \fi\fi
+  \if@tempswa \pcol@restartcolumn \fi
+  \global\pcol@syncfalse}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@shiftspanning}
+% \changes{v1.3-1}{2013/09/17}
+%	{Introduced to shift a spanning text to left if the column-0 is not
+%	 leftmost due to column-swapping.}

+% 

+% The macro $\!\pcol@shiftspanning!\arg{b}$ is used in \!\pcol@makecol! and
+% \!\pcol@output@switch! to let box register $b$ have itself but shifted
+% left by $\WT-w_0=\!\textwidth!-\!\columnwidth!$ so that the left edge of
+% its contents \mctext{} is aligned to the left edge of the leftmost column
+% being different from column-0 due to \cswap, i.e., if
+% $\CSIndex{ifpcol@swapcolumn}=\true$ and $\!\c@page!\bmod2=0$.  Note that
+% \!\c@page! is {\em not} obtained from $\pp^p(p)$ by the invokers but have
+% the value when the \!\output! request is made to let invokers work, and
+% thus have the correct value even when a jump occurs prior to the request.
+% 

+%    \begin{macrocode}
+\def\pcol@shiftspanning#1{%
+  \ifpcol@swapcolumn\ifodd\c@page\else
+    \setbox#1\vbox{\@tempdima\textwidth \advance\@tempdima-\columnwidth
+      \moveleft\@tempdima\box#1}
+  \fi\fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@restartcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Add \cs{pcol@getcurrfoot} to restore parameters of $\kappa_c(\tau)$
+%	 into \cs{footins}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+% The macro \!\pcol@restartcolumn! is invoked from \!\pcol@output@switch! or
+% \!\pcol@freshpage! to restart the \ccolpage{} $d=\!\pcol@nextcol!$ which
+% becomes $c=\!\pcol@currcol!$ by the very first assignment in this macro.
+% Then we restore the \cctext{} in $\cc_c$ by \!\pcol@getcurrcol! and let
+% $p=\cc_c(\vb^p)$ and $\!\@colroom!=\cc_c(\vb^r)$ before returning
+% $\cc_c(\vb)$ to \!\@freelist! by \!\@cons! because it has become useless
+% so far.  We also restore the \pctext{} of $p$ by \!\pcol@getcurrpage!.
+% 

+%    \begin{macrocode}
+\def\pcol@restartcolumn{%
+  \global\pcol@currcol\pcol@nextcol
+  \pcol@getcurrcol
+  \global\pcol@page\count\@currbox
+  \global\@colroom\dimen\@currbox
+  \pcol@Fb
+  \@cons\@freelist\@currbox
+  \pcol@Fe{restartcolumn(col)}%
+  \pcol@getcurrpage
+%    \end{macrocode}
+% 

+% \changes{v1.2-2}{2013/05/11}
+%	{Redesign the footnote insertion mechanism to cope with
+%	 page-wise footnotes.}

+% \changes{v1.2-1}{2013/05/11}
+%	{Add \cs{pcol@restorecst@restart} to return main vertical list
+% 	 with coloring operations.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Rename \cs{pcol@restorecst@restart} as \cs{pcol@putbackmvl}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Change the code structure to move the insertion of page break
+%	 penalty for ordinary column-wise footnotes from below the main
+%	 text to below the footnotes.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add \cs{@colht} and \cs{@tempdimb} as the first and third argument
+%	 of \cs{pcol@shrinkcolbyfn}.}

+% 
+% Then we perform footnote \!\insert!ion as follows.
+% 

+% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
+% \item\label{item:scftop}
+% If footnote typesetting is \scfnote{} and $p=\ptop$, we do the followings.
+% 

+% \begin{enumerate}\def\labelenumii{(\alph{enumii})}
+% \item\label{item:scftop-main}
+% Put the contents of $\cc_c(\vb^b)$ by \!\pcol@putbackmvl! to make
+% the \colorctext{} in |.dvi| consistent with the current |.tex|'s one, and
+% to save \prespan{} into \!\pcol@prespan! if we are opening a \mctext{}.
+% 
+% \item\label{item:scftop-pen}
+% Put $\!\penalty!=10000$ by \!\nobreak! if $\CSIndex{if@nobreak}=\true$ or
+% \!\interlinepenalty! by \!\addpenalty!\footnote{

+% 

+% As done in \!\@specialoutput! but \!\penalty!\!\interlinepenalty! should
+% be sufficient.}
+% 

+% otherwise, as the page break penalty at the returning point.  Note that
+% adding the \!\penalty! will be nullified by \TeX{} if $\cc_c(\vb^b)$ has
+% nothing and thus, if the \colpage{} is still empty when we leave from it,
+% its emptiness without any items is assured.  Also note that the penalty
+% insertion here {\em looks} essential to keep \TeX's page builder from
+% confusing with \scfnote{} footnotes which it has not seen in a
+% \colpage\footnote{

+% 

+% At least a test with tall \scfnote{} footnotes gave us a confusing
+% result.}.
+% 
+% \item\label{item:scftop-fnote}
+% If $\pp^f(p)\neq\bot$, let \!\pcol@currfoot! and then \!\footins! have
+% the footnotes in it by an \!\edef! and \!\pcol@getcurrfoot!, return the
+% \!\insert! for them to \!\@freelist!, invoke \!\pcol@shrinkcolbyfn! to
+% shrink \!\@colht! temporarily by their total height and to remember the
+% exsistence of them with $\!\@tempdimb!=-\!\skip!\!\footins!$, and then
+% \!\insert!  the footnotes so that it contributes to the building process
+% of the \colpage{} to be restarted.  Otherwise, i.e. if $\pp^f(p)=\bot$,
+% \!\@colht! is unchanged and $\!\@tempdimb!=0$.
+% 
+% \item\label{item:scftop-defer}
+% Invoke \!\pcol@deferredfootins! to \!\insert! deferred footnotes in $\df$
+% until their total height reaches (possibly shrunk) \!\@colht!.  This
+% height capping is to keep \TeX's page builder from holding too large
+% number of footnotes unprocessed causing confused ordering on presenting
+% them to \!\output! routine.
+% \end{enumerate}
+% 
+% \item
+% If footnote typesetting is \scfnote{} but $p<\ptop$, we do the followings.
+% 

+% \begin{enumerate}\def\labelenumii{(\alph{enumii})}
+% \item
+% If $\pp^f(p)\neq\bot$, get it into \!\footins! as done in
+% (\ref{item:scftop-fnote}) but giving \!\copy! to \!\pcol@getcurrfoot!
+% because $\pp^f(p)$ has been fixed and thus will be kept until it is
+% shipped out, and then \!\insert! it.
+% 
+% \item
+% Put $\cc_c(\vb^b)$ and the penalty as done in (\ref{item:scftop-main}) and
+% (\ref{item:scftop-pen}).
+% \end{enumerate}
+% 

+% Thes order of footnotes, main vertical list and then penalty is essential
+% to ensure that the \colpage{} in $p<\ptop$ has room for footnotes whose
+% residence in $p$ has already been fixed.
+% 
+% \item
+% If footnote typesetting is \mcfnote{}, we do the followings.
+% 

+% \begin{enumerate}\def\labelenumii{(\alph{enumii})}
+% \item
+% Put $\cc_c(\vb^b)$ as done in (\ref{item:scftop-main}).
+% 
+% \item
+% If $\cc_c(ft)\neq\bot$, get it by \!\pcol@getcurrfoot! returning the
+% \!\insert! to \!\@freelist!, and then \!\insert! it.
+% 
+% \item
+% Put a penalty as done in (\ref{item:scftop-pen}).
+% \end{enumerate}
+% 

+% The order of main vertical list, footnotes and then penalty is appropriate
+% for \Mcfnote{}s because they definitely have space in the \colpage{} and
+% \TeX{} will break the page below the insertion, possibly just below thanks
+% to the penalty, to keep the footnotes and references to them in a page.
+% \end{enumerate}
+% 

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \ifpcol@scfnote
+    \edef\pcol@currfoot{\pcol@footins}%
+    \ifnum\pcol@page=\pcol@toppage
+      \@tempdima\@colht \@tempdimb\z@
+      \pcol@putbackmvl
+      \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi
+      \ifvoid\pcol@footins\else
+        \pcol@Fb
+        \pcol@getcurrfoot\box \@cons\@freelist\pcol@currfoot
+        \pcol@Fe{restartcolumn(pagefn)}%
+        \pcol@Log\pcol@restartcolumn{insert}\footins
+        \pcol@shrinkcolbyfn\@colht\footins\@tempdimb
+        \insert\footins{\unvbox\footins}%
+      \fi
+      \pcol@deferredfootins\pcol@restartcolumn
+      \@colht\@tempdima
+    \else
+      \ifvoid\pcol@footins\else
+        \pcol@getcurrfoot\copy
+        \pcol@Log\pcol@restartcolumn{insdmy}\footins
+        \insert\footins{\unvbox\footins}%
+      \fi
+      \pcol@putbackmvl
+      \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi
+    \fi
+  \else
+    \pcol@putbackmvl
+    \ifvoid\pcol@currfoot\else
+      \pcol@Fb
+      \pcol@getcurrfoot\box \@cons\@freelist\pcol@currfoot
+      \pcol@Fe{restartcolumn(colfn)}%
+      \pcol@Log\pcol@restartcolumn{insert}\footins
+      \insert\footins{\unvbox\footins}%
+    \fi
+    \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@getcurrcol}
+% \changes{v1.1}{2012/05/11}
+% 	{Add assignment $w_c$ to \cs{columnwidth}, \cs{hsize} and
+%	 \cs{linewidth}.}
 
+% \changes{v1.2-5}{2013/05/11}
+% 	{Move assignment $w_c$ to \cs{hsize} and \cs{linewidth} to
+%	 \cs{pcol@invokeoutput}.}

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

+% \changes{v1.3-4}{2013/09/17}
+%	{Remove the argument for $\kappa_c(\mu)\EQ\cs{@mparbottom}$ because it
+%	 is no longer in the column context.}

+% 

+% The macro \!\pcol@getcurrcol! is invoked from the following macros to
+% restore the typesetting parameters of the column $c=\!\pcol@currcol!$ from
+% $\cc_c$, and to let \!\columnwidth! have
+% $\w_c=|\pcol@columnwidth|{\cdot}c$\footnote{

+% 

+% \cs{hsize} and \cs{linewidth} are let have $\w_c$ and $\w_c-\lrm$
+% respectively in \cs{pcol@invokeoutput}.}.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% 

+% \begin{itemize}\item[]\begin{tabular}{lll}
+% \!\pcol@output@start!&\!\pcol@output@switch!&\!\pcol@restartcolumn!\\
+% \!\pcol@flushcolumn!&\!\pcol@measurecolumn!&\!\pcol@synccolumn!\\
+% \!\pcol@makeflushedpage!&\!\pcol@imakeflushedpage!&\!\pcol@iflushfloats!\\
+% \!\pcol@freshpage!&\!\pcol@output@end!
+% \end{tabular}
+% \end{itemize}
+% 

+% Since we represent $\cc_c$ as;
+% 

+% \begin{eqnarray*}
+% &&\Arg{\cc_c(\vb)}\Arg{\cc_c(\ft)}\Arg{\cc_c(\pd)}\Arg{\cc_c(\tl)}
+% \Arg{\cc_c(\ml)}\Arg{\cc_c(\bl)}\Arg{\cc_c(\dl)}\Arg{\cc_c(\tf)}|%|\\
+% &&\Arg{\Arg{\cc_c(\fh)}\Arg{\cc_c(\tn)}\Arg{\cc_c(\tr)}
+%        \Arg{\cc_c(\bn)}\Arg{\cc_c(\br)}\Arg{\cc_c(\cn)}\Arg{\cc_c(\sw)}
+%        \Arg{\cc_c(\ep)}}
+% \end{eqnarray*}
+% 

+% in the body of $|\pcol@col|{\cdot}c$,
+% 

+% \SpecialArrayIndex{c}{\pcol@col}

+% 

+% we restore first eight by \!\pcol@igetcurrcol! giving everything above as
+% its arguments by the expansion of
+% $$
+% \!\csname!| pcol@col|\!\number!\!\pcol@currcol!\!\endcsname!
+% $$
+% and then of the resulting control sequence.  Then this macro gives its
+% nineth argument to \!\pcol@iigetcurrcol! which restores the last eight.  We
+% also do
+% $$
+% \!\global!\!\columnwidth!|\pcol@columnwidth|{\cdot}c
+% $$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% 

+% by a pair of \!\expandafter! for the first two control sequences.
+% 
+% Note that the restore operations are \!\global!, except for $\cc_c(\vb)$
+% and $\cc_d(\ft)$ because they are referred to only in \!\output!,
+% including \CSIndex{if@nobreak} for which \!\@nobreaktrue!  and
+% \!\@nobreakfalse! are defined \!\global! by \LaTeX.  Also note that
+% \!\dimen!-type parameters are saved in the form of integers and thus
+% restoring them needs to specify the unit |sp|.
+% 

+%    \begin{macrocode}
+\def\pcol@getcurrcol{%
+  \expandafter\expandafter\expandafter\pcol@igetcurrcol
+    \csname pcol@col\number\pcol@currcol\endcsname
+  \expandafter\global\expandafter\columnwidth
+    \csname pcol@columnwidth\number\pcol@currcol\endcsname}
+\def\pcol@igetcurrcol#1#2#3#4#5#6#7#8#9{%
+  \def\@currbox{#1}\def\pcol@currfoot{#2}\global\pcol@prevdepth#3sp\relax
+  \gdef\@toplist{#4}\gdef\@midlist{#5}\gdef\@botlist{#6}\gdef\@deferlist{#7}%
+  \global\pcol@textfloatsep#8sp\pcol@iigetcurrcol#9}
+\def\pcol@iigetcurrcol#1#2#3#4#5#6#7#8{%
+  \global\@textfloatsheight#1sp\relax
+  \global\@topnum#2\relax \global\@toproom#3sp\relax
+  \global\@botnum#4\relax \global\@botroom#5sp\relax
+  \global\@colnum#6\relax
+  \global\@afterindentfalse \@nobreaktrue
+  \ifcase#7
+    \@nobreakfalse \or
+    \global\@afterindenttrue \else
+    \relax
+  \fi
+  \global\everypar{#8}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@getcurrfoot}
+% \changes{v1.2-2}{2013/05/11}
+%	{Add an argument being \cs{box} or \cs{copy}}

+% 

+% The macro $\!\pcol@getcurrfoot!\arg{com}$ is invoked from
+% \!\pcol@startcolumn! (\!\copy!, $\pp^f(p)$), 
+% \!\pcol@restartcolumn! (\!\copy!\slash\!\box!, $\pp^f(p)$\slash$\cc_c(\ft)$),
+% \!\pcol@flushcolumn! (\!\box!, $\cc_c(\ft)$) and  \!\pcol@imakeflushedpage!
+% (\!\box!, $\cc_c(\ft)$) to put everything in $\!\pcol@currfoot!$, having
+% the second element in the parens following macro names, into \!\footins!
+% using $\arg{com}$ shown as the first element in parens for the \!\box!
+% component.  That is, if the source $\pp^f(p)$ or $\cc_c(\ft^b)$ is void,
+% we let $\!\box!{\cdot}\!\footins!$ be so.  Otherwise, we move \!\box!,
+% \!\count!, \!\dimen! and \!\skip! of the source into those of
+% \!\footins!\footnote{

+% 

+% Moving \!\count!, \!\dimen! and \!\skip! is redundant almost always
+% because it is very unlikely that these footnote parameters are modified
+% dynamically.  Moreover, dynamic modification of them is hardly consistent
+% with repetitive self-\!\insert!ion of \!\footins! in
+% \!\pcol@restartcolumn! and \!\@reinserts! of \LaTeX.  However, we dare to
+% move them in order to, for example, allow each column has its own footnote
+% parameters.}.
+% 

+% 

+%    \begin{macrocode}
+\def\pcol@getcurrfoot#1{%
+  \ifvoid\pcol@currfoot \global\setbox\footins\box\voidb@x
+  \else
+    \global\setbox\footins#1\pcol@currfoot
+    \global\count\footins\count\pcol@currfoot
+    \global\dimen\footins\dimen\pcol@currfoot
+    \global\skip\footins\skip\pcol@currfoot
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

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

+% \changes{v1.3-4}{2013/09/17}
+%	{Remove $\kappa_c(\mu)\EQ\cs{@mparbottom}$ from the body of
+%	 $\cs{pcol@col}{\cdot}c$ because it is no longer in the column
+%	 context.}

+% 

+% \begin{macro}{\pcol@setcurrcolnf}
+% The macro \!\pcol@setcurrcol! is invoked from \!\pcol@output@switch!,
+% \!\pcol@measurecolumn! and \!\pcol@synccolumn! to save \cctext{} of
+% $c=\!\pcol@currcol!$ in $\cc_c$.  It is also used in \!\pcol@setcurrcolnf!
+% invoked from \!\pcol@output@start!, \!\pcol@flushcolumn!,
+% \!\pcol@imakeflushedpage!, \!\pcol@iflushfloats! and \!\pcol@freshpage! for
+% the saving when the \colpage{} is known to have no footnotes.
+% 
+% The macro \!\pcol@setcurrcol! at first calculates the combined code for
+% \CSIndex{if@nobreak} and \CSIndex{if@afterindent}, and then saves
+% parameters into $\cc_c$ by \!\xdef! to have the sequence shown in the
+% description of \!\pcol@getcurrcol!.  Note that \!\dimen!-type parameters
+% are saved by expansions with \!\number! and thus as decimal integers.
+% 
+% The macro \!\pcol@setcurrcolnf! \!\def!ines $\cc_c(\ft)=\!\pcol@currfoot!$
+% as \!\voidb@x!, and then invoke \!\pcol@setcurrcol! for saving.
+% 

+%    \begin{macrocode}
+\def\pcol@setcurrcol{{\let\@elt\relax
+  \@tempcnta\if@nobreak\if@afterindent\@ne\else\tw@\fi\else\z@\fi
+  \expandafter\xdef\csname pcol@col\number\pcol@currcol\endcsname{%
+    {\@currbox}{\pcol@currfoot}{\number\pcol@prevdepth}%
+    {\@toplist}{\@midlist}{\@botlist}{\@deferlist}{\number\pcol@textfloatsep}%
+    {{\number\@textfloatsheight}%
+     {\number\@topnum}{\number\@toproom}{\number\@botnum}{\number\@botroom}%
+     {\number\@colnum}{\number\@tempcnta}{\the\everypar}}}}}
+\def\pcol@setcurrcolnf{\def\pcol@currfoot{\voidb@x}\pcol@setcurrcol}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@putbackmvl}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to restart a column with coloring.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Renamed from \cs{pcol@restorecst@restart} and the operations to
+%	 save pre-spanning-text stuff is added.}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
+%	 \cs{pcol@prespan} to obey the coding convention.}

+% \changes{v1.34}{2018/05/07}
+%	{Change nullification of
+%	 $\mathit{\Gamma}_s\EQ\cs{pcol@colorstack@saved}$ from \cs{gdef} to
+%	 \cs{box}-assignment of $\bot$ because it is now a \cs{vbox}.}
+% 

+% The macro \!\pcol@putbackmvl!, solely used in
+% \!\pcol@restartcolumn!, has two functions;  \colorstack{} restoration and
+% \prespan{} preservation.  It examines the emptiness of the \colpage{} of the
+% column $c$ to be restarted in $\cc_c(\vb)=\!\@currbox!$.  If so, the
+% \colorstack{} $\CST^c$ is saved into $\csts=\!\pcol@colorstack@saved!$ by
+% \!\pcol@savecolorstack! as the opening \colorctext{} of the \colpage{},
+% and \!\pcol@prespan! for \prespan{} is made $\bot$.
+% 
+% Otherwise, $\csts$ is let $\bot$ because the opening \colorctext{} has
+% already been put when we left from the \colpage{}.  Then if
+% $\CSIndex{ifpcol@sptextstart}=\true$ to mean a \mctext{} is to start, we
+% save $\cc_c(\vb)$ into \!\pcol@prespan! adding the colorling \!\special!s
+% to restore \colorctext{} from $\CST^c$ by
+% \!\pcol@restorecolorstack!\footnote{

+% 

+% If \cs{pcol@prespan} is connected to (the first part of) the \mctext,
+% the reestablishment of the \colorstack{} here correctly places coloring
+% \cs{special}s in \texttt{.dvi}.  On the other hand, if the \mctext{} is
+% slown away to the next page as a whole, the reestablishment here is
+% essential for the correct paring of the pushes and pops, the latter of
+% which are at the bottom of the \colpage{} whose tail is \cs{pcol@prespan}.}.
+% 

+% We also shrink $\cc_c(\vb^r)=\!\@colroom!$ by the height of the \prespan{}
+% so that \mctext{} will be captured by \!\pcol@makecol! if it is broken
+% into two (or more) pages, and put a invisible \!\hrule! to the main
+% vertical list letting $\!\topskip!=0$ to supress \!\topskip! insertion
+% prior to the \mctext{} but instead to make the text led by
+% \!\baselineskip! (or \!\lineskip!) according to the \!\prevdepth!  being
+% the depth of the tallest column and the height of the first \!\hbox! in
+% the \mctext.  Otherwise, i.e., if $\CSIndex{ifpcol@sptextstart}=\false$,
+% we simply put back $\cc_c(\vb)$ into the main vertical list and then the
+% coloring \!\special!s by \!\pcol@restorecolorstack!.
+% 
+% Note that $\CSIndex{ifpcol@sptextstart}$ is temporarily made $\false$ by
+% this macro if the \!\pcol@output@switch! invoking \!\pcol@restartcolumn!
+% did not make \sync{}ed \cswitch{}, i.e., if $\CSIndex{ifpcol@flush}=\true$
+% to mean the page is flushed before the \sync{}ation, or
+% $\CSIndex{ifpcol@sync}=\false$ for \cscan{}ning prior to the \sync{}ation.
+% 

+%    \begin{macrocode}
+\def\pcol@putbackmvl{%
+  \ifpcol@flush \pcol@sptextstartfalse \fi
+  \ifpcol@sync\else \pcol@sptextstartfalse \fi
+  \pcol@ifempty\@currbox
+   {\pcol@savecolorstack
+    \ifpcol@sptextstart \global\setbox\pcol@prespan\box\voidb@x \fi}%
+   {\global\setbox\pcol@colorstack@saved\box\voidb@x
+    \ifpcol@sptextstart
+      \global\setbox\pcol@prespan\vbox{%
+        \unvbox\@currbox \pcol@restorecolorstack}%
+      \global\advance\@colroom-\ht\pcol@prespan
+      \global\topskip\z@ \hrule\@height\z@\@width\z@
+    \else
+      \unvbox\@currbox \pcol@restorecolorstack
+    \fi}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \KeepSpace{3}
+% \subsection{Color Management}
+% \label{sec:imp-sout-color}
+% 

+% \changes{v1.2-1}{2013/05/11}
+%	{Add the subsection ``Color Management'' to describe newly
+%	 introduced macros for coloring.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Move commands outside \cs{output} routine to the newly introduced
+%	 section ``Commands for Text Coloring'' to distinguish
+%	 macros inside and outside \cs{output} routine.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@output@cpush} was introduced for color stack pushing but
+%	 removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@cpush} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@output@icpush} was introduced to implement
+%	 \cs{pcol@output@cpush} but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@icpush} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@output@mcpush} was introduced for coloring specified in
+%	 math mode but removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@mcpush} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@output@imcpush} was introduced for coloring specified in
+%	 math mode but removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@imcpush} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@output@cpop} was introduced for color stack popping but
+%	 removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@cpop} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.2-1}{2013/05/11}
+% 	{\cs{pcol@reset@color@elt} was introduced to implement
+%	 \cs{pcol@reset@color@pop} but removed in v1.34.}
 
+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@reset@color@elt} was moved from the position where
+%	 \cs{pcol@reset@color@pop} was defined 
+%	 because it became to be used only by \cs{pcol@output@cpop}, but
+%	 removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@reset@color@elt} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@output@mcpop} was introduced for coloring specified in
+%	 math mode but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@mcpop} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.24}{2013/07/27}
+%	{\cs{pcol@output@mcpop@elt} was introduced for coloring specified in
+%	 math mode but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@mcpop@elt} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@output@cset} was introduced to set $\gamma_0^c$ but
+%	 removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@cset} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@output@icset} was introduced to implement
+%	 \cs{pcol@output@cset} but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@output@icset} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@return@from@color} was introduced to implement
+%	 \cs{pcol@output@cpush}, \cs{pcol@output@cpop} and
+%	 \cs{pcol@output@cset} but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@return@from@color} is removed according to the change of
+%	 text coloring from \cs{output} to \cs{insert}.}

+% 
+% \begin{macro}{\pcol@magicpenalty}
+% \begin{macro}{\pcol@ifempty}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to examine the emptiness of the box, extracting the code
+% 	 from \cs{pcol@measurecolumn} so as to be used for coloring as
+%	 well.}

+% 

+% The macro $\!\pcol@ifempty!\arg{box}\arg{then}\arg{else}$ is used in
+% \!\pcol@putbackmvl!, \!\pcol@clearcst@unvbox! and
+% \!\pcol@measurecolumn! to examine if $\arg{box}$ is empty, and to perform
+% $\arg{then}$ if so or $\arg{else}$ otherwise.  Since \TeX{} does not
+% provide any convenient way for the examination unfortunately, we perform a
+% series of tricky operations to put the followings into \!\@tempboxa!; a
+% penalty of $\!\pcol@magicpenalty!=12345$ whose existence in the
+% $\arg{box}$ is (almost) impossible; contents of $\arg{box}$ put by
+% \!\unvcopy!; and then a \!\global! \!\def!inition of \!\@gtempa! to let it
+% have the decimal representation of \!\lastpenalty!.  Since \!\lastpenalty!
+% has $\arg{pen}$ if the last item is $\!\penalty!\arg{pen}$, or 0
+% otherwise, $\!\@gtempa!=\!\pcol@magicpenalty!$ iff $\arg{box}$ is empty.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Color Management
+
+\def\pcol@magicpenalty{12345}
+\def\pcol@ifempty#1#2#3{%
+  \setbox\@tempboxa\vbox{\penalty\pcol@magicpenalty
+    \unvcopy#1\xdef\@gtempa{\number\lastpenalty}}%
+  \ifnum\@gtempa=\pcol@magicpenalty\relax \def\reserved@a{#2}%
+  \else                                   \def\reserved@a{#3}%
+  \fi
+  \reserved@a}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@clearcst@unvbox}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to put coloring \cs{special}s above and below of a
+%	 column-page.}

+% \begin{macro}{\pcol@clearcolorstack}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to clear color context.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% 

+% The macro \!\pcol@clearcst@unvbox!$\arg{box}$, invoked from \!\pcol@opcol!
+% and \!\pcol@output@switch!, puts the following above and below
+% $\arg{box}$ containing the main vertical list of a \colpage{} from which
+% we are now leaving, if \!\pcol@ifempty! judges that $\arg{box}$ is not
+% empty.  Above the $\arg{box}$, we put coloring \!\special!s to establish
+% the \colorstack{} of |.dvi| saved in $\csts=\!\pcol@colorstack@saved!$ by
+% \!\pcol@restorecst! as the opening \colorctext{} of the \colpage{}.  The
+% stack $\csts$, however, can be $\bot$ if $\arg{box}$ already has the
+% \!\special!s, i.e., when we visit the \colpage{} it had already had
+% some items.  Below $\arg{box}$, on the other hand, we put uncoloring
+% \!\special!s by \!\pcol@clearcolorstack! to rewind $\CSTraw^c$ to clear the
+% \colorctext{} of the \colpage{} in |.dvi| temporarily so that afterward it
+% is made consistent with that in |.tex|.
+% 
+% The macro \!\pcol@clearcolorstack!, solely invoked from
+% \!\pcol@clearcst@unvbox! shown above\footnote{

+% 

+% But we have this macro to avoid the complication in \cs{def}ining
+% \cs{reserved@a} and \cs{reserved@b} with an argument if we did it in the
+% argument of \cs{pcol@ifempty} in \cs{pcol@clearcst@unvbox}.},
+% 

+% scans $\CSTraw^c=(\Celt^c,\cstraw)$ by \!\pcol@scancst! giving
+% $\cstraw=\!\pcol@colorins!$ to it as its argument.  Since we gives
+% $\cstraw$ to the macro, this scan includes removals of all $\celtpop_i$
+% and $\mceltpop_{i,m}$, all $\celt_i$ having matching $\celtpop_i$, all
+% $\mcelt_{i,m}$ having matching $\mceltpop_{i,m}$, and all elements to
+% update $\Celt^c$, from $\cstraw$ to let \!\pcol@colorins! have $\cst$.
+% Prior to this invocation, we \!\def!ine $\!\reserved@a!\<\celt_i\>$ and
+% $\!\reserved@b!\<\Celt^c\>$ to let them have \!\reset@color! so that
+% uncoloring \!\special! will be put into the main vertical list for each
+% $\celt_i\in\cst$ and $\Celt^c$ before update if any, regardless of
+% coloring \!\special! they have.  That is, we invoke \!\reset@color! as
+% many times as the appearance of $\celt_i\in\cst$ and once if
+% $\Celt^c\neq\bot$ before the invocation, ignoring the color information in
+% each element and the order of elements, expecting \!\reset@color! just
+% pops printer's \colorstack{} to rewind it as we intend.
+% 
+% Note that in some printer |.def|inition could \!\def!ine \!\reset@color! to
+% let printer's text color be \!\current@color! to make the stack rewinding
+% resulting in the sequence of coloring operations with \!\current@color! at
+% the invocation of \!\output!.  This meaningless operations might cause a
+% problem when a colored \colpage{} of $c_1$ is physically followed by another
+% \colpage{} of the succeeding column $c_2$ without any coloring, because the
+% \colpage{} of $c_2$ will be colored with \!\current@color! at the page break
+% in $c_1$.  If this problem is serious, we could initialize $\Celt^c$ with
+% \!\current@color! at \beginparacol{} for all $c$ such that $\Celtshadow^c$
+% is undefined, in order to make sure that any \colpage{} has at least one
+% coloring \!\special! with $\Celt^c$ at its beginning so that, for example,
+% coloring operations at the tail of the \colpage{} of $c_1$ is overridden
+% by that of the default color of $c_2$ placed at the head of its \colpage{}.
+% 

+%    \begin{macrocode}
+\def\pcol@clearcst@unvbox#1{%
+  \pcol@ifempty#1\relax
+   {\pcol@restorecst\pcol@colorstack@saved \unvbox#1\pcol@clearcolorstack}}
+\def\pcol@clearcolorstack{%
+  \def\reserved@a##1{\reset@color}\def\reserved@b##1{\reset@color}%
+  \pcol@scancst\pcol@colorins}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \changes{v1.2-1}{2013/05/11}
+% 	{\cs{pcol@set@color@elt} was introduced to implement color context
+%	 reestablishment but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@set@color@elt} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% 

+% \begin{macro}{\pcol@restorecolorstack}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to reestablish color context.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% \begin{macro}{\pcol@restorecst}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to reestablish color context.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% 

+% The macro \!\pcol@restorecolorstack!, used in \!\pcol@putbackmvl!
+% and \!\pcol@output@end!, makes \colorctext{} in
+% |.dvi| consistent with that in |.tex| by giving $\cst=\!\pcol@colorins!$
+% to \!\pcol@restorecst! to let it scan $\CST^c=(\Celt^c,\cst)$.
+% The callee macro $\!\pcol@restorecst!\arg{box}$, also used in
+% \!\pcol@clearcst@unvbox! with $\arg{box}=\csts=\!\pcol@colorstack@saved!$,
+% invokes \!\pcol@scancst! after \!\def!ining $\!\reserved@a!\<\celt_i\>$ to
+% apply \!\unvbox! to $\celt_i$ in $\cst$ or $\csts$ and
+% $\!\reserved@b!\<\Celt^c\>$ to apply \!\unvcopy! to $\Celt^c$ so that
+% coloring \!\special!s they have will be put into the main vertical list.
+% 

+%    \begin{macrocode}
+\def\pcol@restorecolorstack{\pcol@restorecst\pcol@colorins}
+\def\pcol@restorecst{%
+  \def\reserved@a##1{\unvbox##1}\def\reserved@b##1{\unvcopy##1}%
+  \pcol@scancst}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@scancst}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to implement new text coloring with \cs{insert}.}

+% \begin{macro}{\pcol@iscancst}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to implement new text coloring with \cs{insert}.}

+% 
+% \begin{Sloppy}{1500}
+% The macro $\!\pcol@scancst!\arg{box}$ is invoked from
+% \!\pcol@clearcolorstack! and \!\pcol@restorecst!.  In the former
+% invocation, we have $\arg{box}=\cstraw=\!\pcol@colorins!$ to rewind
+% $\CSTraw=(\Celt^c,\cstraw)$ with $\!\reserved@a!\arg{\celt_i}$ and
+% $\!\reserved@b!\arg{\Celt^c}$ having \!\reset@color!.  In the latter one,
+% we have
+% $\arg{box}\in\{\cst{=}\!\pcol@colorins!,\,\csts{=}\!\pcol@colorstack@saved!\}$
+% to reestablish $\CST^c=(\Celt^c,\cst)$ or $\csts$ with
+% $\!\reserved@a!\arg{\celt_i}$ to apply \!\unvbox! to $\celt_i$ and 
+% $\!\reserved@b!\arg{\Celt^c}$ to apply \!\unvcopy! to $\Celt^c$.
+% Therefore, if $\arg{box}=\!\pcol@colorins!$, we at first put (un)coloring
+% \!\special! for $\Celt^c$, unless it is $\bot$, to the main vertical
+% list applying \!\reserved@b! to it.  This means the \!\special! for
+% $\Celt^c$ is put first prior to those for elements in $\cstraw$ or $\cst$
+% consistently in reestablishing but not in rewinding.  However as we
+% discussed in the description of \!\pcol@clearcolorstack!, the order of
+% rewinding does not affect the result for almost all printers because only
+% the number of pop operations is siginficant for them\footnote{

+% 

+% And even for the minority because multiple updates of printer's color with
+% one particular color are independent of the order of them.}.
+% 

+% Then if $\arg{box}\neq\bot$ we invoke \!\pcol@iscancst! to examine the
+% contents of $\arg{box}$ from its bottom to top.  Prior to the invocation,
+% we do the following;  let \!\@tempboxa! have an empty \!\vbox! as its initial
+% value of reformed $\arg{box}$;  let \!\pcol@tempboxa! have an empty
+% \!\vbox! as its initial value of the sequence of \!\special!s to be put
+% into the main vertical list; let $\npop=\!\@tempcntb!=0$; let
+% $M=\!\reserved@b!=()$ as its initial value of the list of identifiers of
+% math-mode pops; $\CSIndex{if@tempswa}=\true$ to mean the first \!\vbox! to
+% update $\Celt^c$ found in the scan (i.e., the bottommost one) is
+% effective.
+% \end{Sloppy}
+% 
+% In the macro \!\pcol@iscancst!, we repeatedly examine the last \!\vbox! in
+% $\arg{box}$ taken by \!\lastbox! into $\celt=\!\pcol@tempboxb!$ until
+% $\celt$ becomes $\bot$, and perform one of the following for $\celt$.
+% 

+% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
+% \def\HT{\mathit{height}}\def\DP{\mathit{depth}}\def\WD{\mathit{width}}
+% \item
+% If $\HT(\celt)=0$ and $\WD(\celt)=0$ to mean $\celt=\celtpop_i$, increment
+% $\npop$.
+% 
+% \item
+% If $\HT(\celt)=0$ and $\WD(\celt)=m>0$ to mean $\celt=\mceltpop_{i,m}$, let
+% $M=(m,M)$.
+% 
+% \item
+% If $\HT(\celt)\neq0$, $\DP(\celt)=0$ and $\WD(\celt)=0$ to mean
+% $\celt=\celt_i$, decrement $\npop$ if $\npop>0$, or otherwise add $\celt$
+% to the head of \!\@tempboxa! and apply $\!\reserved@a!\arg{\celt}$ to add
+% its result to the head of \!\pcol@tempboxa!.
+% 
+% \item
+% If $\HT(\celt)\neq0$, $\DP(\celt)=0$ and $\WD(\celt)=m>0$ to mean
+% $\celt=\mcelt_{i,m}$, do nothing if $m\in M$, or otherwise add $\celt$
+% to the head of \!\@tempboxa! and apply $\!\reserved@a!\arg{\celt}$ to add
+% its result to the head of \!\pcol@tempboxa!.
+% 
+% \item
+% If $\HT(\celt)\neq0$, $\DP(\celt)\neq0$ to mean $\celt$ has a \!\special!
+% with which $\Celt^c$ is updated.  If $\CSIndex{if@tempswa}=\true$ to mean
+% $\celt$ is the first (bottommost) occurence, $\Celt^c$ is updated
+% acquiring an \!\insert! from \!\@freelist! if it was $\bot$.  In this
+% case of $\bot$, we have to put an uncoloring \!\special! by
+% \!\reset@color!, because \!\pcol@scancst! did not do it but
+% \!\columncolor! or \!\normalcolumncolor! pushed the corresponding color
+% \!\special!.  Then we let $\CSIndex{if@tempswa}=\false$.
+% 
+% Otherwise, i.e., if $\CSIndex{if@tempswa}=\false$ for second or succeeding
+% occurences, we do nothing because updates by them are overridden by the
+% first one.
+% \end{enumerate}
+% 

+% Note that the cases other than (3) and (4) happen only in rewinding, and
+% thus in reestablishing we only have (3) and (4) with $\npop=0$ and $M=()$
+% always so that every $\celt$ is kept into new $\arg{box}$ and a coloring
+% \!\special! for it will be put into the main vertical list.
+% 
+% Then we go back to \!\pcol@scancst! to let $\arg{box}=\!\@tempboxa!$,
+% meaningless in reestablishing but not harmful, and put the contents of
+% \!\pcol@tempboxa! to the main vertical list.
+% 
+% 

+%    \begin{macrocode}
+\def\pcol@scancst#1{%
+  \@tempcnta#1\relax
+  \ifnum\@tempcnta=\pcol@colorins
+    \ifvoid\pcol@ccuse{@box}\else
+      \reserved@b{\pcol@ccuse{@box}}\fi
+  \fi
+  \ifvoid\@tempcnta\else
+    \setbox\@tempboxa\vbox{}\setbox\pcol@tempboxa\vbox{}\@tempcntb\z@
+    \def\reserved@b{}\let\@elt\relax \@tempswatrue \pcol@iscancst
+    \global\setbox\@tempcnta\box\@tempboxa \unvbox\pcol@tempboxa
+  \fi}
+\def\pcol@iscancst{%
+  \setbox\@tempcnta\vbox{%
+    \unvbox\@tempcnta \global\setbox\pcol@tempboxb\lastbox}%
+  \ifvoid\pcol@tempboxb \let\reserved@c\relax
+  \else
+    \let\reserved@c\pcol@iscancst
+    \ifdim\ht\pcol@tempboxb=\z@
+      \ifdim\wd\pcol@tempboxb=\z@ \advance\@tempcntb\@ne
+      \else \edef\reserved@b{\@elt{\number\wd\pcol@tempboxb}\reserved@b}%
+      \fi
+    \else\ifdim\dp\pcol@tempboxb=\z@
+      \ifdim\wd\pcol@tempboxb=\z@
+        \ifnum\@tempcntb>\z@ \advance\@tempcntb\m@ne
+        \else
+          \setbox\@tempboxa\vbox{\copy\pcol@tempboxb \unvbox\@tempboxa}%
+          \setbox\pcol@tempboxa\vbox{%
+            \reserved@a\pcol@tempboxb \unvbox\pcol@tempboxa}%
+        \fi
+      \else
+        \count@\wd\pcol@tempboxb \chardef\reserved@d\z@
+        \def\@elt##1{\ifnum##1=\count@ \chardef\reserved@d\@ne \fi}%
+        \reserved@b \let\@elt\relax
+        \ifnum\reserved@d=\z@
+          \setbox\@tempboxa\vbox{\copy\pcol@tempboxb \unvbox\@tempboxa}%
+          \setbox\pcol@tempboxa\vbox{%
+            \reserved@a\pcol@tempboxb \unvbox\pcol@tempboxa}%
+        \fi
+      \fi
+    \else\if@tempswa
+      \ifvoid\pcol@ccuse{@box}%
+        \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{}}\pcol@ovf
+        \pcol@ccxdef{\@currbox}\reset@color
+      \fi
+      \global\setbox\pcol@ccuse{@box}\vbox{\unvbox\pcol@tempboxb}%
+      \@tempswafalse
+    \fi\fi\fi
+  \fi
+  \reserved@c}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@savecolorstack}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to save the opening color context of a column-page.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% 

+% The macro \!\pcol@savecolorstack! is used in \!\pcol@startcolumn!,
+% \!\pcol@output@start! and \!\pcol@putbackmvl! to save the opening
+% \colorctext{} in $\CST^c$ of a \ccolpage{} $c$ known to be or found empty
+% into $\csts=\!\pcol@colorstack@saved!$.  If both of
+% $\Celt^c=|\pcol@columncolor@box|\cdot c$ and $\cst=\!\pcol@colorins!$ are
+% $\bot$, $\csts$ is let be $\bot$.  Otherwise, $\csts$ is let be a \!\vbox!
+% having a \!\vbox! for $\Celt^c$ at the top if it is not $\bot$ and then the
+% contents of $\cst$ if it is not $\bot$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% 

+%    \begin{macrocode}
+\def\pcol@savecolorstack{%
+  \ifvoid\pcol@colorins \@tempswafalse \else \@tempswatrue \fi
+  \ifvoid\pcol@ccuse{@box}%
+    \setbox\@tempboxa\box\voidb@x
+  \else
+    \setbox\@tempboxa\vbox{\unvcopy\pcol@ccuse{@box}}%
+    \ht\@tempboxa1sp \dp\@tempboxa\z@ \wd\@tempboxa\z@
+    \@tempswatrue
+  \fi
+  \if@tempswa
+    \global\setbox\pcol@colorstack@saved\vbox{%
+      \ifvoid\@tempboxa\else \box\@tempboxa \fi
+      \ifvoid\pcol@colorins\else \unvcopy\pcol@colorins \fi}
+  \else \global\setbox\pcol@colorstack@saved\box\voidb@x
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 

+% \changes{v1.2-1}{2013/05/11}
+% 	{\cs{pcol@colorstack@full} was introduced to represent
+%	 $\string\mathit{\Gamma}^c$ but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@colorstack@full} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% 

+% \KeepSpace{3}
+% \begin{macro}{\pcol@ccuse}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to implement new text coloring with \cs{insert}.}

+% \begin{macro}{\pcol@ifccdefined}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to implement new text coloring with \cs{insert}.}

+% \begin{macro}{\pcol@ccxdef}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to implement new text coloring with \cs{insert}.}

+% 

+% The macro $\!\pcol@ccuse!\arg{pfx}$ is to expand a macro
+% $|\pcol@columncolor|\cdot\arg{pfx}\cdot c$ for the current column $c$.  It
+% is used in \!\pcol@output@start! and \!\pcol@scancst@shadow! with
+% $\arg{pfx}=\hbox{`'}$ to have $\Celtshadow^c$, and in \!\pcol@scancst!,
+% \!\pcol@iscancst!, \!\pcol@savecolorstack!, \!\pcol@output@end! and
+% \!\pcol@icolumncolor! with $\arg{pfx}=|@box|$ to have $\Celt^c$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% 
+% The macro $\!\pcol@ifccdefined!\arg{then}\arg{else}$ is used in
+% \!\pcol@output@start! and \!\pcol@scancst@shadow! to examine whether
+% $\Celtshadow^c=|\pcol@columncolor|\cdot c$ is defined and to do
+% $\arg{then}$ if so or $\arg{else}$ otherwise.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% 
+% The macro $\!\pcol@ccxdef!\arg{body}$ \!\xdef!ines a macro
+% $\Celt^c=|\pcol@columncolor@box|\cdot c$ as $\arg{body}$ for the current
+% column $c$.  It is used in \!\pcol@output@start!, \!\pcol@iscancst! and
+% \!\pcol@icolumncolor!  with $\arg{body}=\!\@currbox!$ when an \!\insert!
+% for $\Celt^c$ is acquired, and in \!\pcol@output@end! with
+% $\arg{body}=\!\voidb@x!$ after releasing $\Celt^c$ to \!\@freelist!.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% 

+%    \begin{macrocode}
+\def\pcol@ccuse#1{\@nameuse{pcol@columncolor#1\number\pcol@currcol}}
+\def\pcol@ifccdefined#1#2{%
+  \expandafter\ifx\csname pcol@columncolor\number\pcol@currcol\endcsname\relax
+  #2\else#1\fi}
+\def\pcol@ccxdef#1{%
+  \expandafter\xdef
+    \csname pcol@columncolor@box\number\pcol@currcol\endcsname{#1}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \subsection{Footnote Handling}
+% \label{sec:imp-sout-scfnote}
+% \changes{v1.2-2}{2013/05/11}
+%	{Add the subsection ``Footnote Handling'' to describe newly
+%	 introduced macros for page-wise footnotes.}

+% 
+% \begin{macro}{\pcol@savefootins}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to save footnotes in multiple occasions.}

+% 

+% The macro $\!\pcol@savefootins!\arg{cs}$, invoked from \!\pcol@makecol!
+% for \Scfnote{}s and from \!\pcol@output@switch! for both \mcfnote{} and
+% \Scfnote{}s, saves \!\footins! to an \!\insert! register obtained by
+% \!\@next! from \!\@freelist!, and \!\def!ines $\arg{cs}$ being
+% \!\pcol@currfoot! or \!\pcol@footins! so that it has the register as its
+% body and the register is then saved into $\pp^f(p)$ or $\cc_c(\ft)$.  We
+% save not only \!\box! component of \!\footins! but also \!\count!,
+% \!\dimen! and \!\skip!\footnote{

+% 

+% Knowing these three components are virtually constants.}.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Footnote Handling
+
+\def\pcol@savefootins#1{%
+  \@next#1\@freelist{%
+    \global\setbox#1\box\footins
+    \global\count#1\count\footins
+    \global\dimen#1\dimen\footins
+    \global\skip#1\skip\footins}{\def#1{\voidb@x}\pcol@ovf}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@shrinkcolbyfn}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to shrink \cs{@colht} temporarily by the
+%	 height-plus-depth of page-wise footnotes and the natural size
+% 	 of the skip above them.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add the first argument $\langle\string\mathit{height}\rangle$ for
+%	 the user \cs{pcol@ioutputelt}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add the third argument $\langle\string\mathit{skip}\rangle$ to
+%	 avoid accidental destruction of \cs{@tempdimb} which was modified
+%	 unconditionally.}

+% 

+% The macro $\!\pcol@shrinkcolbyfn!\arg{height}\arg{ins}\arg{skip}$, invoked
+% from \!\pcol@makecol!, \!\pcol@ioutputelt!, \!\pcol@startcolumn!,
+% \!\pcol@restartcolumn!, \!\pcol@flushcolumn! and \!\pcol@makeflushedpage!,
+% shrinks $\arg{height}\in\{\!\@colht!,\!\@tempdima!\}$ temporarily so that a
+% column or the set of all columns resides in a page with \Scfnote{}s in the
+% \!\insert! $\arg{ins}$.  The shrinkage is calculated by adding the sum of
+% the height plus depth of all footnotes, i.e., that of $\arg{ins}$, and the
+% natural component of $\!\skip!\arg{ins}$, i.e., the vertical space
+% inserted between the columns and the footnotes.  Note that the stretch and
+% shrink components of $\!\skip!\arg{ins}$ cannot be incorporated into the
+% calculation but their contribution to each \colpage{} is taken care of by
+% the following macro \!\pcol@unvbox@cclv! if required.  Also note that the
+% inverse of $\!\skip!\arg{ins}$ is kept in $\arg{skip}$ if it is not
+% \!\relax! so that \!\pcol@deferredfootins! knows $\arg{ins}\neq\bot$ when
+% this macro is invoked from \!\pcol@startcolumn! and
+% \!\pcol@restartcolumn! with $\arg{skip}=\!\@tempdimb!$.
+% 

+%    \begin{macrocode}
+\def\pcol@shrinkcolbyfn#1#2#3{%
+  \ifx#3\relax\else #3-\skip#2\relax \fi
+  \advance#1-\ht#2\advance#1-\dp#2\advance#1-\skip#2\relax}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@unvbox@cclv}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to add stretch/shrink components of
+%	 \cs{skip}\cs{footins} at the bottom of a column-page if the page has
+%	 page-wise footnotes.}

+% 

+% The macro $\!\pcol@unvbox@cclv!\arg{ins}$, invoked from \!\pcol@makecol! and
+% \!\pcol@flushcolumn! when they work on a column-page with \Scfnote{}s,
+% adds the stretch and shrink components of $\!\skip!\arg{ins}$ at the end
+% of \!\box!|255|, where $\arg{ins}$ is non-void $\pp^f(p)$ having
+% \Scfnote{}s.  Before the addition, the macro goes back to the baseline of
+% \!\box!|255|\footnote{

+% 

+% The comparison of the depth of \cs{box}\texttt{255} and \cs{@maxdepth} and
+% taking the latter if it is smaller is really just-in-case.}
+% 

+% to nullify the baseline progress mechanism so as to make it sure the exact
+% amount of the vertical skip is added.  Then it adds the stretch and shrink
+% by at first adding the skip itself and then the negative amount of its
+% natural component.
+% 

+%    \begin{macrocode}
+\def\pcol@unvbox@cclv#1{%
+  \@tempdima\dp\@cclv \unvbox\@cclv
+  \vskip \ifdim\@tempdima>\@maxdepth -\@maxdepth \else -\@tempdima \fi
+  \vskip\skip#1\@tempdima\skip#1\vskip-\@tempdima}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@deferredfootins}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to insert deferred footnotes.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Fix the bug that the height cap was underestimated by the duplicated
+%	 subtraction of \cs{skip}\cs{footins} if the page has already have
+%	 non-deferred footnotes.}

+% 

+% The macro $\!\pcol@deferredfootins!\arg{macro}$, invoked from
+% \!\pcol@startcolumn! and \!\pcol@restartcolumn!, tries to \!\insert! some
+% of leading deferred footnotes in $\df$ through \!\footins!\footnote{

+% 

+% The argument $\arg{macro}$ has the invoker itself shown in debug
+% messages.}.
+% 

+% In order to avoid that \!\footins! has footnotes across three or more
+% pages to make confusion in the order of footnotes kept inside of \TeX, we
+% cap the total height of footnotes by $h=\!\@colht!$ if it has already
+% shrunk by non-deferred footnotes in the page we are working on indicated
+% by $\!\@tempdimb!<0$, or $h=\!\@colht!-\!\skip!\!\footins!$ if the page
+% does not have non-deferred footnotes indicated by $\!\@tempdimb!=0$.  That
+% is, we extract leading elements of $\df$ by \!\vsplit! until their total
+% height reaches $h$ and, if some elements are obtained in \!\@tempboxa!,
+% \!\insert!  them through \!\footins!.  As for the remaining elements if
+% any, we add a leading \!\penalty!\!\interlinepenalty! which should have
+% been removed by \!\vsplit!.
+% 
+% Note that we temporarily let $\!\splitmaxdepth!=\!\@maxdepth!$,
+% $\!\splittopskip!=0$ and $\!\vbadness!=\infty$ at the \!\vsplit! so that
+% the depth of the split first half is \!\@maxdepth! at deepest, the second
+% half does not have any skip at its top, and \TeX{} will not complain of
+% (almost) inevitable underfull.  Also note that the successful extraction
+% of the leading elements is examined by checking \!\ht!\!\@tempboxa! and
+% thus we need to \!\unvbox!  it in itself because \!\vsplit! makes the
+% height $h$ regardless of its contents.
+% 

+%    \begin{macrocode}
+\def\pcol@deferredfootins#1{%
+  \ifdim\@tempdimb=\z@ \@tempdimb\@colht \advance\@tempdimb-\skip\footins
+  \else \@tempdimb\@colht
+  \fi
+  \ifvoid\pcol@topfnotes\else \ifdim\@tempdimb>\z@
+    \begingroup
+      \splitmaxdepth\@maxdepth \splittopskip\z@ \vbadness\@M
+      \setbox\@tempboxa\vsplit\pcol@topfnotes to\@tempdimb
+      \ifvoid\pcol@topfnotes\else
+        \global\setbox\pcol@topfnotes\vbox{\penalty\interlinepenalty
+          \unvbox\pcol@topfnotes}%
+      \fi
+      \setbox\@tempboxa\vbox{\unvbox\@tempboxa}%
+      \ifdim\ht\@tempboxa>\z@
+        \pcol@Log#1{add}\@tempboxa
+        \insert\footins{\unvbox\@tempboxa}%
+      \fi
+    \endgroup
+  \fi\fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@combinefootins}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to put footnotes into pre-environment stuff.}

+% \changes{v1.35-4}{2018/12/31}
+% 	{Add the insertion of vertical skip \cs{belowfootnoteskip}.}

+% \begin{macro}{\pcol@putfootins}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to put page-wise footnotes to a page.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Change users \cs{pcol@outputelt} to \cs{pcol@ioutputelt}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Remove \cs{pcol@output@end} from users.}

+% 

+% The macro $\!\pcol@combinefootins!\arg{b}\arg{f}$, invoked solely from
+% \!\pcol@makenormalcol!\footnote{

+% 

+% And thus having the arguments $\arg{b}$ and $\arg{f}$ is unnecessary, but
+% we keep this implementation to avoid unnecessary recoding from a
+% development version.},
+% 

+% constructs the \preenv{} in \!\@outputbox!, combining the stuff in the box
+% $b$ and pre-environment footnotes in the \!\insert! $f$.  It is almost
+% equivalent to the \cs{else} part of \!\@makecol! in which the main
+% vertical list and \Mcfnote{}s are combined.  The operation to put
+% footnotes is almost equivalent to the second half of the \cs{else} part
+% except that \!\insert!  is not always \!\footins! but $f$ and is done by
+% \!\pcol@putfootins! in which a null vertical skip is added after $f$ but
+% this skip is removed by \!\unskip! after the invocation.  The other
+% difference is that the vertical space of \!\belowfootnoteskip! is added if
+% it is not 0\footnote{

+% 

+% We avoid null space insertion to minimize the difference from older
+% versions in traced output.}
+% 

+% to have some space between non-merged \Preenv{} footnotes and the first
+% lines in a \env{paracol} environment.
+% 
+% The null vertical skip is put for \Scfnote{}s, for which the macro
+% \!\pcol@putfootins! is invoked from \!\pcol@ioutputelt! and
+% \!\pcol@makeflushedpage!.  Since we shrink the height of \colpage{}s by
+% the height-plus-depth of \Scfnote{}s, the natural height of the box in
+% which \colpage{}s and \Scfnote{}s are combined would be less than
+% \!\textheight! due to the depth of the last footnote line if we simply
+% made the footnotes the last items of the box.  Though this shortage at
+% most \!\maxdepth! is expected to be covered by the stretch factor of
+% \!\skip!\!\footins! without too large badness causing an underfull
+% message\footnote{

+% 

+% With default settings of $\cs{maxdimen}=5\,|pt|$ and the stretch factor
+% 4\,|pt| of \cs{skip}\cs{footins}, the badness $100\times(5/4)^3\approx195$
+% is significantly less than the default $\cs{vbadness}=1000$.},
+% 

+% someday we could face an underfull with some unusual settings of
+% \!\maxdimen!, \!\skip!\!\footins! and/or \!\vbadness!.  Therefore, we put a
+% null vertical skip so that the real bottom of the footnotes, instead of
+% the last baseline, is placed at the baseline of the box, to make the
+% natural height of the box is \!\textheight! exactly.  Note that this
+% shifting \Scfnote{}s up will not make last baselines of footnotes among
+% pages unaligned, because the last line have a strut.
+% 

+%    \begin{macrocode}
+\def\pcol@combinefootins#1#2{%
+  \setbox\@outputbox\vbox{%
+    \boxmaxdepth\@maxdepth
+    \unvbox#1\relax
+    \pcol@putfootins#2\unskip
+    \ifdim\belowfootnoteskip=\z@\else \vskip\belowfootnoteskip \fi}}
+\def\pcol@putfootins#1{%
+  \vskip\skip#1\relax
+  \color@begingroup
+    \normalcolor
+    \footnoterule
+    \unvbox#1\relax
+  \color@endgroup \vskip\z@}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% 
+% 
+% \KeepSpace{3}
+% \subsection{Marginal Notes}
+% \label{sec:imp-sout-mpar}
+% \changes{v1.3-4}{2013/09/17}
+%	{Add this section ``Marginal Notes''.}

+% 
+% \begin{macro}{\@addmarginpar}
+% \changes{v1.3-4}{2013/09/17}
+%	{Made \cs{let}-equal to \cs{pcol@addmarginpar} in
+%	 \string\texttt{paracol} environments.}

+% \begin{macro}{\pcol@addmarginpar}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to make a margin sharable by marginal notes from
+%	 different columns.}

+% \changes{v1.35-3}{2018/12/31}
+% 	{Fix the bug referring to \cs{@marbox} inappropriately.}

+% \changes{v1.35-3}{2018/12/31}
+% 	{Add vertical shifting of marginal note to emulate of
+%	 \cs{marginnote}.}

+% \begin{macro}{\pcol@@addmarginpar}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to keep the original definition of \cs{@addmarginpar}.}

+% \def\swap{\mathit{swap}}
+% 

+% The macro \!\pcol@addmarginpar! is our own version of \!\@addmarginpar!,
+% which \!\pcol@zparacol! makes \!\let!-equal to \!\pcol@addmarginpar!
+% keeping its original definition in \!\pcol@@addmarginpar!.  Therefore, in
+% an \env{paracol} environment, the \!\output! request made by \LaTeX's
+% \!\marginpar! in the column $c$ and page $p$ is processed by
+% \!\pcol@addmarginpar! through our own \!\output! routine being
+% \!\pcol@output!, \!\pcol@specialoutput! and \LaTeX's \!\@specialoutput!.
+% What we do in this macro are as follows;  determine the margin which a
+% marginal note goes to; temporarily modify the parameter
+% $m_w=\!\marginparwidth!$ or $m_s=\!\marginparsep!$ according to the margin
+% and the column; determine the position to place the marginal note
+% consulting $\pp^m(p)=\!\pcol@mparbottom!$ obtained by
+% \!\pcol@getcurrpage!: and update $\pp^m(p)$ according to the postion.
+% 
+% First, there are the following parameters to determine the margin, and thus
+% the value of $\CSIndex{if@firstcolumn}$ referred to in \LaTeX's
+% \!\@addmarginpar! and meaning left if $\true$ or right if $\false$.
+% 

+% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
+% \item
+% The macros \!\pcol@mpthreshold@l! and \!\pcol@mpthreshold@r! defined by
+% \!\marginpar~threshold!\ give us the threshold of the column number to let
+% columns less than it go to the left margin while those equal to or greater
+% than it to the right, according to the \parapag{}e the column belongs to.
+% Therefore, we let $\CSIndex{if@firstcolumn}=\true$ iff
+% $c<\!\pcol@mpthreshold@l!\land c<\CL$ or $c<\!\pcol@mpthreshold@r!\land
+% c\geq\CL$, as the fundamental setting.
+% 
+% \item
+% If $\CSIndex{ifpcol@swapmarginpar}=\true$ because the specifier `|m|' is
+% given to \!\twosided! explicitly or implicitly, the decision in (1) is
+% reversed if $\page(p)\bmod2=0$, and then this decision is reversed again
+% if $c\geq\CL$ and $\CSIndex{ifpcol@paired}=\false$ to mean $c$ is in a
+% \npaired{} right \parapag{}e.  The second reversal is done because
+% $\page(p)$ is \emph{common} to both left and right \parapag{}es and is for
+% the left page in usual cases without page number jumps.  Therefore,
+% $(\page(p)\bmod2)$ is for left \parapag{}es and thus for right counterparts
+% the decision should be made by $((\page(p)+1)\bmod2)$ and thus the result
+% should be reversed.
+% 
+% \item
+% If \CSIndex{if@reversemargin} is made $\true$ by \LaTeX's
+% \!\reversemarginpar!, the decision made by (1) and then possibly reversed
+% by (2) is finally reversed.
+% \end{enumerate}
+% 

+% Second, we calculate
+% $$
+% D=\!\@tempdima!=\sum_{d=\Cfrom}^{\swap(c)-1}(w_{\swap(d)}+g_{\swap'(d)})
+% $$
+% where $x'=swap(x)$ is given by
+% $\!\pcol@swapcolumn!\<x\>\<x'\>\<\Cfrom\>\<\Cto\>$ to let
+% $x'=\Cto-(x-\Cfrom)-1$ if $\CSIndex{ifpcol@swapcolumn}=\true$ and
+% $\page(p)\bmod2=0$ or $x'=x$ otherwise,
+% $\swap'(x)=\!\pcol@colsepid!\in\{\swap(x)-1,x\}$ according to swapped or
+% not, $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$ according to $c<\CL$ or not,
+% and $\w_x$ and $\gap_x$ are the width of $x$-th column and gap given by
+% $|\pcol@columnwidth|{\cdot}x$ and $|\pcol@columnsep|{\cdot}x$
+% respectively.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% That is, $D$ is the distance from the left edge of the column $c$ to that
+% of leftmost column in the (paralell-)
+% 

+% \Index{parallel-paging}
+% 

+% page in which $c$ resides.  Then if $\CSIndex{if@firstcolumn}=\true$ to
+% let the margial note go to the left margin, we add $D$ to
+% $m_w=\!\marginparwidth!$ so that \LaTeX's \!\@addmarginpar! being
+% \!\pcol@@addmarginpar! aligns the left edge of the marginal note at the
+% point apart from the column's left edge by $(D+m_w)+m_s$ rather than
+% $m_w+m_s$, or in other words $m_w+m_s$ apart from the left edge of the
+% leftmost column.  On the other hand if $\CSIndex{if@firstcolumn}=\false$,
+% we add $\WT-(D+w_c)$ where $\WT$ is \!\textwidth!, being the distance from
+% the right edge of the column $c$ to that of the rightmost column, to
+% $m_s=\!\marginparsep!$ so that \!\pcol@@addmarginpar!  aligns the left
+% edge of the marginal note at the point apart from the column's right edge
+% by $\WT-(D+w_c)+m_s$ rather than $m_s$, or in other words $m_s$ apart from
+% the right edge of the rightmost column.
+% 
+% Third, we let \Midx{\!\pcol@marbox!} be the first element of \!\@currlist!
+% obtained by \!\@xnext! for the right marginal note if
+% $\CSIndex{if@firstcolumn}=\false$, or \!\@currbox! for the left marginal
+% note otherwise.  Then we let $t=\!\@tempdima!$ be the distance from the
+% top edge of the column to that of the marginal note, namely \!\@pageht!
+% minus the height of \!\pcol@marbox! plus |\dimen|\!\@currbox! being
+% downward shift amount optionally given by \!\marginnote!.  We also let
+% $h=\!\@tempdimb!$ be the height-plus-depth of the box \!\pcol@marbox!
+% plus \!\marginparpush!, or in other words the vertical space the marginal
+% note requires.  Then we give $t$ and $h$ to \!\pcol@getmparbottom! to let
+% \!\@mparbottom! have the bottom of the exisiting marginal text below which
+% we put the margial text in \!\pcol@marbox!, and to let \!\pcol@mpblist!
+% have the new list to be replaced with $\mpb_{\{L,R\}}^{\{l,r\}}$ in
+% $\pp^m(p)$.
+% 
+% Forth, we update $\pp^m(p)$ with the new list in \!\pcol@mpblist! by a
+% process similar to \!\pcol@setpageno! but with \!\pcol@setmpbelt! to scan
+% the list of pages $\PPP$.
+% 
+% Fifth, we shift down \!\pcol@marbox! by |\dimen|\!\@currbox! and, if the
+% shift amount is greater than the height of the box and thus the height of
+% shifting result is zero, decrement \!\@mparbottom! by the amount to
+% deceive \LaTeX's \!\@addmarginpar! into believing \!\@mparbottom! is above
+% the real one by the amount.  In other words, by the decrement we let
+% \!\@addmarginpar! see the top edge of the shifted marginal note in the
+% box, rather than that of the box itself, for the placement with
+% \!\@mparbottom!.
+% 
+% Finally, we invoke \LaTeX's original \!\@addmarginpar! being
+% \!\pcol@@addmarginpar! to put the marginal note according to
+% \CSIndex{if@firstcolumn}, temporarily modified \!\marginparsep! and
+% \!\marginparwidth!, and \!\@mparbottom!.  Note that since
+% \!\pcol@zparacol! lets $\CSIndex{if@twocolumn}\~=\true$,
+% \!\pcol@@addmarginpar! determine the margin only by
+% \CSIndex{if@firstcolumn}.  Also note that it can be $\!\@mparbottom!>t$
+% (before decrement with the positive shift amount) to mean the marginal
+% note should be shifted down from its natural position, and if so
+% \!\pcol@@addmarginpar!  will give us a warning as the correct consequence
+% of the placement.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Marginal Notes
+
+\def\pcol@addmarginpar{%
+  \pcol@getcurrpage \@firstcolumntrue
+  \ifnum\pcol@currcol<\pcol@ncolleft
+    \let\reserved@a\z@ \let\reserved@b\pcol@ncolleft
+    \ifnum\pcol@mpthreshold@l>\pcol@currcol\else \@firstcolumnfalse \fi
+  \else
+    \let\reserved@a\pcol@ncolleft \let\reserved@b\pcol@ncol
+    \ifnum\pcol@mpthreshold@r>\pcol@currcol\else \@firstcolumnfalse \fi
+  \fi
+  \ifpcol@swapmarginpar
+    \ifodd\c@page\else
+      \if@firstcolumn \@firstcolumnfalse \else \@firstcolumntrue \fi
+    \fi
+    \ifpcol@paired\else \ifnum\pcol@currcol<\pcol@ncolleft\else
+      \if@firstcolumn \@firstcolumnfalse \else \@firstcolumntrue \fi
+    \fi\fi
+  \fi
+  \if@reversemargin
+    \if@firstcolumn \@firstcolumnfalse \else \@firstcolumntrue \fi
+  \fi
+  \pcol@swapcolumn\pcol@currcol\count@\reserved@a\reserved@b
+  \@tempdima\z@
+  \@tempcnta\reserved@a \@whilenum\@tempcnta<\count@\do{%
+    \pcol@swapcolumn\@tempcnta\@tempcntb\reserved@a\reserved@b
+    \advance\@tempdima\csname pcol@columnwidth\number\@tempcntb\endcsname\relax
+    \advance\@tempdima\csname pcol@columnsep\pcol@colsepid\endcsname\relax
+   \advance\@tempcnta\@ne}%
+  \if@firstcolumn \advance\marginparwidth\@tempdima
+  \else
+    \advance\marginparsep\textwidth \advance\marginparsep-\@tempdima
+    \advance\marginparsep-\columnwidth
+  \fi
+  \expandafter\@xnext\@currlist\@@\pcol@marbox\@gtempa
+  \if@firstcolumn\let\pcol@marbox\@currbox \fi
+  \@tempdima\@pageht \advance\@tempdima-\ht\pcol@marbox
+  \advance\@tempdima\dimen\@currbox
+  \@tempdimb\ht\pcol@marbox \advance\@tempdimb\dp\pcol@marbox
+  \advance\@tempdimb\marginparpush
+  \pcol@getmparbottom\@tempdima\@tempdimb
+  \begingroup
+    \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
+    \edef\reserved@a{\pcol@pages\pcol@currpage}%
+    \global\let\pcol@pages\@empty \global\let\pcol@currpage\@empty
+    \let\@elt\pcol@setmpbelt \reserved@a
+  \endgroup
+  \ifdim\dimen\@currbox=\z@\else
+    \ifdim\dimen\@currbox>\ht\pcol@marbox
+       \advance\@mparbottom-\dimen\pcol@marbox
+    \fi
+    \setbox\pcol@marbox\hbox{\lower\dimen\@currbox\box\pcol@marbox}%
+  \fi
+  \pcol@@addmarginpar}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{3}
+% \begin{macro}{\pcol@getmparbottom}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to find the space where a marginal note is placed.}

+% \begin{macro}{\pcol@getmparbottom@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to find the space where a marginal note is placed.}

+% \begin{macro}{\pcol@getmpbelt}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to find the space where a marginal note is placed.}

+% \changes{v1.33-1}{2016/11/19}
+% 	{Fix the bug by which $t_k$ such that $t_k\geq t$ and $t_k-t\geq h$
+%	 but $t_k-b_{k-1}<h$ is found.}
+% 

+% The macro $\!\pcol@getmparbottom!\<t\>\<h\>$ is solely used in
+% \!\pcol@addmarginpar!\footnote{

+% 

+% Thus giving $t$ and $h$ as arguments is not necessary but we dare to do
+% it.}
+% 

+% to let $B=\!\@mparbottom!$ point the bottom of the marginal note below
+% which a new marginal note $m$, whose natural top is at $t$ and occupancy
+% height is $h$, in the current column $c$ and the page $p$ is placed, or 0
+% if the side margin has had no marginal notes yet.  It is also \!\def!ines
+% $M'=\Midx{\!\pcol@mpblist!}$ having $\mpar(t',t'{+}h)$ for the new marginal
+% note $m$ placed at $t'$ in it and being replaced with one of
+% $\mpb_{\{L,R\}}^{\{l,r\}}$ in $\pp^m(p)$ by \!\pcol@setmpbelt!.
+% 
+% First we examine if $\pp^m(p)=\!\pcol@mparbottom!$ is empty and if so we
+% simply let $B=0$ and $M'=(\mpar(t,t+h))$ because there are no marginal
+% notes in the page $p$ at all.  Otherwise we obtain
+% $M\in\Set{\mpb_X^x}{X\in\{L,R\},\;x\in\{l,r\}}$ in \!\reserved@a! according
+% to the side margin to which the new marginal note $m$ goes to, i.e.,
+% according to $\CSIndex{if@firstcolumn}$ and $c<\CL$ or not, by
+% \!\pcol@getmparbottom@i! giving it the body of $\pp^m(p)$ by
+% \!\expandafter!.  Then we apply $\!\pcol@getmpbelt!$ to each
+% $\mpar(t_i,b_i)\in M$ to have
+% $t_k=\min\Set{t_i}{t_i\geq{t},\;t_i-\max(t,b_{i-1})\geq{h}}$ and let
+% $B=b_{k-1}$ and
+% 

+% \begin{eqnarray*}
+% M'&=&(\mpar(t_1,b_1),\;\ldots,\;\mpar(t_{k-1},b_{k-1}),\;
+%       \mpar(\max(t,B),\,\max(t,B)+h),\\
+% &&\phantom{\LP}
+%       \mpar(t_k,b_k),\;\ldots,\;\mpar(t_n,b_n))
+% \end{eqnarray*}
+% 

+% where $n=\Abs{M}$, assuming $b_0=0$.  That is, we try to find the first
+% avilable gap between marginal notes below $t$ to accommodate the
+% marginal note $m$ of $h$ tall.  Then if such $t_k$ is not found because
+% $t>t_n$ to mean $m$ appears below the last marginal note as in natural
+% cases, or $t_i-\max(t,b_{i-1})<h$ for all $t_i$ s.t.\ $t_i>t$ to mean
+% there are no available gaps, we let $B=t_n$ and
+% $M'=(M,\mpar(\max(t,B),\,\max(t,B)+h))$ to place $m$ at the bottom.
+% 

+%    \begin{macrocode}
+\def\pcol@getmparbottom#1#2{%
+  \global\@mparbottom\z@
+  \ifx\pcol@mparbottom\@empty
+    \begingroup
+      \@tempdimc#2\relax \advance\@tempdimc#1\relax \let\@elt\relax
+      \xdef\pcol@mpblist{\@elt{\number#1}{\number\@tempdimc}}%
+    \endgroup
+  \else
+    \expandafter\pcol@getmparbottom@i\pcol@mparbottom
+    \begingroup
+      \@tempdima#1\relax \@tempdimb#2\relax \@tempswafalse
+      \let\@elt\pcol@getmpbelt \global\let\pcol@mpblist\@empty \reserved@a
+      \if@tempswa\else
+        \ifdim\@tempdima<\@mparbottom \@tempdima\@mparbottom \fi
+        \advance\@tempdimb\@tempdima
+        \@cons\pcol@mpblist{{\number\@tempdima}{\number\@tempdimb}}%
+      \fi
+    \endgroup
+  \fi}
+\def\pcol@getmparbottom@i#1#2#3#4{%
+  \ifnum\pcol@currcol<\pcol@ncolleft
+    \if@firstcolumn \def\reserved@a{#1}\else\def\reserved@a{#2}\fi
+  \else
+    \if@firstcolumn \def\reserved@a{#3}\else\def\reserved@a{#4}\fi
+  \fi}
+\def\pcol@getmpbelt#1#2{%
+  \ifdim#1sp<\@tempdima
+    \global\@mparbottom#2sp\relax \@cons\pcol@mpblist{{#1}{#2}}%
+    \ifdim\@tempdima<#2sp\relax \@tempdima#2sp\relax \fi
+  \else
+    \@tempdimc\@tempdima \advance\@tempdimc\@tempdimb
+    \ifdim#1sp<\@tempdimc
+      \@tempdima#2sp\relax \global\@mparbottom#2sp\relax
+      \@cons\pcol@mpblist{{#1}{#2}}%
+    \else
+      \@cons\pcol@mpblist{{\number\@tempdima}{\number\@tempdimc}\@elt{#1}{#2}}%
+      \@tempswatrue
+      \def\pcol@getmpbelt##1##2{\@cons\pcol@mpblist{{##1}{##2}}}
+    \fi
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@setmpbelt}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to update $\pi^m(p)$.}

+% \begin{macro}{\pcol@setmpbelt@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to update $\pi^m(p)$.}

+% 

+% The macro $\!\pcol@setmpbelt!
+% \Arg{\pp^p(q)}\<\pp^i(q)\>\<\pp^f(q)\>\Arg{\pp^s(q)}\Arg{\pp^m(q)}$ is
+% used solely in \!\pcol@addmarginpar! and is applied to $\PPP$ to update an
+% element $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in{l,r}}$ in $\pp^m(p)$ with
+% $M'=\!\pcol@mpblist!$ given by \!\pcol@getmparbottom!.  The structure of
+% the macro is similar to \!\pcol@setpnoelt! to upadate $\pp^p(q)$ s.t.\
+% $q\geq p$, but in this macro the target of the update is only $p$.  Then
+% for $q=p$, we invoke \!\pcol@setmpbelt@i! giving it the body of $\pp^m(p)$
+% being
+% $\Arg{\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$, or
+% $\<\emptyset\>\<\emptyset\>\<\emptyset\>\<\emptyset\>$ if
+% $\pp^m(p)=\emptyset$, to obtain what $\pp^m(p)$ should have in
+% $\pp_{\mathit{new}}^m(p)=\!\reserved@a!$ in which $\mpb_X^x$ is replaced
+% with $M'$, where $X=L$ or $X=R$ if $c<\CL$ or not respectively, and $x=l$
+% or $x=r$ if $\CSIndex{if@firstcolumn}=\true$ or not respectively, and then
+% update $\pp^m(p)$ by $\!\pcol@defcurrpage!
+% \Arg{\pp^p(p)}\<\pp^i(p)\>\<\pp^f(p)\>\Arg{\pp^s(p)}
+% \Arg{\pp_{\mathit{new}}^m(q)}$.
+% 

+%    \begin{macrocode}
+\def\pcol@setmpbelt#1#2#3#4#5{%
+  {\let\@elt\relax \xdef\pcol@pages{\pcol@pages\pcol@currpage}}%
+  \ifnum\@tempcnta=\z@
+    \def\reserved@a{#5}%
+    \ifx\reserved@a\@empty \pcol@setmpbelt@i{}{}{}{}\else \pcol@setmpbelt@i#5\fi
+    \pcol@defcurrpage{#1}{#2}{#3}{#4}{\reserved@a}%
+  \else \gdef\pcol@currpage{\@elt{#1}#2#3{#4}{#5}}%
+  \fi
+  \advance\@tempcnta\m@ne}
+\def\pcol@setmpbelt@i#1#2#3#4{%
+  \ifnum\pcol@currcol<\pcol@ncolleft
+    \if@firstcolumn \def\reserved@a{{\pcol@mpblist}{#2}{#3}{#4}}%
+    \else           \def\reserved@a{{#1}{\pcol@mpblist}{#3}{#4}}%
+    \fi
+  \else
+    \if@firstcolumn \def\reserved@a{{#1}{#2}{\pcol@mpblist}{#4}}%
+    \else           \def\reserved@a{{#1}{#2}{#3}{\pcol@mpblist}}%
+    \fi
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@mparbottom@zero}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to give the default of \cs{pcol@mparbottom@out}.}

+% \begin{macro}{\pcol@mparbottom@out}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to keep the last elements of $\pi^m(p_t)$ at
+%	 \cs{end}\string\texttt{\char`\{paracol\char`\}.}}

+% 

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

+%    \begin{macrocode}
+\gdef\pcol@mparbottom@zero{{\@elt{0}{0}}{\@elt{0}{0}}{\@elt{0}{0}}{\@elt{0}{0}}}
+\global\let\pcol@mparbottom@out\pcol@mparbottom@zero
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\pcol@do@mpbout}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to do specified operations on $\string\cal{M}$ and its
+%	 element $M_L^x$ acccording to the side margin for marginal notes
+%	 outside \texttt{paracol} environments.}

+% \begin{macro}{\pcol@do@mpbout@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to do specified operations on $\string\cal{M}$ and its
+%	 element $M_L^x$ acccording to the side margin for marginal notes
+%	 outside \texttt{paracol} environments.}

+% \begin{macro}{\pcol@do@mpbout@whole}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to do a specified operation on $\string\cal{M}$.}

+% \begin{macro}{\pcol@do@mpbout@elem}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to do a specified operation on an element $M_L^x$ in
+%	 $\string\cal{M}$.}

+% 

+% The macro \!\pcol@do@mpbout! is used in \!\pcol@output@start! and
+% \!\pcol@output@end! to perform operations specified by
+% \!\pcol@do@mpbout@whole!  and \!\pcol@do@mpbout@elem!.  The macro just
+% invokes \!\pcol@do@mpbout@i! giving it all
+% $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$ by \!\expandafter!.
+% 
+% Then \!\pcol@do@mpbout@i! determines the side margin $x\in\{l,r\}$ letting
+% $x=l$ iff $\CSIndex{if@mparswitch}=\true$, $\page(p)\bmod2=0$ and
+% $\CSIndex{if@reversemargin}=\false$, to invoke \!\pcol@do@mpbout@whole!
+% giving it all $M$ but $\mpb_L^x$ whose sole element $\mpar(t,b)$
+% may be modified by $\!\pcol@do@mpbout@elem!\!\@elt!\Arg{t}\Arg{b}$.
+% 
+% In \!\pcol@output@start!, \!\pcol@do@mpbout@whole! is to \!\xdef!ine
+% $\mpbout$ with all $M$ and \!\pcol@do@mpbout@elem! is expanded to
+% $\mpar(0,B)$, where $B=\!\@mparbottom!$, regardless of $\mpb_L^x$ so that
+% it is replaced with $(\mpar(0,B))$ in the modified $\mpbout$ keeping other
+% elements unchanged.  In \!\pcol@output@end!, \!\pcol@do@mpbout@whole! is
+% to throw all $M$ away into a \!\hbox! while \!\pcol@do@mpbout@elem! lets
+% $B=b$ so that the bottom of the last marginal note in the side margin
+% specified by $x$ is passed to \postenv{} through \!\@mparbottom!.
+% 

+%    \begin{macrocode}
+\def\pcol@do@mpbout{\expandafter\pcol@do@mpbout@i\pcol@mparbottom@out}
+\def\pcol@do@mpbout@i#1#2#3#4{\@tempcnta\@ne
+  \if@mparswitch \ifodd\c@page\else \@tempcnta\m@ne \fi\fi
+  \if@reversemargin \@tempcnta-\@tempcnta \fi
+  \ifnum\@tempcnta<\z@
+    \pcol@do@mpbout@whole{\pcol@do@mpbout@elem#1}{#2}{#3}{#4}%
+  \else
+    \pcol@do@mpbout@whole{#1}{\pcol@do@mpbout@elem#2}{#3}{#4}%
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@bias@mpbout}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to perform coordinate transformation of the elements in
+% 	 $\string\cal{M}$.}

+% \begin{macro}{\pcol@bias@mpbout@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to perform coordinate transformation of the elements in
+% 	 $\string\cal{M}$.}

+% 

+% The macro $\!\pcol@bias@mpbout!\Arg{y}$ is used in \!\pcol@output@start!
+% with $-y$ being the heigh-plus-depth of \preenv{}, in
+% \!\pcol@output@end! with $y$ being that of \spanning{} in the \lpage, and
+% in $\!\pcol@getmparbottom@last!\Arg{y}$ with its argument $y$.  The macro
+% modifies $\mpar(t,b)$ in all $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$
+% of $\mpbout$ so that they have $\mpar(t{+}y,b{+}y)$ for the transformation
+% from text area coordinates to columns in the first and third, while for
+% the reverse transformation in the second, by invoking \!\pcol@do@mpb@all!
+% giving it $\mpbout$ and letting \!\reserved@a! have
+% $\!\pcol@bias@mpbout@i!\Arg{y}$.  That is,
+% $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$ is then
+% invoked in \!\pcol@do@mpb@all@ii! with $t$ and $b$ from $\mpar(t,b)$ in
+% each $M$, and then it \!\def!ines \!\reserved@b! with $\mpar(t{+}y,b{+}y)$
+% so that updated $M$ has it.
+% 

+%    \begin{macrocode}
+\def\pcol@bias@mpbout#1{\def\reserved@a{\pcol@bias@mpbout@i{#1}}%
+  \pcol@do@mpb@all\pcol@mparbottom@out}
+\def\pcol@bias@mpbout@i#1\@elt#2#3\@nil{%
+  \dimen@#2sp\relax \advance\dimen@#1\relax
+  \dimen@ii#3sp\relax \advance\dimen@ii#1\relax
+  \def\reserved@b{\@elt{\number\dimen@}{\number\dimen@ii}}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@getmparbottom@last}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to let $\string\cal{M}$ have the occupancy information of
+%	 the bottom marginal note in each margin.}

+% \begingroup\let\small\footnotesize
+% \begin{macro}{\pcol@getmparbottom@last@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to let $\string\cal{M}$ have the occupancy information of
+%	 the bottom marginal note in each margin.}

+% 

+% The macro $\!\pcol@getmparbottom@last!\Arg{y}$ is used solely in
+% \!\pcol@output@end! to let
+% $\mpbout=\Arg{m_L^l}\Arg{m_L^r}\Arg{m_R^l}\Arg{m_R^r}$, where
+% $m_X^x=\mpar(t_n,b_n)\in\mpb_X^x$, $n=\Abs{\mpb_X^x}$ asuming
+% $\mpar(t_0,b_0)={\mpar}(y,y)$, and $y$ is the negative counterpart of the
+% height-plus-depth of the \spanning{} in the \lpage.  Therefore, $\mpbout$
+% is let have the occupancy information of the last marginal note if any, or
+% the top edge of text area otherwise, in each margin.
+% 
+% The macro at first examines if $\pp^m(\ptop)=\emptyset$ and, if so, lets
+% all elements in $\mpbout$ have $(\mpar(y,y))$ by letting it $\mpboutz$ and
+% then adding $y$ to each $t=b=0$ by \!\pcol@bias@mpbout! giving it $y$.
+% Otherwise, i.e., if $\pp^m(\ptop)\neq\emptyset$, it invokes
+% \!\pcol@do@mpb@all! giving it $\pp^m(\ptop)$ and letting \!\reserved@a!
+% have $\!\pcol@getmparbottom@last@i!\Arg{y}$.  That is,
+% $\!\pcol@getmparbottom@last@i!\Arg{y}\~\mpar(t_1,b_1)\cdots
+% \mpar(t_n,b_n)\!\@nil!$ is then invoked in \!\pcol@do@mpb@all@ii! for each
+% $\mpb_X^x$ to let \!\reserved@b! have $\mpar(y,y)$ at first and then to
+% let it have $\mpar(t_i,b_i)$ for all $i\in[1,n]$.  Therefore,
+% \!\reserved@b! should finally have $\mpar(t_n,b_n)$ assuming $t_0=b_0=y$,
+% and then becomes $m_X^x$.
+% \end{macro}\endgroup
+% 

+%    \begin{macrocode}
+\def\pcol@getmparbottom@last#1{%
+  \ifx\pcol@mparbottom\@empty
+    \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
+    \pcol@bias@mpbout{#1}%
+  \else
+    \def\reserved@a{\pcol@getmparbottom@last@i{#1}}%
+    \pcol@do@mpb@all\pcol@mparbottom
+  \fi}
+\def\pcol@getmparbottom@last@i#1#2\@nil{%
+  \edef\reserved@b{\@elt{\number#1}{\number#1}}%
+  \def\@elt##1##2{\def\reserved@b{\@elt{##1}{##2}}}%
+  #2\let\@elt\relax}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@do@mpb@all}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to implement \cs{pcol@bias@mpbout} and
+%	 \cs{pcol@getmparbottom@last}.}

+% \begin{macro}{\pcol@do@mpb@all@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to implement \cs{pcol@bias@mpbout} and
+%	 \cs{pcol@getmparbottom@last}.}

+% \begin{macro}{\pcol@do@mpb@all@ii}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to implement \cs{pcol@bias@mpbout} and
+%	 \cs{pcol@getmparbottom@last}.}

+% 

+% The macro $\!\pcol@do@mpb@all!\<L\>$ is used in \!\pcol@bias@mpbout! with
+% $L=\mpbout$ and in \!\pcol@getmparbottom@last! with $L=\pp^m(\ptop)$, to
+% process all four elements $\mpb_X^x$ in $L$ applying \!\reserved@a! to
+% each of them and to let $\mpbout$ have the result through \!\reserved@b!.
+% The macro simply invokes \!\pcol@do@mpb@all@i! giving it the body of $L$
+% by \!\expandafter!.  Then $\!\pcol@do@mpb@all@i!
+% \Arg{\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$ initialize
+% $\mpbout=\emptyset$ and then invokes \!\pcol@do@mpb@all@ii! four times
+% giving it each $\mpb_X^x$.  Then
+% $\!\pcol@do@mpb@all@ii!\,\mpar(t_1,b_1)\cdots\~{\mpar}(t_n,b_n)\!\@nil!$
+% invokes \!\reserved@a! giving it all of $\mpar(t_i,b_1)$ at once to
+% process them and to have the result in \!\reserved@b! being added to
+% $\mpbout$.
+% 

+%    \begin{macrocode}
+\def\pcol@do@mpb@all#1{\expandafter\pcol@do@mpb@all@i#1}
+\def\pcol@do@mpb@all@i#1#2#3#4{\begingroup \let\@elt\relax
+  \gdef\pcol@mparbottom@out{}%
+  \pcol@do@mpb@all@ii#1\@nil\pcol@do@mpb@all@ii#2\@nil
+  \pcol@do@mpb@all@ii#3\@nil\pcol@do@mpb@all@ii#4\@nil
+  \endgroup}
+\def\pcol@do@mpb@all@ii#1\@nil{%
+  \reserved@a#1\@nil
+  \xdef\pcol@mparbottom@out{\pcol@mparbottom@out{\reserved@b}}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \subsection{Synchronization}
+% \label{sec:imp-sout-sync}
+% 
+% \begin{macro}{\pcol@sync}
+% \changes{v1.0}{2011/10/10}
+%	{Add measurement of $D_T$.}

+% \changes{v1.2-3}{2013/05/11}
+%	{Modify the action on the page overflow to return from \cs{output}
+%	 without flushing so that the page is broken outside \cs{output} to
+%	 place top floats above the synchronization point set in the next
+%	 page.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.2-2}{2013/05/11}
+% 	{Add pre-flushing column height check taking page-wise
+%	 footnotes into account.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add the initialization of
+%	 $\cs{ifpcol@dfloats}\EQ\string\mathit{false}$ before invoking
+%	 \cs{pcol@measurecolumn}.}

+% 

+% The macro \!\pcol@sync! is invoked solely from \!\pcol@output@switch! for
+% \exsync{} in the following three cases in which
+% $\CSIndex{ifpcol@sync}\lor\CSIndex{ifpcol@clear}=\true$ commonly.
+% 

+% \begin{itemize}
+% \item
+% $\CSIndex{ifpcol@sync}\land\lnot\CSIndex{ifpcol@clear}$ to mean ordinary
+% \sync{}ed \cswitch.
+% 
+% \item
+% $\CSIndex{ifpcol@sync}\land\CSIndex{ifpcol@clear}$ to mean \pfcheck.
+% 
+% \item
+% $\lnot\CSIndex{ifpcol@sync}\land\CSIndex{ifpcol@clear}$ to mean page
+% flushing.
+% \end{itemize}
+% 

+% In any cases\footnote{

+% 

+% In the last case of page flushing, invoking \!\pcol@flushcolumn! is
+% redundant because it is made $p=\ptop$ by \pfcheck{} always preceding the
+% flushing, but the invocation is harmless.},
+% 

+% first we invoke \!\pcol@flushcolumn! for all $c\In0\C$ to flush the
+% \ccolpage{} of $c$ into $\S_c$ if the \colpage{} is not in $\ptop$, i.e.,
+% $\cc_c(\vb^p)<\ptop$ and then, if we have deferred floats, to ship out
+% following \fpage{}s up to $\ptop-1$ into $\S_c$ and to place them in
+% $\ptop$.  This float placement in $\ptop$ is only for top and bottom
+% floats in \sync{}ed \cswitch{}, while a \fcolumn{} may be made in other
+% cases.  Then we ship out all pages $p$ such that $p<\ptop$ by
+% \!\pcol@outputcolumns! giving argument 1.  After that, we obtain the
+% \pctext{} of $\ptop$ by \!\pcol@getcurrpinfo!.
+% 
+% Next, we measure the vertical sizes of the contents in the \ccolpage{} of
+% $c$ which is now in $\ptop$ for all $c\In0\C$ by \!\pcol@measurecolumn! as
+% follows, where $h(x)$ and $d(x)$ are the height and depth of an object $x$
+% respectively.
+% 

+% \begin{eqnarray*}
+% \sigma&=&\rlap{\!\floatsep!}\hskip8em
+% \sigma_t=\cases{\cc_c(\tf)&     $\cc_c(\tf)<\infty$\cr
+% 		    \!\textfloatsep!&$\cc_c(\tf)=\infty$}\qquad
+% \sigma_b=\!\textfloatsep!\\
+% \Uidx\fc(t)&=&\rlap{$\displaystyle(\cc_c(\tl)\neq())$}\hskip8em
+%     \fc(m)=(\cc_c(\vb)\neq\!\vbox!|{}|)\\
+% \fc(f)&=&\rlap{$\displaystyle(\cc_c(\ft)\neq\bot)$}\hskip8em
+%     \fc(b)=\fc(b')=(\cc_c(\bl)\neq())\\
+% \Uidx\Fc(X)&=&\rlap{$\displaystyle\exists x\in X:\fc(x)$}\hskip8em
+%     f_b=\CSIndex{ifpcol@bfbottom}\\
+% \Uidx\vc(t)&=&\!\skip!{\cdot}\cc_c(\vb)=
+% 	\sum_{\Sub{\phi\in\cc_c(\tl)}}(h(\phi)+d(\phi))+
+% 	(\Abs{\cc_c(\tl)}-1)\cdot\sigma+\sigma_t\\
+% \vc(m)&=&h(\cc_c(\vb))+d(\cc_c(\vb))\\
+% \vc(f)&=&h(\cc_c(\ft))+d(\cc_c(\ft))\\
+% \vc(b)&=&\sum_{\Sub{\phi\in\cc_c(\bl)}}(h(\phi)+d(\phi))+
+% 	(\Abs{\cc_c(\bl)}-1)\cdot\sigma+\sigma_b\\
+% \vc(b')&=&\vc(b)+\sigma_b\\
+% \pd_c&=&\cases{\cc_c(\pd)&$\fc(m)$\cr
+%                \infty   &$\lnot \fc(m)$}\\
+% \Uidx\size_c(x)&=&\cases{\vc(x)&$\fc(x)$\cr
+%                     0     &$\lnot \fc(x)$}\\
+% \Uidx\Size_c(X)&=&\cases{\displaystyle\sum_{x\in X}\size_c(x)&$\Fc(X)$\cr
+%                          -\infty&                         $\lnot \Fc(X)$}\\
+% \Uidx\VT&=&\!\@tempdima!=\max_{0\leq c<\C}\{\Size_c(\{t,m\})\}\\
+% \Uidx\VB&=&\!\@tempdimb!=\max_{0\leq c<\C}\{\size_c(f)+\size_c(b)\}\\
+% \Uidx\VP&=&\!\@pageht!=\max_{0\leq c<\C}\{\Size_c(\{t,m,f,b\})\}\\
+% \Uidx\VPP&=&\!\pcol@colht!=\max_{0\leq c<\C}\{\Size_c(\{t,m,f,b'\})\}\\
+% \Uidx\DT&=&\!\@tempdimc!=\min\Set{\pd_c}{\Size_c{\{t,m\}=\VT}}\\
+% \Uidx\dc&=&\cases{
+%   0&			$\fc(b)\land(\lnot \fc(f)\lor f_b)$\cr
+%   d(\cc_c(\ft))&	$\fc(f)\land(\lnot \fc(b)\lor\lnot f_b)$\cr
+%   d(\cc_c(\pd))&	$\lnot \fc(b)\land\lnot \fc(f)$}\\
+% \Uidx\DP&=&\!\@pagedp!=\min\Set{\dc}{\Size_c(\{t,m,f,b'\})=\VPP}\\
+% \Uidx\cmax&=&\!\@tempcntb!=\ARG\max_{0\leq c<\C}\{\Size_c(\{t,m,f,b\})\}
+% \end{eqnarray*}
+% 

+% That is, $\VT$ is the maximum of combined vertical size (height plus
+% depth) of the top floats and the main vertical list, $\VB$ is that of
+% the footnotes and bottom floats, and $\VP$ is that of all items.
+% $\VPP$ is similar to $\VP$ but we add \!\textfloatsep! to the size of
+% bottom floats.  Note that $\VT$, $\VP$ and $\VPP$ are $-\infty$ if any
+% \colpage{}s don't have corresponding items, while $\VB=0$ if so.
+% Also note that $\cmax$ is the ordinal of the column whose size is $\VP$.
+% 
+% $\DT$ and $\DP$ are the minimum $\pd_c$ and $\dc$ respectively among those
+% gives $\VT$ and $\VPP$ respectively, where $\pd_c$ is $\cc_c(\pd)$ if
+% $f_m=\true$ or $\infty$ otherwise, and $\dc$ is 0 if $c$ has bottom float,
+% or the depth of the last footnote if any and without any bottom float, or
+% $\cc_c(\pd)$ otherwise.  The reason why $\DT$ and $\DP$ have minimums is
+% that they are set into \!\prevdepth! for the items just following the
+% \sync{}ation point, and thus a smaller value results in a larger interline
+% skip and the special value $-1000\,|pt|$ to inhibit the skip by, e.g.,
+% \!\nointerlineskip!, is given the highest priority.
+% 
+% Note that $\VPP$ and $\DP$ are only for the \lpage{} and thus referred to
+% by \!\pcol@output@end! to close the environment, and the former is done by
+% \!\pcol@makeflushedpage! if it works on the page.  The reason why we add
+% \!\textfloatsep! to $\VPP$ is to make the last page well separated from
+% the \postenv{} if the tallest column, taking the addition into account,
+% has bottom floats.  Also note that we let
+% $\CSIndex{ifpcol@dfloats}=\false$ before scanning columns with
+% \!\pcol@measurecolumn! so that the switch becomes $\true$ after the scan
+% iff a column has deferred floats (in the \lpage{}).
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Synchronization
+
+\def\pcol@sync{%
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@flushcolumn
+  \pcol@outputcolumns\@ne
+  \pcol@getcurrpinfo{\global\c@page}{\global\@colht}{\global\topskip}%
+  \@tempdima-\maxdimen \@tempdimb-\maxdimen \pcol@colht-\maxdimen
+  \@pageht-\maxdimen \@tempdimc\maxdimen \@pagedp\maxdimen \@tempcntb\z@
+  \pcol@dfloatsfalse
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@measurecolumn
+%    \end{macrocode}
+% 
+% As described above, any items can be empty, naturally for top floats,
+% footnotes and bottom floats, but also including main vertical lists if the
+% \ccolpage{}s were not in $\ptop$ before the invocation of
+% \!\pcol@flushcolumn!.  Moreover, all main vertical lists can be empty if
+% all \lcolpage{}s just have started (by \!\newpage!, for example).  More
+% weirdly, the case of all-empty main vertical lists can be accompanied with
+% other non-empty items when columns have floats or footnotes which cannot
+% be in $\ptop-1$ but are found their places in $\ptop$.
+%
+% Taking it into account that any items can be empty and the other item
+% of \Scfnote{}s, we have to determine whether the following two operations
+% are taken;  invocation of \!\pcol@synccolumn! for each \colpage{} to set a
+% \sync{}ation point or to add an infinite stretch (and shrink) to its
+% bottom;  and the examination of the height of each \colpage{}, taking the
+% \sync{}ation point to be set into account, to tell the necessity of
+% explicit page break with $\CSIndex{ifpcol@flush}=\true$.  For the latter
+% we calculate the examination target $V=\!\@tempdimb!$ to be compared with
+% $\pp^h(\ptop)$, while for the former we determine the value of a switch
+% $f=\CSIndex{if@tempswa}$ so that we invoke \!\pcol@synccolumn! iff
+% $f=\true$ and $V\geq0$.
+% 
+% For \sync{}ed \cswitch{} with $\CSIndex{ifpcol@clear}=\false$, we let
+% $f=(\VT\geq0)$ to mean at least one \colpage{} has a top float or
+% non-empty main vertical list, i.e., $\Fc(\{t,m\})={\true}$ for some
+% $c\In0\C$.  That is if $\VT<0$, since the next items added to all
+% \colpage{}s are placed at the top of the page\footnote{

+% 

+% In usual cases, but it can mean some of them have negative vertical
+% sizes.  Even though we can detect such a very unlikely special case, it is
+% very tough to define the reasonable \sync{}ation point above the top of
+% $\ptop$.  Therefore, we assume the point is at the top of $\ptop$ and thus
+% do nothing.},
+% 

+% we don't need to set \sync{}ation points in them.  As for $V$, we let
+% $V=\max(\VT,0)+\max(\VB,0)+v^f$ where $v^f$ is the sum of
+% height-plus-depth of $\pp^f(\ptop)$ and $\!\skip!{\cdot}\pp^f(\ptop)$ if
+% $\ptop$ has \Scfnote{}s, or 0 otherwise\footnote{

+% 

+% In the real implementation, $V=-\infty$ if $\VT=\VB=-\infty$ and no
+% \Scfnote{}s are presented, but this difference does not affect the
+% decisoins because $f\land(V\geq0)=(\VT<0)\land(V\geq0)=\false$ and
+% $V\leq\pp^f(\ptop)$ with either $V=0$ or $V=-\infty$.}.
+% 

+% Note that it can be $\VP+v^f\leq\pp^h(\ptop)<\VT+\VB+v^f=V$ to mean
+% setting the \sync{}ation point at $\VT$ below $\ptop$'s top edge would
+% push bottom stuff beyond its bottom edge and thus we need an explicit page
+% break to place the point at the top of $\ptop+1$ (in usual cases).
+% 
+% For \pfcheck{} or page flushing with $\CSIndex{ifpcol@clear}=\true$ on
+% the other hand, we let $f=\lnot\!\pcol@sync!$ to invoke \!\pcol@synccolumn!
+% only for page flushing and thus not for \pfcheck{}.  As for $V$, we let
+% $V'=\VPP$ or $V'=\VP$ according as we working on \lpage{} or not, and
+% then let $V=\max(V',0)+v^f$ or $V=V'$ according as $\ptop$ has \Scfnote{}s
+% or not.  That is, we have to invoke \!\pcol@synccolumn! unless $\ptop$ is
+% perfectly empty.
+% 
+% Then if $\CSIndex{ifpcol@clear}=\false$ and
+% $\max(V,\;V-D'_T+\VE)>\pp^h(\ptop)$ where $D'_T=\DT$ if $0\leq\DT<\infty$ or
+% 0 otherwise, or $\CSIndex{ifpcol@clear}=\true$ and
+% $V>\pp^h(\ptop)$\footnote{

+% 

+% The examination is redundant in page flushing with
+% $\CSIndex{ifpcol@sync}=\false$ because it is assured that no overflow
+% happens in any \colpage{} by \pfcheck{} and explicit page breaking, but is
+% not harmful.},
+% 

+% we flush the page.  That is, if the condition above holds,
+% we let $\CSIndex{ifpcol@flush}=\true$ and $d=\!\pcol@nextcol!={\cmax}$ to
+% tell \!\pcol@switchcol! or \!\pcol@flushclear! to make an explicit page
+% break in the column $\cmax$ from which we restart, and $f=\false$ to skip
+% \!\pcol@synccolumn! to postpone the \exsync{}.  Note that the bias
+% $\VE=\!\pcol@@ensurevspace!$ in \sync{}ed \cswitch{} is to avoid breaking a
+% \colpage{} just below the \sync{}ation point due to too small space below
+% the point, less than \!\baselineskip! in default but can be other
+% threshold explicitly defined by \!\ensurevspace!.  That is,
+% since $V-\DT+k\!\baselineskip!$ usually means the vertical position at
+% which $k$-th baseline below the \sync{}ation point is placed, the flushing
+% condition with $\VE=k\!\baselineskip!$ ensures that the page is flushed
+% iff the space below the point cannot accommodate $k$ lines.  Also note that
+% necessary flushing with $V>\pp^h(p)$ assuredly takes place even when
+% $\DT$ is unusually large and/or $\VE$ is negative to make $-\DT+\VE<0$.
+% 
+% Finally if $V\geq0$ and $f=\true$, we invoke \!\pcol@synccolumn! for each
+% column $c\In0\C$ to set a \sync{}ation point in it or to add an infinite
+% stretch (and shrink) at its bottom for flushing.
+% 

+% \changes{v1.3-6}{2013/09/17}
+%	{Modify the flushing condition of synchronized column switching from
+%	 $V\GT\pi^h(p)$ to $\max(V,V-D_T+V_E)\GT\pi^h(p)$ to avoid page
+%	 break just below the synchronization point as much as possible.}

+% 

+%    \begin{macrocode}
+  \@tempswatrue \global\pcol@flushfalse
+  \ifpcol@clear
+    \ifpcol@lastpage \@tempdimb\pcol@colht \else \@tempdimb\@pageht \fi
+    \ifpcol@sync \@tempswafalse \fi
+  \else
+    \ifdim\@tempdima<\z@      \@tempswafalse
+    \else\ifdim\@tempdimb<\z@ \@tempdimb\@tempdima
+    \else                     \advance\@tempdimb\@tempdima
+    \fi\fi
+  \fi
+  \ifpcol@scfnote\ifvoid\pcol@footins\else
+    \ifdim\@tempdimb<\z@ \@tempdimb\z@ \fi
+    \advance\@tempdimb\ht\pcol@footins \advance\@tempdimb\dp\pcol@footins
+    \advance\@tempdimb\skip\pcol@footins
+  \fi\fi
+  \dimen@\@tempdimb
+  \ifpcol@clear\else \ifdim\dimen@<\z@\else
+    \ifdim\@tempdimc=\maxdimen\else \ifdim\@tempdimc<\z@\else
+      \advance\dimen@-\@tempdimc
+    \fi\fi
+    \advance\dimen@\pcol@@ensurevspace
+    \ifdim\dimen@<\@tempdimb \dimen@\@tempdimb \fi
+  \fi\fi
+  \ifdim\dimen@>\@colht
+    \global\pcol@flushtrue \@tempswafalse \pcol@nextcol\@tempcntb
+  \fi
+  \ifdim\@tempdimb<\z@\else \if@tempswa
+    \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@synccolumn
+  \fi\fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@flushcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}

+% \changes{v1.0}{2011/10/10}
+%	{Add \cs{vfil} at the bottom of flushed column-page.}

+% \changes{v1.0}{2011/10/10}
+%	{Change order of the garbage collection of \cs{pcol@currfoot} and
+%	 \cs{pcol@getcurrfoot}.}
 
+% \changes{v1.2-2}{2013/05/11}
+% 	{Revise reflecting the redesign of \cs{pcol@getcurrfoot}.}

+% \changes{v1.2-2}{2013/05/11}
+% 	{Add operations for page-wise footnotes.}

+% \changes{v1.2-2}{2013/05/11}
+% 	{Add the examination of $\kappa_c(\rho)\EQ\infty$ to cope with a
+%	 rare-case interaction of pre-flushing column height check and float
+%	 columns in last pages.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Save \cs{ifpcol@lastpage} into \cs{ifpcol@lastpagesave} and turn
+% 	 \cs{ifpcol@lastpage} $\string\mathit{false}$ temporarily during
+% 	 the macro works on non-top and thus non-last pages to fix the bug
+%	 that \cs{@makecol} and \cs{pcol@makefcolumn} misunderstand the page
+%	 they work on is last.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Replace \cs{@makecol} with \cs{pcol@@makecol} to cap the depth of
+%	 \cs{@outputbox} by \cs{@maxdepth} even with p\string\LaTeX.}

+% \changes{v1.21}{2013/06/06}
+%	{Add page and column numbers to logging.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Fix the problem that a flushed column in a non-top page causes
+% 	 overfull due to its hight-plus-depth greater than $\pi^h(p)$.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add \cs{@colht} and \cs{relax} as the first and third argument
+%	 of \cs{pcol@shrinkcolbyfn} for all of three invocations of it.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add \cs{@maxdepth} as the first argument of \cs{pcol@@makecol}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+% The macro \!\pcol@flushcolumn! is invoked for each column $c\In0\C$ from
+% \!\pcol@sync! to ship out the \ccolpage{} of $c$ into $\S_c$ if it is not
+% leading one\Index{leading column-page}, i.e., $p=\cc_c(\vb^p)<\ptop$.  The
+% macro also ships out \fpage{}s from $p+1$ up to $\ptop-1$ if we have
+% deferred floats to fill them and, if this float flushing still leaves
+% deferred floats, puts some of them to the \lcolpage{} being
+% current\Index{current column-page}{} now as its top and/or bottom floats.
+% 
+% First we obtain the \cctext{} in $\cc_c$ by \!\pcol@getcurrcol! and
+% examines if $p=\cc_c(\vb^p)<\ptop$.  If it does not hold to mean $c$ has
+% \lcolpage{}, we do nothing.
+% 
+% Otherwise, we save \CSIndex{ifpcol@lastpage} into
+% \CSIndex{ifpcol@lastpagesave} turning the former switch $\false$ because we
+% are working on a non-\lcolpage{} definitely in a non-\lpage.  Then we put
+% the contents of the \ccolpage{} $\cc_c(\vb^b)$ adding \!\vfil! at its tail
+% into \!\box!|255| being the \TeX's standard interface to carry the main
+% vertical list for \!\output!  routine.  We also move everything in
+% $\cc_c(\ft)$ obtained by \!\pcol@getcurrfoot! into \!\footins! and return
+% $\cc_c(\ft)$ to \!\@freelist! if $\cc_c(\ft^b)$ is not void.
+% 
+% Then we obtain $p$'s \pctext{} by \!\pcol@getcurrpage! and, if it has
+% \Scfnote{}s in $\pp^f(p)$, we shrink \!\@colht! by the space required for
+% the footnotes using \!\pcol@shrinkcolbyfn! and add the stretch\slash
+% shrink compontents of $\!\skip!\cdot\pp^f(p)$ at the bottom of
+% \!\box!|255| by \!\pcol@unvbox@cclv!, as we did in \!\pcol@makecol!.
+% Otherwise we take a special care of the case that the height-plus-depth of
+% $\cc_c(\vb^b)$ is greater than $\pp^h(p)$ due to that its height is almost
+% equal to $\pi^h(p)$ and thus its depth makes the hight-plus-depth
+% exceeding $\pi^h(p)$.  This excess is revealed by the \!\vfil! we just
+% have added making the height-plus-depth the height of \!\box!|255|, and
+% would cause overfull in \!\@makecol! and \!\pcol@@makecol! because they
+% need the height, i.e., not height-plus-depth, of \!\box!|255| not
+% exceeding $\pp^h(p)$.  Therefore if it happens, we we remove the \!\vfil!
+% and cap the height of \!\box!|255| by \!\@maxdepth!  to pretend as if the
+% box is directly passed from \TeX's page builder.
+% 
+% Next we examine if $\cc_c(\tr)$ was made $\infty$ by \!\pcol@makefcolumn!
+% invoked from this macro itself when it processed the \colpage{} in the
+% previous \pfcheck{} for environment closing, which found a page break
+% should be done.  That is, $\cc_c(\tr)=\infty$ means the \ccolpage{} was
+% once judged to be in the \lpage{} but \pfcheck{} forced a page break to
+% make it non-last, it should have all deferred floats now listed in
+% $\cc_c(\tl)$ at \Endparacol{}, but their total size is less than the
+% threshold to make a usual \fcolumn{} for the \lpage.  If so, since the page
+% is not last now, we put all floats in $\cc_c(\tl)$ by \!\pcol@makefcolpage!
+% as the ship-out image in \!\@outputbox!, ignoring the contents added to
+% \!\box!|255| in the operations above because $\cc_c(\vb^b)$ should be
+% empty, and letting $\cc_c(\tr)=0$ to mean the floats have been
+% processed\footnote{

+% 

+% $\cc_c(\tl)$ can have any values other than $\infty$ because definitely it
+% will not be referred to in its inherent sense in the situation with no
+% further float additions and no deferred floats.}.
+% 
+% Otherwise, since the \colpage{} can be put as usual, we invoke
+% \!\pcol@@makecol!\footnote{

+% 

+% Neither \cs{pcol@makecol} because \!\box!\texttt{255} has \!\vfil! at its
+% tail and the \colpage{} should be short enough, nor \cs{@makecol} because
+% we need to ensure the depth of resulting \cs{@outputbox} is capped.}
+% 

+% giving \!\@maxdepth! to it to build the complete \colpage{} in
+% \!\@outputbox! with depth capping and with the following setting\footnote{

+% 

+% \LaTeX's has another \!\insert! named \!\@kludgeins! for \!\enlargepage!
+% but \Paracol{} does not cares about it.}.
+% $$
+% \begin{array}{lll}
+% \!\box!|255|=\cc_c(\vb^b)&
+% \!\footins!=\cc_c(\ft)&
+% \!\@colht!=\pp^h(\cc_c(\vb^p))\\
+% \!\@midlist!=\cc_c(\ml)&
+% \!\@toplist!=\cc_c(\tl)&
+% \!\@botlist!=\cc_c(\bl)
+% \end{array}
+% $$
+% Finally, regardless of $\cc_c(\tr)=\infty$ or not, the resulting
+% \!\@outputbox! becomes $\s_c(p)$ and is added to the tail of $\S_c$
+% by \!\@cons!.
+% 

+%    \begin{macrocode}
+\def\pcol@flushcolumn{%
+  \pcol@getcurrcol
+  \ifnum\count\@currbox<\pcol@toppage
+    \ifpcol@lastpage \pcol@lastpagesavetrue \else \pcol@lastpagesavefalse \fi
+    \pcol@lastpagefalse
+    \pcol@page\count\@currbox
+    \setbox\@cclv\vbox{\unvbox\@currbox \vfil}%
+    \ifvoid\pcol@currfoot\else
+      \pcol@Fb
+      \@cons\@freelist\pcol@currfoot
+      \pcol@Fe{flushcolumn(colfn)}%
+    \fi
+    \pcol@getcurrfoot\box
+    \pcol@getcurrpage
+    \ifvoid\pcol@footins
+      \ifdim\ht\@cclv>\@colht
+        \setbox\@cclv\vbox{\boxmaxdepth\@maxdepth \unvbox\@cclv \unskip}%
+      \fi
+    \else
+      \pcol@shrinkcolbyfn\@colht\pcol@footins\relax
+      \setbox\@cclv\vbox{\pcol@unvbox@cclv\pcol@footins}%
+    \fi
+    \pcol@Logstart{\pcol@flushcolumn(\number\c@page:\number\pcol@currcol)}
+    \ifdim\@toproom=\maxdimen
+      \setbox\@outputbox\pcol@makefcolpage \global\@toproom\z@
+    \else
+      \pcol@@makecol\@maxdepth
+    \fi
+    \pcol@Logend\pcol@flushcolumn
+    \global\setbox\@currbox\box\@outputbox
+    \expandafter\@cons\csname pcol@shipped\number\pcol@currcol\endcsname
+      \@currbox
+%    \end{macrocode}
+% 
+% Then for each $q\in[p{+}1,\ptop{-}1]$, we repeat the followings; get $q$'s
+% \pctext{} by \!\pcol@getcurrpage!; shrink \!\@colht! by
+% \!\pcol@shrinkcolbyfn! if $q$ has \Scfnote{}s; try to make a \fcolumn{} in
+% \!\@outputbox! by \!\@makefcolumn! giving it \!\@deferlist! being
+% $\cc_c(\dl)$ at initial but will be shrunk; if the \fcolumn{} is made,
+% acquire an \!\insert! by \!\@next! to keep the contents of \!\@outputbox!
+% and to be added to the tail of $\S_c$ by \!\@cons!.
+% 

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{@colht} shrinking by page-wise footnotes.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+    \advance\pcol@page\@ne
+    \ifx\@deferlist\@empty\else
+      \@whilenum\pcol@page<\pcol@toppage\do{%
+        \pcol@getcurrpage
+        \ifvoid\pcol@footins\else
+          \pcol@shrinkcolbyfn\@colht\pcol@footins\relax
+        \fi
+        \@makefcolumn\@deferlist
+        \if@fcolmade
+          \pcol@Fb
+          \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}%
+            \pcol@ovf
+          \pcol@Fe{flushcolumn(fcol)}%
+          \expandafter\@cons
+            \csname pcol@shipped\number\pcol@currcol\endcsname\@currbox
+        \fi
+       \advance\pcol@page\@ne}%
+    \fi
+%    \end{macrocode}
+% 
+% Next, since we reach $\ptop$ and thus restore \CSIndex{ifpcol@lastpage}
+% from \CSIndex{ifpcol@lastpagesave} because the \tpage{} can be last.
+% Then we acquire the \ccolpage{} of $c$ which is now in $\ptop$ and thus
+% empty, by \!\@next!.  Then we let $\!\@colht!=\!\@colroom!=\pp^h(\ptop)$
+% by \!\pcol@getcurrpinfo! but shrinking them by \!\pcol@shrinkcolbyfn! if
+% $\ptop$ has \Scfnote{}s, and reinitialize the float placement parameters by
+% \!\pcol@floatplacement!.  Then, if $\cc_c(\dl)$ still has some floats,
+% we make a \fcolumn{} for some of them in the \tpage{} by
+% \!\pcol@makefcolumn! if $\CSIndex{ifpcol@clear}={}\true$ meaning flushing,
+% or try to move some of them to $\cc_c(\tl)=\!\@toplist!$ and/or
+% $\cc_c(\bl)=\!\@botlist!$ by \!\pcol@trynextcolumn! otherwise.  Note that
+% since \!\@colroom! is used in \!\pcol@makefcolumn! as a working register,
+% we let $\!\@colroom!=\pp^h(\ptop)$ again after its invocation.  After that
+% we save \cctext{} including those given by \!\pcol@floatplacement! and
+% modified by \!\pcol@makefcolumn! or \!\pcol@trynextcolumn! into $\cc_c$ by
+% \!\pcol@setcurrcolnf!  because all footnotes are shipped out, and let
+% $\cc_c(\vb^p)=\ptop$.  We also let $\cc_c(\vb^r)=\!\@colroom!$ possibly
+% modified by \!\pcol@trynextcolumn! but after canceling the shrinkage of
+% \!\@colht! due to \Scfnote{}s, i.e.,
+% $\cc_c(\vb^r)\gets\cc_c(\vb^r)+(H-H')$ where $H$ and $H'$ are \!\@colht!
+% before and after the shrinkage respectively.
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Add $\cs{@colht}\EQ\pi^h(p)$.}

+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{pcol@trynextcolumn} with \cs{pcol@makefcolumn} for the
+%	 case of $\cs{ifpcol@clear}\EQ\mathit{true}$.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{@colht} shrinking by page-wise footnotes.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Add the restore of \cs{ifpcol@lastpage} from
+%	 \cs{ifpcol@lastpagesave}.}

+% \changes{v1.21}{2013/06/06}
+%	{Fix the bug that $\kappa_c(\beta^p)$ is let have \cs{pcol@page},
+%        which can be less than $p_t\EQ\cs{pcol@toppage}$, to cause the column
+%	 $c$ is lost or moved to a wrong page.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+    \ifpcol@lastpagesave \pcol@lastpagetrue \fi
+    \pcol@Fb
+    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{}}\pcol@ovf
+    \pcol@Fe{flushcolumn(col)}%
+    \pcol@getcurrpinfo\@tempcnta{\global\@colht}\@tempskipa
+    \@pageht\@colht
+    \ifvoid\pcol@footins\else \pcol@shrinkcolbyfn\@colht\pcol@footins\relax \fi
+    \global\@colroom\@colht \pcol@floatplacement
+    \ifx\@deferlist\@empty\else
+      \ifpcol@clear
+        \pcol@makefcolumn \global\@colroom\@colht
+      \else
+        \pcol@trynextcolumn
+    \fi\fi
+    \pcol@setcurrcolnf
+    \global\count\@currbox\pcol@toppage
+    \advance\@pageht-\@colht \advance\@pageht\@colroom
+    \global\dimen\@currbox\@pageht
+  \fi %\ifnum\count\@currbox<\pcol@toppage
+  \advance\pcol@currcol\@ne}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@makefcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to take special care of the float-column in the last
+%	 page. }

+% \changes{v1.2-2}{2013/05/11}
+%	{Encapsulate the float column in a \cs{vbox} of \cs{@colht} so that
+% 	 vertical skips at the top and bottom are not lost when the column
+%	 is put back to the main vertical list, and makes the assignment to
+%	 \cs{@currbox} global because the box is now referred to after
+%	 \cs{output} is completed.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Replace the sequence of operations to make a usual float column
+%	 with \cs{@toplist} with the newly introduced
+%	 \cs{pcol@makefcolpage}.}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Remove a space after the \cs{vbox} to be assigned to \cs{@currbox}
+%	 to obey the coding convention.}

+% 

+% The macro \!\pcol@makefcolumn! is invoked solely from \!\pcol@flushcolumn!
+% to put deferred floats in the currently empty \colpage{} of $c$ in the
+% \tpage{} $\ptop$ which is being flushed.  Since we have to take special care
+% of the case of environment closing, we cannot do this operation by
+% \!\@makefcolumn!, while in other cases for \!\flushpage! and \!\clearpage!
+% we also have to pay a small attention.
+% 
+% First, we scan the copy of $\cc_c(\dl)$ applying \!\pcol@makefcolelt! to
+% each element to have the floats to be put in \!\@toplist!, which is
+% assuredly empty because the \ccolpage{} of $c$ has already been shipped
+% out to empty it, and those still deferred in $\cc_c(\dl)$.  Prior to scan,
+% we let $H_r=\pp^h(\ptop)\footnotemark+\alpha$\footnotetext{

+% 

+% $\pp^h(\ptop)$ referred in this macro may have been shrunk by \Scfnote{}s
+% in \cs{pcol@flushcolumn}.},
+% 

+% as the space initially available for
+% floats each of which being $\phi$ is assumed to consume
+% $v(\phi)=h(\phi)+d(\phi)+\alpha$, and $H_t=\!\@colroom!=-\alpha$ as the
+% initial value of the accumulated size of $v(\phi)$ for all $\phi$ to be
+% put, where $\alpha=\!\floatsep!$ if $\CSIndex{ifpcol@lastpage}=\true$
+% 

+% \SpecialIndex{\ifpcol@lastpage}

+% 

+% as discussed afterward, or $\alpha=\!\@fpsep!$ otherwise.
+% 
+% Then if the resulting \!\@toplist! is not empty\footnote{

+% 

+% It can happen if the first float is larger than $\pp^h(\ptop)$.},
+% 

+% we examine if $\ptop$ is the \lpage{} ($|\ifpcol@|\~|lastpage|=\true$)
+% 

+% \SpecialIndex{\ifpcol@lastpage}
+% 

+% and $\cc_c(\dl)$ is empty to mean the last \colpage{} have all deferred
+% floats.  This case is subtle because if we make the \colpage{} a \fcolumn{}
+% it can be sparse and unnecessarily throw the \postenv{} to the next
+% page.  Therefore, we intend to pack floats to the page top as top floats
+% and thus have let $\alpha=\!\floatsep!$ in the building process of
+% \!\@toplist! above\footnote{

+% 

+% We dare to do it knowing the natural component of \!\floatsep! is a little
+% bit (4pt) larger than that \!\@fpsep! and the possibility of having
+% fewer floats than those given by \!\@makefcolumn!.},
+% 

+% but it may make a too tall \colpage{} only having floats shrinking
+% the \postenv{} in the page.  In addition, if other columns have
+% \fpage{}s in the \lpage, packing the floats as top floats should give
+% inconsistent appearance but we don't know whether the columns following
+% $c$ has \fpage{}s.  Therefore, we performs this float packing if making
+% the \fpage{} gives too sparse, more specifically if
+% $H_t<\!\floatpagefraction!\times\pp^h(\ptop)=\!\@fpmin!$, but postpone the
+% final decision until the \colpage{} is eventually shipped out by
+% \!\pcol@flushcolumn! or \!\pcol@makeflushedpage!.  That is, if the all
+% conditions above hold, we keep \!\@toplist! so that it is saved in
+% $\cc_c(\tl)$ and let $\cc_c(\tr)=\infty$ to indicate that the column has
+% pending floats.  Note that the floats are shipped out by
+% \!\pcol@flushcolumn! if the \pfcheck{} currently being performed finds a 
+% too tall column in $\ptop$ to force a page break making $\ptop$ non-last.
+% Also note that, in any cases, letting $\cc_c(\tr)=\infty$ is safe because
+% no longer we will have any float additions to the \colpage.
+% 
+% Otherwise, i.e., if we are working on a non-\lpage{} to be flushed or a
+% \fcolumn{} is to be made for the \lpage, we put all floats in \!\@toplist!
+% in a \!\vbox! of $\pp^h(\ptop)$ tall by \!\pcol@makefcolpage! and then 
+% let $\cc_c(\vb^b)$ be another \!\vbox! having it.  This encapsulation of
+% the \fcolumn{} is necessary because $\cc_c(\vb^b)$ can be put back to the
+% main vertical list after the \pfcheck{} to remove skips above and below
+% the floats, namely \!\@fptop! and \!\@fpbot!, if the contents were not
+% encapsulated.
+% 

+%    \begin{macrocode}
+\def\pcol@makefcolumn{%
+  \ifpcol@lastpage \@tempdimc\floatsep \else \@tempdimc\@fpsep \fi
+  \@tempdima\@colht \advance\@tempdima\@tempdimc \global\@colroom-\@tempdimc
+  \begingroup
+    \let\@elt\pcol@makefcolelt
+    \let\reserved@b\@deferlist
+    \global\let\@deferlist\@empty
+    \reserved@b
+  \endgroup
+  \ifx\@toplist\@empty\else
+    \@tempswatrue
+    \ifpcol@lastpage \ifx\@deferlist\@empty \ifdim\@colroom<\@fpmin
+      \@tempswafalse \global\@toproom\maxdimen
+    \fi\fi\fi
+    \if@tempswa \global\setbox\@currbox\vbox{\pcol@makefcolpage}\fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@makefcolelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to take special care of the float-column in the last
+%	 page. }

+% 

+% The macro $\!\pcol@makefcolelt!\<\phi\>$ is invoked solely from
+% \!\pcol@makefcolumn! to be applied to each float element $\phi$ in (the
+% copy of) $\cc_c(\dl)$.  We examine if $v(\phi)=h(\phi)+d(\phi)+\alpha\leq
+% H_r$ to mean the \fcolumn{} being built has room large enough for the float
+% $\phi$.  If so, we add $\phi$ to \!\@toplist! by \!\@cons!, and let
+% $H_r\gets H_r-v(\phi)$ and $H_t\gets H_t+v(\phi)$.  Otherwise, we add
+% $\phi$ to $\cc_c(\dl)$ by \!\@cons! to make it deferred again, and
+% let $H_r=-\infty$ so that the examinations for any succeeding elements
+% fail.
+% 

+%    \begin{macrocode}
+\def\pcol@makefcolelt#1{%
+  \@tempdimb\ht#1{}\advance\@tempdimb\dp#1{}\advance\@tempdimb\@tempdimc
+  \ifdim\@tempdimb>\@tempdima \@cons\@deferlist#1\relax
+    \@tempdima-\maxdimen
+  \else \@cons\@toplist#1\relax
+    \advance\@tempdima-\@tempdimb \global\advance\@colroom\@tempdimb
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@makefcolpage}
+% \changes{v1.2-7}{2013/05/11}
+% 	{Introduced to implement the operations to make a float column
+%	 performed in three macros.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add {\tt\%} to the end of the line to open \cs{vbox} to obey the
+%	 coding convention.}
 
+% 

+% The macro \!\pcol@makefcolpage! is invoked from \!\pcol@flushcolumn!,
+% \!\pcol@makefcolumn! and \!\pcol@imakeflushedpage! to build a \fcolumn{}
+% having floats in \!\@toplist!, which is then returned to \!\@freelist! and
+% then emptied.  The floats are put in a \!\vbox! of \!\@colht! tall with
+% vertical skips of \!\@fptop!, \!\@fpsep! and \!\@fpbot! above, between and
+% below them respectively.  The box is then let be $\s_c(p)$ or
+% $\cc_c(\vb^b)$ explictly or implicitly by the invokers, with an
+% encapsulation in the case of \!\pcol@makefcolumn!.
+% 

+%    \begin{macrocode}
+\def\pcol@makefcolpage{\vbox to\@colht{%
+    \vskip\@fptop \vskip-\@fpsep
+    \def\@elt##1{\vskip\@fpsep\box##1}\@toplist \vskip\@fpbot}%
+  \pcol@Fb
+  \xdef\@freelist{\@freelist\@toplist}\global\let\@toplist\@empty
+  \pcol@Fe{makefcolpage}%
+}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@measurecolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Drastically changed to measure $D_T$, to deal with empty
+%	 main vertical list, and to omit \cs{topfigrule} and \cs{botfigrule}
+%	 from float size measurement.}
 
+% 

+% The macro \!\pcol@measurecolumn! is invoked for each column $c\In0\C$ from
+% \!\pcol@sync! to measure the sizes of the top floats $\size_c(t)$, main
+% vertical list $\size_c(m)$, footnotes $\size_c(f)$ and bottom floats
+% $\size_c(b)$ in the \ccolpage{} in the page $\ptop$.  After obtaining the
+% \cctext{} in $\cc_c$ by \!\pcol@getcurrcol!, we calculate
+% $\size_c(t)=\!\skip!{\cdot}\cc_c(\vb)$ by \!\pcol@addflhd! giving it
+% $\cc_c(\tl)$ and $\cc_c(\tf)=\!\pcol@textfloatsep!$ as its arguments also
+% to have $\CSIndex{if@tempswa}={\fc(t)}$.  Note that $\cc_c(\tf)=\infty$ means
+% the \colpage{} does not have any \sync{}ation points yet and thus
+% \!\textfloatsep! is used in the calculation as the skip between the top
+% floats and main vertical list, while the value itself possibly for a
+% \mvlfloat{} discussed later is used if $\cc_c(\tf)<\infty$.  We also
+% calculate $\size_c(m)=h(\cc_c(\vb))+d(\cc_c(\vb))$, and then the sum of it
+% and $\size_c(t)$.
+% 

+%    \begin{macrocode}
+\def\pcol@measurecolumn{%
+  \pcol@getcurrcol
+  \@tempswafalse
+  \dimen@\z@ \pcol@addflhd\@toplist\pcol@textfloatsep
+  \global\skip\@currbox\dimen@
+  \advance\dimen@\ht\@currbox \advance\dimen@\dp\@currbox \dimen@ii\dimen@
+%    \end{macrocode}
+% 
+% Next we examine if the main vertical list $\cc_c(\vb^b)$ is empty by
+% \!\pcol@ifempty! and, if so, we let $\pd_c=\cc_c(\pd)=\infty$ and save it
+% (together with others) by \!\pcol@setcurrcol! so that, if the column
+% defines the $\VT$ finally by its top floats, $\DT$ is let $\infty$ and the
+% fact that the column has empty list is remembered.  Otherwise, we let
+% $\pd_c=\cc_c(\pd)$ and $\CSIndex{if@tempswa}=\true$ to represent
+% $\Fc(\{t,m\})=f_t\lor f_m$ because $f_m=\true$.  Then we invoke
+% \!\pcol@measureupdate! to let $\VT=\size_c(t)+\size_c(m)=\Size_c(\{t,m\})$
+% and $\DT=\pd_c$ if $\Fc(\{t,m\})=\true$ and $\VT<\Size_c(\{t,m\})$.
+% 

+%    \begin{macrocode}
+  \pcol@ifempty\@currbox
+   {\global\pcol@prevdepth\maxdimen \pcol@setcurrcol}%
+   {\@tempswatrue}%
+  \pcol@measureupdate\@tempdima\dimen@ii\@tempdimc\pcol@prevdepth
+%    \end{macrocode}
+% 

+% \changes{v1.2-2}{2013/05/11}
+%	{Add calculation of $V_P$ and $c_{\string\max}$.}

+% 
+% Next we let $\size_c(f)=0$ if $\cc_c(\ft^b)$ is void, or otherwise let
+% $\size_c(f)=h(\cc_c(\ft^b))+d(\cc_c(\ft^b))+{}\cc_c(\ft^s)$\footnote{

+% 

+% We ignore the height and depth of \!\footnoterule! because they are
+% expected to be 0 and are so in the default setting.}
+% 

+% and $\CSIndex{if@tempswa}=\true$ because $\fc(f)=\true$ and thus
+% $\Fc(\{t,m,f\})=\true$.  After that, we calculate $\size_c(f)+\size_c(b)$
+% by \!\pcol@addflhd! giving it $\cc_c(\bl)$ and $\infty$ to mean
+% \!\textfloatsep! should be used for the calculation as its argument also
+% to have $\CSIndex{if@tempswa}={\Fc}(\{t,m,f,b\})$.  Then we let
+% $\VB=\size_c(f)+\size_c(b)$ if $\VB<\size_c(f)+\size_c(b)$, and let
+% $\VP=\size_c(t)+\size_c(m)+\size_c(f)+\size_c(b)=\Size_c(\{t,m,f,b\})$ and
+% $c_{\max}=c$ if $\Fc(\{t,m,f,b\})=\true$ and $\VP<\Size_c(\{t,m,f,b\})$.
+% 

+%    \begin{macrocode}
+  \ifvoid\pcol@currfoot \dimen@\z@
+  \else
+    \dimen@\ht\pcol@currfoot \advance\dimen@\dp\pcol@currfoot
+    \advance\dimen@\skip\pcol@currfoot
+    \@tempswatrue
+  \fi
+  \pcol@addflhd\@botlist\maxdimen
+  \ifdim\dimen@>\@tempdimb \@tempdimb\dimen@ \fi
+  \advance\dimen@\dimen@ii
+  \if@tempswa \ifdim\dimen@>\@pageht
+    \@pageht\dimen@ \@tempcntb\pcol@currcol
+  \fi\fi
+%    \end{macrocode}
+% 
+% Next, we let $\dc$ be the depth of the lowest non-empty items among the
+% main vertical list, footnotes and bottom floats.  That is, we let
+% $\dc\gets\cc_c(\pd)$ at first, and then, if
+% $\CSIndex{ifpcol@bfbottom}={\true}$, override it by $\dc\gets
+% d(\cc_c(\ft^b))$ if there are footnotes, and finally override it by
+% $\dc\gets0$ for the bottom floats if exist adding \!\textfloatsep! to
+% $\Size_c(\{t,m,f,b\})$ to have $\Size_c(\{t,m,f,b'\})$.  This overriding
+% order of $d(\cc_c(\ft^b))$ and then 0 by bottom floats is reversed when
+% $\CSIndex{ifpcol@bfbottom}=\false$ according to the implementation of
+% \!\@makecol!.  Then, we invoke \!\pcol@measureupdate! again to let
+% $\VPP=\Size_c(\{t,m,f,b'\})$ and $\DP=\dc$ if $\Fc(\{t,m,f,b\})=\true$ and
+% $\VPP<\Size_c(\{t,m,f,b'\})$.  It also lets $\DP=\dc$ if
+% $\Fc(\{t,m,f,b\})=\true$, $\VPP=\Size_c(\{t,m,f,b'\})$ and $\DP>\dc$.
+% 
+% Finally, we let $\CSIndex{ifpcol@dfloats}=\true$ if
+% $\cc_c(\dl)\neq\emptyset$ to tell \!\pcol@makeflushedpage! that the
+% \lpage{} must be {\em full size} and \!\pcol@output@end! to flush the
+% deferred \cwise{} floats.
+% 

+% \changes{v1.3-6}{2013/09/17}
+%	{Revise the mechanism to tell \cs{pcol@makeflushedpage} and
+%	 \cs{pcol@output@end} that a column in a last page has deferred
+%	 column-wise floats with newly introduced \cs{ifpcol@dfloats}.}

+% 

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

+% \begin{macro}{\pcol@addflhd}
+% \changes{v1.0}{2011/10/10}
+%	{Drastically changed to omit \cs{topfigrule} and \cs{botfigrule}
+%	 from float size measurement, to take care of top float enlargement,
+%	 to add the measurement of $D_T$, and to revise the definition of
+%	 $D_P$.}

+% 

+% \begin{macro}{\pcol@hdflelt}
+% \def\xl{\lambda_x}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add a user \cs{pcol@makecol}.}

+% 

+% The macro $\!\pcol@addflhd!\arg{list}\arg{tfs}$ is invoked twice from
+% \!\pcol@measurecolumn! for a column $c$ to measure $\size_c(x)$
+% ($x\in\{t,b\}$) of top ($x=t$) or bottom ($x=b$) floats.
+% The arguments and registers referred to in the macro have the folloiwngs
+% according to $x=t$ or $x=b$.
+% $$
+% \nosv\begin{array}{l|ll}
+% &		x=t&			x=b\\\hline
+% \arg{list}&	\cc_c(\tl)&		\cc_c(\bl)\\
+% \arg{tfs}&	\!\pcol@textfloatsep!&	\!\maxdimen!\\
+% \CSIndex{if@tempswa}&
+%		\false&			\Fc(\{t,m,f\})\\
+% \!\dimen@!&	0&			\size(f)
+% \end{array}
+% $$
+% The macro is also used in \!\pcol@makecol! and \!\pcol@output@switch! for
+% $x=t$ but with \!\dimen@! having the height of \!\pcol@prespan! for the
+% measurement of the total height of \prespan{} including top
+% floats\footnote{

+% 

+% In these invocations, \CSIndex{if@tempswa} is meaningless and not examined
+% by the invokers.}.
+% 
+% The macro at first examines if $\cc_c(\xl)=\arg{list}$ is empty and does
+% nothing if so.  Otherwise, \CSIndex{if@tempswa} is turned $\true$ to have
+% $\fc(t)=\true$ for $x=t$ or $\Fc(\{t,m,f,b\})=\true$ for $x=b$.  Then we
+% scan all floats in $\arg{list}$ applying \!\pcol@hdflelt! to each float
+% $\phi$ to add $h(\phi)+d(\phi)+\!\floatsep!$ to \!\dimen@!, from/to which
+% we then subtract \!\floatsep! and add $\sigma_x$ because the last\slash
+% first float is followed\slash preceded by the vertical skip of $\sigma_x$
+% instead of \!\floatsep!, to have $\size_c(t)$ for $x=t$ or
+% $\size_c(f)+\size_c(b)$ for $x=b$ being {\em returned} to
+% \!\pcol@measurecolumn!.
+% 
+% Note that $\sigma_t$ is $\arg{tfs}=\!\pcol@textfloatsep!$ if it is less
+% than $\infty$ or \!\textfloatsep! otherwise, while
+% $\sigma_b=\!\textfloatsep!$ always because $\arg{tfs}=\!\maxdimen!$.  Also
+% note that $\sigma_t$ can be biased by 10000\,|pt| and thus larger than
+% 5000\,|pt|, if we have a \mvlfloat{} in top floats as discussed later.
+% Another caution is that we ignore the contribution by \!\topfigrule! nor
+% \!\botfigrule! because they should insert vertical items whose total
+% height and depth are 0.
+% 

+%    \begin{macrocode}
+\def\pcol@addflhd#1#2{%
+  \ifx#1\@empty\else
+    \@tempswatrue
+    \let\@elt\pcol@hdflelt
+    #1\advance\dimen@-\floatsep
+    \ifdim#2=\maxdimen \advance\dimen@\textfloatsep
+    \else
+      \advance\dimen@\pcol@textfloatsep
+      \ifdim\pcol@textfloatsep>5000\p@ \advance\dimen@-\@M\p@ \fi
+    \fi
+    \let\@elt\relax
+  \fi}
+\def\pcol@hdflelt#1{\advance\dimen@\ht#1\advance\dimen@\dp#1%
+  \advance\dimen@\floatsep}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@measureupdate}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to let $D_T$ and $D_P$ have the minimum depth of items
+%	 among those which give $V_T$ and $V_P$.}

+% 

+% The macro $\!\pcol@measureupdate!\<V\>\<v\>\<D\>\<d\>$ is invoked
+% twice in \!\pcol@measurecolumn! for $c$ to update $V\in\{\VT,\VPP\}$
+% and $D=\{\DT,\DP\}$ as follows if \CSIndex{if@tempswa}, being
+% $\Fc(\{t,m\})$ for $V=\VT$ or $\Fc(\{t,m,f,b\})$ for $V=\VPP$, is $\true$.
+% $$
+% V\gets\max(V,v)\qquad
+% D\gets\cases{\min(D,d)&$V=v$\cr
+%              D&        $V\neq v$}
+% $$
+% The arguments $v$ and $d$ have the followings according to $V$.
+% $$
+% \arraycolsep0pt
+% \begin{array}{rll}
+% V=\VT \;{:}\;&v=\Size_c(\{t,m\})&\quad d=\delta_c\\
+% V=\VPP\;{:}\;&v=\Size_c(\{t,m,f,b'))&\quad d=\dc
+% \end{array}
+% $$
+% 

+%    \begin{macrocode}
+\def\pcol@measureupdate#1#2#3#4{\if@tempswa
+  \ifdim#1<#2\relax#1#2\relax#3#4\relax
+  \else\ifdim#1=#2\ifdim#3>#4\relax#3#4\fi\fi\fi\fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@synccolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Drastically changed to correctly implement the top float
+%	 enlargement and MVL-float.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Change code structure removing the case for overflown synchronized
+%	 pages.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Remove \cs{penalty}\string\texttt{-10000} made unnecessary by the
+%	 redesign of overflow synchronized pages.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add an shrink of $1/10000\,\string\texttt{fil}$ to the bottom of
+%	 flushed column pages to cancel finite shrinks just below
+%	 synchronization points.}

+% 

+% The macro \!\pcol@synccolumn! is invoked for each column $c\In0\C$ from
+% \!\pcol@sync! to set a \sync{}ation point at $\VT$ from the top of the
+% \ccolpage{} of $c$ if $\CSIndex{ifpcol@clear}={\false}$, or flush it
+% otherwise.  After obtaining $c$'s \cctext{} $\cc_c$ by
+% \!\pcol@getcurrcol!, we process one of the following three cases.
+% 
+% The first case is for flushing with $\CSIndex{ifpcol@clear}=\true$.  In
+% this case we simply add \!\vfil! at the tail of the main vertical list in
+% $\cc_c(\vb^b)$ to make the whole \colpage{} possibly with other items fit
+% in a box of \!\@colht! tall and, if $\cc_c(\tf)\neq\infty$ to mean the
+% column to be flushed has a \sync{}ation point, we also add an infitite
+% shrink of $1/10000\,|fil|$ so as to cancel a finite shrink just below the
+% point, as done in \!\pcol@makecol!\footnote{

+% 

+% Just in case, because it looks impossible that the natural height of the
+% \colpage{} exceeds $\pp^h(\ptop)$ with \pfcheck.}.
+% 

+% We also let $\cc_c(\pd)=1000\,|pt|$ to mimic \TeX's mechanism of
+% \!\prevdepth! with the empty main vertical list in the next
+% \colpage{}\footnote{

+% 

+% The author is not sure if this setting is really necessary but, at least,
+% it looks working well (though other setting looks all right too).}.
+% 

+%    \begin{macrocode}
+\def\pcol@synccolumn{%
+  \pcol@getcurrcol
+  \ifpcol@clear
+    \global\pcol@prevdepth\@m\p@
+    \global\setbox\@currbox\vbox{\unvbox\@currbox
+      \ifdim\pcol@textfloatsep=\maxdimen \vfil
+      \else \vskip\z@\@plus1fil\@minus.0001fil
+      \fi}%
+%    \end{macrocode}
+% 

+% The second and third cases are for \sync{}ed \cswitch{}.  The second case
+% is for $\DT=\infty$ to mean the \sync{}ation point is set just below the
+% top floats of a column whose main vertical list is empty because it is
+% definitely $\VT\geq0>-\infty$.  In this case, we should not put anything
+% back to the main vertical list, because the column having defined the
+% point will restart from the top of its \colpage{} with \!\topskip! and
+% thus other columns should do so for the stuff following the point.
+% Therefore, we put $\cc_c(\vb^b)$ as the last top float, namely
+% {\em\Uidx\mvlfloat} because it is for the main vertical list, acquiring an
+% \!\insert! from \!\@freelist! by \!\@next! and assigning it to
+% \Midx{\!\pcol@float!} so that we pretend main vertical lists of all
+% columns are empty.
+% 
+% The float has zero height and depth, and contains the
+% followings if we have some real floats; a vertical skip of $-\!\floatsep!$
+% to go back to the bottom of the last real float; \!\topfigrule! and a skip
+% of \!\textfloatsep! to separate $\cc_c(\vb^b)$ from the last real float;
+% and $\cc_c(\vb^b)$ followed by \!\vss! to avoid overfull and underfull.
+% Otherwise, i.e., we don't have any real floats, neither of the skips nor
+% \!\topfigrule! are put in the \mvlfloat{} because we let
+% $\!\floatsep!=\!\textfloatsep!=0$ and $\!\topfigrule!=\!\relax!$
+% temporarily in a group.  Then we set the \sync{}ation point by enlarging
+% the space below the \mvlfloat{} so that the total size of all floats
+% including \!\floatsep! and \!\textfloatsep!, which may be 0 as set in the
+% process above, is equal to $\VT$.  This enlarging is done by letting
+% $\cc_c(\tf)=\VT-(\vc(t)-\!\textfloatsep!+\!\floatsep!)$, the second term
+% of which is the vertical size of the top float sequence up to the
+% \mvlfloat, and by replacing \!\textfloatsep! with $\cc_c(\tf)$ in the top
+% float insertion process in \!\pcol@cflt! so that the top floats including
+% the \mvlfloat{} consumes $\VT$ as a whole\footnote{

+% 

+% This enlarging cannot be done by making the float's height
+% $\VT-\vc(t)-\!\floatsep!$ (or \!\textfloatsep!) because the height can be
+% negative.}.
+% 
+% Note that the process above involves \!\floatsep! and \!\textfloatsep!
+% with some finite stretch and shrink, but these factors will not contribute
+% the final result because they are canceled by \!\vss! in the \mvlfloat{}
+% and by the small inifinite stretch and shrink put by \!\pcol@makecol! and
+% this macro for flushing.  Also note that $\cc_c(\tf)$ is then biased by
+% 10000\,|pt| so that \!\pcol@cflt!  will not put \!\topfigrule! because it
+% has been already put as a part of the \mvlfloat{} or we don't have any
+% real floats.  We also let $\cc_c(\pd)=1000$ to mean the \colpage{}'s main
+% vertical list is empty, so as to mimic \TeX's mechanism of \!\prevdepth!
+% with an empty list again.
+% 
+% Another attention we have to pay is that \colpage{}s with
+% $\cc_c(\tf)=\infty$ does not have any \sync{}ation points, and thus
+% $\cc_c(\tf)<\infty$ means a \sync{}ation has already taken place in them.
+% If this $\cc_c(\tf)<\infty$ happens with $\DT=\infty$\footnote{

+% 

+% This can happen when a \sync{}ation with $\DT=\infty$ is immediately
+% followed by another \sync{}ation or, more unlikely, by additions of
+% items whose total amount is negative and then a \sync{}ation.},
+% 

+% we cannot update $\cc_c(\tf)$ because \!\pcol@measurecolumn! took care of
+% its value on measuring $\vc(t)$.  Therefore, we do nothing if
+% $\cc_c(\tf)<\infty$ but just let succeeding stuff be added to the main
+% vertical list as in \cswitch{} without \sync{}ation.
+% 

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
+%	 \cs{pcol@float} to obey the coding convention.}
 
+% 

+%    \begin{macrocode}
+  \else
+    \@tempdimb\@tempdima
+    \advance\@tempdimb-\skip\@currbox
+    \ifdim\@tempdimc=\maxdimen
+      \ifdim\pcol@textfloatsep=\maxdimen \begingroup
+        \ifx\@toplist\@empty
+          \textfloatsep\z@ \floatsep\z@ \let\topfigrule\relax
+        \fi
+        \pcol@Fb
+        \@next\pcol@float\@freelist{\global\setbox\pcol@float\vbox to\z@{%
+          \vskip-\floatsep \topfigrule \vskip\textfloatsep
+          \unvbox\@currbox \vss}}\pcol@ovf
+        \pcol@Fe{synccolumn(topfloat)}%
+        \@cons\@toplist\pcol@float
+        \advance\@tempdimb\textfloatsep \advance\@tempdimb-\floatsep
+        \advance\@tempdimb\@M\p@
+        \global\pcol@prevdepth\@m\p@
+        \global\pcol@textfloatsep\@tempdimb
+      \endgroup \fi
+%    \end{macrocode}
+% 

+% The third and last case is for $\DT<\infty$ and thus most usual.  In this
+% case, we enclose everything in $\cc_c(\vb^b)$ in a \!\vbox!  whose height
+% is $h_c^v=\VT-\vc(t)$ and let $\cc_c(\vb^b)$ have it so that the item
+% following the \sync{}ation point start at $\VT$.  An attention we have to
+% pay is that it can be $h_c^v<\!\topskip!$ to let \TeX{} insert a vertical
+% skip of the difference between them when the box is returned to the main
+% vertical list pushing down the \sync{}ation point a little bit\footnote{

+% 

+% This can happen not very unlikely especially with $\vc(t)$ a little bit
+% less than $\VT$ and $\cc_c(\vb^b)$ being empty.}.
+% 

+% Therefore, if so, we let $\cc_c(\vb^b)$ have the followings; a \!\vbox! of
+% \!\topskip! tall having its old contents at its top above which no
+% vertical skip will be inserted; a vertical skip $-\!\topskip!$ going back
+% to the page top; and a vertical skip $h_c^v$ going down to the
+% \sync{}ation point.
+% 
+% The encapsulation of the old contents $\cc_c(\vb^b)$ in the box of $h_c^v$
+% tall gives us the following two features desirable for \sync{}ation.
+% First, all vertical glues in the box are {\em frozen}, nullifying finite
+% stretches in them because we insert an infinite stretch of
+% $1/10000\,|fil|$ at the bottom of $\cc_c(\vb^b)$ to push up its old
+% contents respecting other infinite stretches if any, as done by
+% \!\raggedbottom!, and also nullifying finite and infinite shrinks because
+% $h_c^v\geq\vc(m)$ definitely.  This freezing and nullification keeps
+% \sync{}ation points already in $\cc_c(\vb^b)$ from being observed moving a
+% little bit vertically.  That is, if we have a glue just below a
+% \sync{}ation point and it were {\em visible} to \TeX's page builder, the
+% item below the glue could move up/down when the builder found a break
+% point with some shrink\slash stretch.  Though this moving up/down is
+% inhibited by the small infinite stretch\slash shrink which the \colpage{}
+% will at its bottom finally, it is undesirable to make \TeX{}
+% misunderstanding that the glues are strethable\slash shrinkable though
+% they are not in reality.
+% 
+% Second, since the boxes in all \colpage{} are zero deep due to the
+% infinite stretch at their bottoms and these bottoms are aligned at the
+% \sync{}ation point, we have a clear view of the baseline progress after
+% the \sync{}ation regardless of their contents.  That is, we let
+% $\cc_c(\pd)=\DT$ to {\em broadcast} $\DT$ to all columns, so that 
+% the baselines of first items following the \sync{}ation
+% point are aligned \!\baselineskip! below the bottom baseline of the column
+% which defines $\DT$\footnote{

+% 

+% Since $\DT$ is given by one of the tallest columns whose depth is smallest
+% among them, it is very likely that the bottom baseline of the column is
+% lowest among all columns.  However, another column can have the lowest one
+% when its vertical size is a little bit shorter than $\VT$ and its depth is
+% small (e.g., 0).  Though of course we can define $\DT$ being $\VT$ minus
+% the height of the column having the largest height to make the first
+% baseline below the \sync{}ation point apart from the lowest one by
+% \cs{baselineskip}, we dare to choose the definition of $\DT$ because such
+% lowest baseline often means that the column have some skip at its bottom
+% to give us the impressoin that the space between the baselines of the
+% tallest column and its first item is a little bit too large.},
+% 

+% if $\DT$ plus the hight of each item is less than \!\baselineskip!.
+% 
+% In addition, we let $\cc_c(\tf)=\!\textfloatsep!$ to
+% indicate the \colpage{} has the \sync{}ation point we just have set, if it
+% was $\infty$ to mean the point is the first one.  By this setting,
+% \!\pcol@makecol! and this macro itself will know that the \colpage{} needs
+% to have a small infinite shrink at its bottom to cancel finite ones below
+% the \sync{}ation point, while \!\pcol@cflt! acts as \LaTeX's \!\@cflt!
+% because it should be $\cc_c(\tf)\leq5000\,|pt|$ to mean the \colpage{}
+% does not have a \mvlfloat.
+% 

+% \changes{v1.33-2}{2016/11/19}
+% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
+%	 \cs{@currbox} and two lines for \cs{vbox}es in it to obey the
+%	 coding convention.}
 
+% 

+%    \begin{macrocode}
+    \else
+      \global\pcol@prevdepth\@tempdimc
+      \ifdim\pcol@textfloatsep=\maxdimen
+        \global\pcol@textfloatsep\textfloatsep \fi
+      \global\setbox\@currbox\vbox{%
+        \ifdim\@tempdimb<\topskip
+          \vbox to\topskip{\unvbox\@currbox \vskip\z@\@plus.0001fil}%
+          \vskip-\topskip \vskip\@tempdimb
+        \else
+          \vbox to\@tempdimb{\unvbox\@currbox \vskip\z@\@plus.0001fil}%
+        \fi}%
+    \fi
+  \fi
+%    \end{macrocode}
+% 

+% Finally, we let $\cc_c(\tn)=0$ to inhibit futher addition of top floats
+% because we have fixed the space for them\footnote{

+% 

+% Allowing the addition is tremendously tough even when the \colpage{} has
+% sufficiently large space above the \sync{}ation point.},
+% 

+% and save it and other \cctext{} members into $\cc_c$ by \!\pcol@setcurrcol!.
+% 

+%    \begin{macrocode}
+  \global\@topnum\z@ \pcol@setcurrcol
+  \advance\pcol@currcol\@ne}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \subsection{Page Flushing}
+% \label{sec:imp-sout-flush}
+% 
+% \begin{macro}{\pcol@output@flush}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@makelastpage} as \cs{pcol@makeflushedpage}.}

+% \changes{v1.0}{2011/10/10}
+%	{Remove unnecessary assignment of \cs{@colht}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add depth capping of \cs{pcol@rightpage}.}

+% 

+% The macro \!\pcol@output@flush! is invoked solely from
+% \!\pcol@specialoutput! to process the \!\output! request made by
+% \!\flushpage!.  We invoke \!\pcol@makeflushedpage! giving it \!\@colht! as
+% the height of each \colpage{} to have the ship-out image of the
+% \tpage{} including its \spanning{} and \Scfnote{}s in \!\@outputbox! whose
+% height is then set to be \!\textheight!\footnote{

+% 

+% Just in case because the height of source \cs{@outputbox} should be exactly
+% \cs{textheight} though not specified so on its construction in
+% \cs{pcol@makeflushedpage}.},
+% 

+% ensureing that its depth is capped by $\!\boxmaxdepth!=\!\@maxdepth!$.  We
+% also perform these height setting and depth capping on \!\pcol@rightpage!
+% if $\CL<\C$ to mean \parapag{}ing.  Then we invoke \!\@outputpage! for
+% shipping out, and then finally \!\pcol@freshpage! to have a new page to
+% start new \colpage{}s in it.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Page Flushing
+
+\def\pcol@output@flush{%
+  \pcol@makeflushedpage\@colht
+  \pcol@Logstart\pcol@output@flush
+  \setbox\@outputbox\vbox to\textheight{\boxmaxdepth\@maxdepth
+    \unvbox\@outputbox}%
+  \ifnum\pcol@ncolleft<\pcol@ncol
+    \setbox\pcol@rightpage\vbox to\textheight{\boxmaxdepth\@maxdepth
+      \unvbox\pcol@rightpage}%
+  \fi
+  \pcol@Logend\pcol@output@flush
+  \@outputpage
+  \pcol@freshpage}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@output@clear}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@makelastpage} as \cs{pcol@makeflushedpage}.}

+% \changes{v1.0}{2011/10/10}
+%	{Remove unnecessary increment of \cs{pcol@page} and assignment of
+%	 \cs{@colht}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add depth capping of \cs{pcol@rightpage} and building an empty
+%	 right parallel-page for each page-wise float page.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add background painting of float pages.}

+% \changes{v1.32-3}{2015/10/10}
+% 	{Add $\hbox{\cs{f@depth}}\EQ0$ to override
+%	 $\hbox{\cs{f@depth}}\EQ\hbox{\texttt{1sp}}$ done by
+%	 \cs{@dblfloatplacement}.}
+% 

+% The macro \!\pcol@output@clear! is invoked solely from
+% \!\pcol@specialoutput! to process the \!\output! request made by
+% \!\clearpage!.  The first part up to \!\@outputpage! and the last line of
+% this macro are same as \!\pcol@output@flush! to flush the \tpage{} and to
+% have a newpage.  In the remaining mid part, we invoke \!\pcol@flushfloats!
+% to ship out all deferred \cwise{} floats in all columns if any, and
+% then do it for \pwise{} floats by the following invocations enclosed in a
+% group; letting $\!\pcol@rightpage!=\bot$ for ordinary paging;
+% \!\@dblfloatplacement! to set up placement parameters followed by
+% $\!\f@depth!=0$ to nullify the setting $\!\f@depth!=|1sp|$ possiblly done
+% by it as discussed in the item-(\ref{item:ovv-float-@dblfloatplacement})
+% of \secref{sec:imp-ovv-float}; \!\@makefcolumn!  with
+% \!\@dbldeferlist! to have a \fpage{} in \!\@outputbox! if any; and a loop
+% of \bgpaint{} of \!\@outputbox! and, if $\CL<\C$, of empty
+% \!\pcol@rightpage!, and \!\@outputpage! followed by \!\@makefcolumn!
+% repeated while we have a \fpage{}, i.e., $\CSIndex{if@fcolmade}=\true$.
+% 
+% Note that the mid part is same as that found in \!\@doclearpage! but we
+% omit various adjuncts surrouding it as follows;  examination of
+% \CSIndex{if@twocolumn} because we should have multiple columns;
+% examination of \CSIndex{if@firstcolumn} because we have to clear the page
+% immediately even when we are not in the first column;  concatenating
+% \!\@dbltoplist! with \!\@dbldeferlist! and clearing it because the author
+% believes \!\@dbltoplist! must be empty on the invocation of this macro;
+% and letting $\!\@colht!=\!\textheight!$ because \!\pcol@flushfloats! did
+% it.
+% 

+%    \begin{macrocode}
+\def\pcol@output@clear{%
+  \pcol@makeflushedpage\@colht
+  \pcol@Logstart\pcol@output@clear
+  \setbox\@outputbox\vbox to\textheight{\boxmaxdepth\@maxdepth
+    \unvbox\@outputbox}%
+  \ifnum\pcol@ncolleft<\pcol@ncol
+    \setbox\pcol@rightpage\vbox to\textheight{\boxmaxdepth\@maxdepth
+      \unvbox\pcol@rightpage}%
+  \fi
+  \pcol@Logend\pcol@output@clear
+  \@outputpage
+  \pcol@flushfloats
+  \begingroup
+    \setbox\pcol@rightpage\box\voidb@x
+    \@dblfloatplacement \let\f@depth\z@
+    \@makefcolumn\@dbldeferlist
+    \@whilesw\if@fcolmade\fi{%
+      \def\pcol@bg@floatheight{\pcol@bg@textheight}%
+      \setbox\@outputbox\vbox to\textheight{%
+        \pcol@bg@paintbox{Ff}\unvbox\@outputbox}%
+      \ifnum\pcol@ncolleft<\pcol@ncol
+        \setbox\pcol@rightpage\vbox to\textheight{\pcol@bg@paintbox{Ff}\vfil}%
+      \fi
+      \@outputpage
+      \@makefcolumn\@dbldeferlist}%
+  \endgroup
+  \pcol@freshpage}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@makeflushedpage}
+% \changes{v1.0}{2011/10/10}
+%	{Renamed from \cs{pcol@makelastpage}.}

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

+% \changes{v1.0}{2011/10/10}
+%	{Judge the last page is empty if $V_P\EQ-\infty$ instead of $V_P<0$.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Revise reflecting the redesign of page context.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Completely redesigned with new macro \cs{pcol@imakeflushedpage}.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add background painting of page-wise floats, and a part of
+%	 opreations for column-separation rule drawing and background
+%	 painting of page-wise footnotes.} 

+% \changes{v1.3-6}{2013/09/17}
+%	{Revise the mechanism of special care about last page introducing
+%	 \cs{ifpcol@dfloats}.}

+% 

+% The macro $\!\pcol@makeflushedpage!\arg{ht}$ is invoked from
+% \!\pcol@output@flush! or \!\pcol@output@clear! with $\arg{ht}=\!\@colht!$
+% and from \!\pcol@output@end! with $\arg{ht}=\!\pcol@colht!$.  At first, we
+% invoke \!\pcol@output@switch! with setting $\CSIndex{ifpcol@clear}=\true$
+% to flush all pages up to $\ptop-1$ and to let $\cc_c(\vb^b)$ have the
+% ship-out image of the main vertical list of each \colpage{} $c$ in
+% $\ptop$.  This invocatoin also lets $\!\pcol@colht!=\VPP$ so that hereafter
+% we will refer $\VPP$ throuth $\arg{ht}$ if it is $\!\pcol@colht!$ for
+% \lpage.  Then after obtaining $\ptop$'s \pctext{} to have
+% $\page(\ptop)=\pp^p(\ptop)$, $\!\@colht!=\pp^h(\ptop)$ and
+% \CSIndex{ifpcol@nospan} by \!\pcol@getcurrpinfo!, we build the ship-out
+% image of $\ptop$ in \!\@outputbox!, and \!\pcol@rightpage! if
+% \parapag{}ing, taking special care of the \lpage{} case as follows.
+% 

+% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
+% \item\label{item:mfp-nonlast}
+% If $\CSIndex{ifpcol@lastpage}=\false$, each of $\cc_c(\vb^b)$ has ship-out
+% image even if some or all of them are empty.  It is unecessary to be aware
+% of the perfectly empty case because it should mean the page $\ptop$ is
+% made blank intentionally.
+% 
+% \item\label{item:mfp-last-dfloats}
+% If $\CSIndex{ifpcol@lastpage}=\true$ but $\CSIndex{ifpcol@dfloats}=\true$
+% too, the last page must have {\em full size} because we will have parallel
+% columned pages having \fcolumn{}s for deferred floats.  However, if the
+% page has nothing, i.e., $\pp^i(\ptop)=\pp^f(\ptop)=\bot$ and
+% $\VPP=-\infty$, we must let $\!\@outputbox!=\bot$ (and
+% $\!\pcol@rightpage!=\bot$ as well) to avoid an unnecessary blank page is
+% shipped out.  On the other hand, if $\pp^i(\ptop)\neq\bot$ or
+% $\pp^f(\ptop)\neq\bot$ while $\VPP=-\infty$, we build a full size page as
+% usual but letting $\!\@textbottom!=\!\vfil!$ temporarily to avoid underfull
+% in the process of building columns.  Note that if $\pp^f(\ptop)\neq\bot$,
+% the \Scfnote{}s are always put into \!\@outputbox! regardless
+% \CSIndex{ifpcol@mgfnote} because the \lpage{} is not combined with
+% \postenv.
+% 
+% \item\label{item:mfp-last-empty}
+% If $\CSIndex{ifpcol@lastpage}=\true$, $\CSIndex{ifpcol@dfloats}=\false$
+% and $\VPP=-\infty$, we have to let $\!\@outputbox!=\bot$ unless
+% $\pp^i(\ptop)\neq\bot$ or $\pp^f(\ptop)\neq\bot$ having non-\Mgfnote{}s.
+% If $\pp^f(\ptop)$ has non-\Mgfnote{}s, \!\@outputbox! and
+% \!\pcol@rightpage!  must have $\pp^f(\ptop)$ possibly with $\pp^i(\ptop)$
+% but without any columns, and must be put into the main vertical list as
+% the leading part of \postenv{} by modifying $\VPP=0$.  On the other hand
+% $\pp^f(\ptop)=\bot$ or it has \Mgfnote{}s, \!\@outputbox! must have only
+% $\pp^i(\ptop)$\footnote{

+% 

+% \!\pcol@rightpage! must have the couterpart in right \parapag{}e if the
+% \spanning{} is \preenv, while it is made $\bot$ by \!\pcol@output@end! if
+% the \spanning{} are \pwise{} floats.}.
+% 

+% Since \pwise{} floats become ordinary floats in \postenv, we cannot paint
+% its \bground{} and must remove \!\dbltextfloatsep! at the bottom of
+% $\pp^i(\ptop)$.
+% 
+% \item\label{item:mfp-last-nonempty}
+% If $\CSIndex{ifpcol@lastpage}=\true$, $\CSIndex{ifpcol@dfloats}=\false$
+% and $\VPP>-\infty$, \!\@outputpage! and \!\pcol@rightpage! must have short
+% columns of $\VPP$ tall, together with $\pp^i(\ptop)$ as in non-\lpage{}s
+% but without $\pp^f(\ptop)$ if it has \Mgfnote{}s.
+% \end{enumerate}
+% 

+% To implement a part of special cares above, we at first let
+% $\CSIndex{if@tempswa}=\true$ iff $\cs{ifpcol@}\~|lastpage|=\false$,
+% 

+% \CSINDEX{ifpcol@lastpage}

+% 

+% $\VPP>-\infty$ or $\pp^f(\ptop)\neq\bot$.
+% 

+%    \begin{macrocode}
+\def\pcol@makeflushedpage#1{%
+  \pcol@cleartrue \pcol@output@switch \pcol@clearfalse
+  \pcol@getcurrpinfo{\global\c@page}{\global\@colht}\@tempskipa
+  \ifpcol@lastpage \@tempswafalse \else \@tempswatrue \fi
+  \ifdim\pcol@colht=-\maxdimen\else \@tempswatrue \fi
+  \ifvoid\pcol@footins\else \@tempswatrue \fi
+%    \end{macrocode}
+% 
+% Next, if $\CSIndex{ifpcol@nospan}=\true$ to mean the page $\ptop$ does not
+% have \spanning{} in $\pp^i(\ptop)$, we initialize both \!\@outputbox!  and
+% \!\pcol@rightpage! to be $\bot$.  Otherwise, after letting
+% $\CSIndex{if@tempswa}=\true$ if $\CSIndex{ifpcol@dfloats}=\true$ to make the
+% \lpage{} full size if we are working on it as discussed in\Tie
+% (\ref{item:mfp-last-dfloats}), we put $\pp^i(\ptop)$ in \!\@outputbox!,
+% and paint its \bground{} by \!\pcol@bg@paintbox!  \!\edef!ining the height
+% paramenter \!\pcol@bg@floatheight! with $h$ being the height-plus-depth of
+% $\pp^i(\ptop)$ with the following two exceptions; one is the case of
+% $\CSIndex{ifpcol@firstpage}={\true}$ to mean we are in \spage{} and thus
+% the \spanning{} is \preenv{} having already been painted by
+% \!\pcol@output@start!; and the other is the case of
+% $\CSIndex{if@tempswa}=\false$ to mean we are working on a truly \lpage{}
+% being empty except for the \spanning{} itself and thus the \pwise{}
+% floats become a part of deferred floats in \postenv{} as discussed in\Tie
+% (\ref{item:mfp-last-empty}).  In the latter exceptional case, excluding
+% the case that the \lpage{} is also the \spage\footnote{

+% 

+% Extremely exceptional because the closing environment does not have
+% anything.},
+% 

+% we also remove the last skip being \!\dbltextfloatsep! so that those
+% floats are naturally connected with other floats given in
+% \postenv{} also as discussed in\Tie(\ref{item:mfp-last-empty}).  Then we
+% {\em pack} the \!\@outputbox! in itself by \!\vbox! so that any
+% stretch\slash shrink factors in it cannot affect the ship-out image
+% especially when we paint its \bground{}\footnote{

+% 

+% Though that hardly happens.}.
+% 

+% Then we do the similar procedure for \!\pcol@rightpage! and make its height
+% and depth equal to those of \!\@outputbox!\footnote{

+% 

+% If \pwise{} floats become a part of \postenv's floats, \!\pcol@rightpage!
+% will be made $\bot$ by \!\pcol@output@end! afterward.}.
+% 

+% Finally we temporarily add $h$ to \!\topmargin! as done in
+% \!\pcol@ioutputelt! so that \bgpaint{} of columns and so on with
+% \bginfext{} can reach the paper top edge.
+% 

+% \changes{v1.3-6}{2013/09/17}
+%	{Revise the condition of leaving page-wise floats as ordinary
+%	 post-environment floats using \cs{if@tempswa} with
+%	 \cs{ifpcol@dfloats}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \begingroup
+    \ifpcol@nospan
+      \global\setbox\@outputbox\box\voidb@x
+      \global\setbox\pcol@rightpage\box\voidb@x
+    \else
+      \ifpcol@dfloats \@tempswatrue \fi
+      \let\@elt\relax
+      \edef\pcol@bg@floatheight{%
+        \@elt{\number\ht\pcol@spanning sp}\@elt{\number\dp\pcol@spanning sp}}%
+      \def\reserved@a{%
+        \ifpcol@firstpage\else \if@tempswa \pcol@bg@paintbox{Ff}\fi\fi}%
+      \@tempdima\ht\pcol@spanning \advance\@tempdima\dp\pcol@spanning
+      \global\setbox\@outputbox\vbox{%
+        \reserved@a \unvbox\pcol@spanning
+        \ifpcol@firstpage\else \if@tempswa\else \unskip \fi\fi}%
+      \global\setbox\@outputbox\vbox{\box\@outputbox}%
+      \pcol@Fb
+      \@cons\@freelist\pcol@spanning
+      \pcol@Fe{makeflushedpage(spanning)}%
+      \ifnum\pcol@ncolleft<\pcol@ncol
+        \global\setbox\pcol@rightpage\vbox{%
+          \ifpcol@paired\else \advance\c@page\@ne \fi
+          \reserved@a \unvbox\pcol@rightpage}%
+        \global\ht\pcol@rightpage\ht\@outputbox
+        \global\dp\pcol@rightpage\dp\@outputbox
+        \global\setbox\pcol@rightpage\vbox{\box\pcol@rightpage}%
+      \fi
+      \advance\topmargin\@tempdima
+    \fi
+%    \end{macrocode}
+% 
+% Next, after \!\global!ly letting $\CSIndex{ifpcol@firstpage}=\false$ because
+% we will ship a page which may be the \spage{} shortly, we build the
+% ship-out image of columns if required fundamentally by
+% $\CSIndex{if@tempswa}=\true$.  First,
+% if the page $\ptop$ has \Scfnote{}s, we shrink
+% $\!\@colht!={\pp^h}(\ptop)$ by \!\pcol@shrinkcolbyfn! to keep the room for
+% the footnotes, to have $H=\!\@pageht!$ being the possibly shrunk
+% $\pp^h(\ptop)$ for the reference
+% in \!\pcol@imakeflushedpage! after the further possible modification of
+% \!\@colht! we will make shortly.  Second, if
+% $\CSIndex{ifpcol@lastpage}=\true$ but $\CSIndex{ifpcol@dfloats}=\true$
+% too, we turn $\CSIndex{ifpcol@lastpage}=\false$ because we need a
+% full-sized \lpage{}, temporarily letting $\!\@textbottom!=\!\vfil!$ if
+% $\VPP=-\infty$ to avoid underfull due to perfectly empty \colpage{}s as
+% discussed in\Tie(\ref{item:mfp-last-dfloats})\footnote{

+% 

+% Each \colpage{} $cc_c(\vb^b)$ itself exists because the empty \colpage{}
+% has been visited by \cscan{} prior to \!\output! request for environment
+% closing.}.
+% 

+% Third, if we are working on a truly \lpage{} and $\arg{ht}<H$ to mean the
+% tallest column is shorter than $H$, we let $\!\@colht!=\arg{ht}$ to let
+% \!\@makecol! build short \colpage{}s.  Note that it is definitely
+% $\arg{ht}\leq H$ because the \pfcheck{} on the \lpage{} makes that sure.
+% Fourth and finally, unless all columns in truly \lpage{} are empty as
+% discussed in (\ref{item:mfp-last-empty}), we invoke
+% $\!\pcol@imakeflushedpage!\<\Cfrom\>\<\Cto\>\<b\>$ once or twice, to put
+% columns in right \parapag{}e to $b=\!\pcol@rightpage!$ with
+% $\LBRP\Cfrom\Cto=\LBRP\CL\C$ if $\CL<\C$, and then to put left ones in
+% $b=\!\@outputbox!$ with $\LBRP\Cfrom\Cto=\LBRP0\CL$ always\footnote{

+% 

+% The order of right to left is not essential in this macro but we follow
+% the convention in \!\pcol@outputelt!.}.
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Let \cs{@colht} be $\langle\mathit{ht}\rangle$ if the former is
+%	 less than the latter.}

+% \changes{v1.0}{2011/10/10}
+%	{Add special care of the float column in the last page.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{@colht} shrinking by page-wise footnotes.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add \cs{@colht} and \cs{relax} as the first and third argument
+%	 of \cs{pcol@shrinkcolbyfn} for all of three invocations of it.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Remove empty column scan for \cs{if@fcolmade} because it is now
+%	 unnecessary thanks to \cs{ifpcol@dfloats}.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Revise the condition of column-page building and setting of
+%	 \cs{@colht}.}

+% 

+%    \begin{macrocode}
+    \global\pcol@firstpagefalse
+    \if@tempswa
+      \ifvoid\pcol@footins\else
+        \pcol@shrinkcolbyfn\@colht\pcol@footins\relax
+      \fi
+      \let\pcol@@hfil\relax \@pageht\@colht
+      \ifpcol@lastpage \ifpcol@dfloats
+        \ifdim\pcol@colht<\z@ \def\@textbottom{\vfil}\fi
+        \pcol@lastpagefalse
+      \fi\fi
+      \ifpcol@lastpage \ifdim#1<\@colht \@colht#1\fi\fi
+      \ifdim\@colht<\z@ \else
+        \ifnum\pcol@ncolleft<\pcol@ncol
+          \pcol@imakeflushedpage\pcol@ncolleft\pcol@ncol\pcol@rightpage
+        \fi
+        \pcol@imakeflushedpage\z@\pcol@ncolleft\@outputbox
+      \fi
+    \fi
+%    \end{macrocode}
+%
+% After putting all \colpage{}s, we examine if the page $\ptop$ has
+% \Scfnote{}s in $\pp^f(\ptop)$.  If so, and unless $\ptop$ is a truly
+% \lpage{} and \Mgfnote{} typesetting is in effect to mean the \Scfnote{}s
+% will be merged with \postenv{}, we put the footnotes in $\pp^f(\ptop)$
+% below the \colpage{}s.  Prior to this however, we let
+% \Midx{\!\pcol@fnheight@lpage!} have the height-plus-depth of the footnote,
+% so that \!\pcol@output@end! know the size for the \bgpaint{} of the
+% footnotes, which \!\pcol@imakeflushedpage!  performed for non-\lpage{}s.
+% We also put an empty box of the size into \!\pcol@rightpage! by
+% \!\pcol@phantom! together with the \!\skip! component of $\pp^f(\ptop)$ to
+% keep the space necessary especially when $\ptop$ is the \lpage.  Then we
+% put the footnotes in $\pp^f(\ptop)$ into \!\@outputpage!  by
+% \!\pcol@putfootins!, reclaiming the contents of $\pp^f(\ptop)$ and letting
+% $\pp^f(\ptop)=\bot$ so that \!\pcol@output@end!  will be unaware of the
+% footnotes.  We also let $\VPP=\!\pcol@colht!=0$ if $\ptop$ is a truly
+% \lpage{} and it had $-\infty$ to indicate that the \lpage{} is not empty
+% but has footnotes as discussed in\Tie(\ref{item:mfp-last-empty}).
+% 

+% \changes{v1.2-2}{2013/05/11}
+%	{Add incorporation of page-wise footnotes.}

+% \changes{v1.3-6}{2013/09/17}
+%	{page-wise footnotes for the last page followed by pages for
+%	 deferred column-wise floats are now put by this macro.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+    \gdef\pcol@fnheight@lpage{0pt}%
+    \ifvoid\pcol@footins\else
+      \@tempswatrue \ifpcol@lastpage \ifpcol@mgfnote \@tempswafalse \fi\fi
+      \if@tempswa
+        \pcol@Log\pcol@makeflushedpage{output}\pcol@footins
+        \@tempdima\ht\pcol@footins \advance\@tempdima\dp\pcol@footins
+        \xdef\pcol@fnheight@lpage{\number\@tempdima sp}%
+        \ifnum\pcol@ncolleft<\pcol@ncol
+          \global\setbox\pcol@rightpage\vbox{\unvbox\pcol@rightpage
+            \vskip\skip\pcol@footins \nointerlineskip
+            \pcol@phantom\pcol@footins \vskip\z@}%
+        \fi
+        \global\setbox\@outputbox\vbox{%
+          \unvbox\@outputbox \pcol@putfootins\pcol@footins}%
+        \pcol@Fb
+        \@cons\@freelist\pcol@footins \gdef\pcol@footins{\voidb@x}%
+        \pcol@Fe{makeflushedpage(pagefn)}%
+        \ifdim\pcol@colht=-\maxdimen \global\pcol@colht\z@ \fi
+      \fi
+    \fi
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@imakeflushedpage}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Implement column-separating rule and background paiting of
+%	 columns, column-separating gaps, spanning texts and page-wise
+%	 footnotes.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Implement variable-width column-separating gaps.}

+% 
+% The macro $\!\pcol@imakeflushedpage!\<\Cfrom\>\<\Cto\>\arg{b}$ is invoked
+% solely in \!\pcol@makeflushedpage! but can be twice with
+% $(\Cfrom,\Cto,b)=(\CL,\C,\!\pcol@rightpage!)$ if \parapag{}ing is in effect
+% and with $(\Cfrom,\Cto,b)=(0,\CL,\!\@outputbox!)$ always, to build the
+% ship-out image of the right or left \parapag{}e $\ptop$ in the box $b$
+% already having \spanning{} or its blank counterpart if any, respectively.
+% 
+% After opening the \!\vbox! of the ship-out image for $b$, at first we
+% examine if $\CSIndex{ifpcol@paired}={\false}$ and $\Cfrom>0$, and if so we
+% temporarily increment $\page(\ptop)$ by one so that we check its parity
+% for \mirror{}ed \bgpaint{} correctly.  Then if the page $\ptop$ has
+% \Scfnote{}s in $\pp^f(\ptop)$, we paint its \bground, or that of its blank
+% counterpart, by \!\pcol@bg@paintbox! \!\def!ining the parameter
+% \!\pcol@bg@footnoteheight!  with the height-plus-depth of $\pp^f(\ptop)$,
+% as the very first element of the ship-out image as done in
+% \!\pcol@ioutputelt!, unless $\ptop$ is the truely \lpage{} for which the
+% \bgpaint{} is done in \!\pcol@output@end!.  Then we put \spanning{} in $b$
+% itself if any.
+% 
+% Next, we invoke \!\pcol@buildcolseprule! for \cseprule{} drawing and
+% \bgpaint{} giving it $H$ in \!\@colht! possibly shurnk from $\pp^h(\ptop)$
+% by \Scfnote{}s, $\LBRP\Cfrom\Cto$ for the set of columns to be put, and
+% \!\@maxdepth! for non-\lpage{}s to paint the \bground{}s of columns and
+% \csepgap{}s so that those of the last segment reach the page bottom, while
+% for \lpage{} we give 0 to let the bottom be the real bottom of the
+% columns.  Then we put the painted \bground{}s in \!\@tempboxa!
+% immediately.
+% 

+%    \begin{macrocode}
+\def\pcol@imakeflushedpage#1#2#3{\global\setbox#3\vbox{%
+  \ifpcol@paired\else\ifnum#1=\z@\else \advance\c@page\@ne \fi\fi
+  \ifvoid\pcol@footins\else \ifpcol@lastpage\else
+    \def\pcol@bg@footnoteheight{%
+      \@elt{\ht\pcol@footins}\@elt{\dp\pcol@footins}}%
+    \pcol@bg@paintbox{Nn}%
+  \fi\fi
+  \unvbox#3\nointerlineskip
+  \ifpcol@lastpage \pcol@buildcolseprule\@colht#1#2\z@
+  \else            \pcol@buildcolseprule\@colht#1#2\@maxdepth
+  \fi
+  \unvbox\@tempboxa
+%    \end{macrocode}
+% 
+% Now we put columns in a \!\hbox! of $\WT=\!\textwidth!$ wide.  That is,
+% for each $c$, being $c'$ or $\C-1-c'$ for the $c'$-th iteration determined
+% by \!\pcol@swapcolumn! according to the effectiveness of \cswap{} and the
+% parity of $\page(\ptop)$, we obtain $c$'s \cctext{} $\cc_c$ by
+% \!\pcol@getcurrcol!, move $\cc_c(\vb^b)$ into \!\box!|255|, and let
+% $\!\footins!=\cc_c(\ft)$ by \!\pcol@getcurrfoot! returning it to
+% \!\@freelist! if $c$ has \Mcfnote{}s.
+% 
+% After that we examine if $\cc_c(\tr)=\infty$ to mean we are working on the
+% \lpage{} and the \colpage{} is for a \fcolumn{} whose floats can be put as
+% top floats, and let $\!\topfigrule!=\!\relax!$ temporarily because the
+% floats are not top ones in reality, if so.  Note that the abnormal setting
+% $\cc_c(\tr)=\infty$ is not recovered because it will never be referred to
+% and the register \!\@toproom! it represents will be updated with correct
+% value before it is referred to in \postenv.  Then we also check
+% $\arg{ht}=H$ to mean the \lpage{} is full size.  If both of them hold,
+% the floats in $\cc_c(\tl)$ should be (or may be) put in the \fcolumn{} as
+% usual and thus we put them in \!\@outputbox! of $H$ tall by
+% \!\pcol@makefcolpage!.  Otherwise we invoke \!\pcol@@makecol!\footnote{

+% 

+% Not \cs{pcol@makecol} because the main vertical list has \!\vfil! and, if
+% it has a \sync{}ation point, a infinite shrink by \cs{pcol@synccolumn} at
+% its tail already, and we should not do any special operations for
+% \Scfnote{}s.  Also it is not \cs{@makecol} because we need to ensure the
+% depth of resulting \cs{@outputbox} is capped.},
+% 

+% to have the ship-out image of the \colpage{} in \!\@outputbox!, possibily
+% only for the deferred floats in $\cc_c(\tl)$ but without \!\topfigrule! in
+% this case.  Note that we don't take care of the stretch\slash shrink of
+% \!\skip!\!\footins!  for \Scfnote{}s because \pfcheck{} on the \colpage{}
+% makes it sure that the natural height of the \colpage{} cannot be greater
+% than \!\@colht!.  Also note that we give \!\@maxdepth! to
+% \!\pcol@@makecol! for non-\lpage{}s for depth capping, but for the
+% \lpage{} we pass 0 to the macro because $H=\!\@colht!$ should be large
+% enough to accommodate everything in the column including its last box even
+% if the box is unusually deep.
+% 
+% Then we put the \!\@outputbox! above in a \!\hbox! of \!\columnwidth! wide
+% preceded by \!\pcol@@hfil! being \!\relax! for the first column, while
+% it is $\!\pcol@hfil!\<c^g\>$, where $c^g=\!\pcol@colsepid!$ being $c$ or
+% $c-1$ without or with \cswap{} respectively, to put a \csepgap{} possibly
+% with \cseprule{} segments in \!\pcol@tempboxa! built by
+% \!\pcol@buildcolseprule!.  Finally, we save \cctext{} especially those
+% for float parameters into $\cc_c$ by \!\pcol@setcurrcolnf! because all
+% \Mcfnote{}s have been shipped out.
+% 

+% \changes{v1.2-4}{2013/05/11}
+%	{Add column-swapping for even pages if specified.}

+% \changes{v1.2-2}{2013/05/11}
+% 	{Revise reflecting the redesign of \cs{pcol@getcurrfoot}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Enclose the column-page building process in a group to fix the bug
+%	 which lets $\cs{topfigrule}\EQ\cs{relax}$ affecting to another
+%	 column.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Replace the sequence of operations to make a usual float column
+%	 with \cs{@toplist} with the newly introduced
+%	 \cs{pcol@makefcolpage}.}

+% \changes{v1.2-7}{2013/05/11}
+% 	{Replace \cs{@makecol} with \cs{pcol@@makecol} to cap the depth of
+%	 \cs{@outputbox} by \cs{@maxdepth} even with p\string\LaTeX.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add \cs{@maxdepth} or 0 as the argument of \cs{pcol@@makecol} to
+%	 fix the problem that the last page is too large due to
+%	 \cs{@maxdepth}, by the latter.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Remove the examination of $\kappa_c(\lambda_d)$ for
+%	 \cs{if@fcolmade} because it is made unnecesary now by
+%	 \cs{ifpcol@dfloats}.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \hb@xt@\textwidth{%
+    \@tempcntb#1\@whilenum\@tempcntb<#2\do{%
+      \pcol@swapcolumn\@tempcntb\pcol@currcol#1#2\relax
+      \pcol@getcurrcol
+      \setbox\@cclv\box\@currbox
+      \ifvoid\pcol@currfoot\else
+        \pcol@Fb
+        \@cons\@freelist\pcol@currfoot
+        \pcol@Fe{imakeflushedpage(colfn)}%
+      \fi
+      \pcol@getcurrfoot\box
+      \@tempswafalse
+      \begingroup
+        \ifdim\@toproom=\maxdimen
+          \let\topfigrule\relax \ifdim\@colht=\@pageht \@tempswatrue \fi
+        \fi
+        \if@tempswa
+          \pcol@Logstart{\pcol@makeflushedpage(1)}%
+          \setbox\@outputbox\pcol@makefcolpage
+          \pcol@Logend{\pcol@makeflushedpage(1)}%
+        \else
+          \pcol@Logstart{\pcol@makeflushedpage(2)}%
+          \ifpcol@lastpage \pcol@@makecol\z@ \else \pcol@@makecol\@maxdepth \fi
+          \pcol@Logend{\pcol@makeflushedpage(2)}%
+        \fi
+        \pcol@@hfil \hb@xt@\columnwidth{\box\@outputbox\hss}%
+      \endgroup
+      \edef\pcol@@hfil{\noexpand\pcol@hfil{\pcol@colsepid}}%
+      \pcol@setcurrcolnf
+     \advance\@tempcntb\@ne}}}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@flushfloats}
+% \changes{v1.0}{2011/10/10}
+%	{Add reinitialization of \cs{@colht}.}

+% \changes{v1.2-4}{2013/05/11}
+%	{Add column-swapping for even pages if specified.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Completely redesigned with new macro \cs{pcol@iflushfloats}.}

+% \begin{macro}{\pcol@iflushfloats}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced for parallel-paging.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Implement column-separating rule and background paiting of
+%	 columns and column-separating gaps}

+% \changes{v1.3-4}{2013/09/17}
+%	{Implement variable-width column-separating gaps.}

+% 

+% The macro \!\pcol@flushfloats! is invoked from \!\pcol@output@clear! and
+% \!\pcol@output@end! to flush all deferred \cwise{} floats in each
+% column if any.  After letting $\!\@colht!=\!\textheight!$ for
+% \fcolumn{}s, we iterate shipping out a page having \fcolumn{}s while
+% $\CSIndex{if@fcolmade}=\exists c\In0\C:(\cc_c(\dl)\neq())$.
+% 
+% In the loop, we initialize $\CSIndex{if@fcolmade}=\false$, and then
+% invoke \!\pcol@iflushfloats! twice or once according to $\CL<\C$ or not to
+% mean \parapag{}ing is in effect or not, respectively.  That is, if
+% $\CL<\C$ we invoke the macro with $\LBRP\CL\C$ and \!\pcol@rightpage! for
+% the right \parapag{}e, and do it with $\LBRP0\CL$ and \!\@outputbox!
+% always.  Note that if $\CL=\C$, we let $\!\pcol@rightpage!=\bot$ to tell
+% \!\@outputpage!, which we invoke at the end of the loop to ship out a page
+% or a \parapag{}e pair, that the \parapag{}ing is not in effect.
+% 
+% The macro $\!\pcol@iflushfloats!\<\Cfrom\>\<\Cto\>\<b\>$ opens
+% a \!\vbox! to be set into $b$.  Then if $\CSIndex{ifpcol@paired}={\false}$
+% and $\Cfrom>0$ to mean we are working on a right \npaired{} \parapag{}e,
+% we temporarily add \!\c@page! by one for page parity examination for
+% \mirror{}ed \bgpaint.  Then, the macro \!\pcol@buildcolseprule! is invoked
+% with $\!\@colht!=\!\textheight!$ and $\LBRP\Cfrom\Cto$ for \cseprule{}
+% drawing in \!\pcol@tempboxa! and \bgpaint{} for columns and \csepgap{}s in
+% \!\@tempboxa! put into $b$ immediately.
+% 
+% Then we open a \!\hbox! of \!\textwidth! wide and initialize
+% $f=\CSIndex{if@tempswa}$ to be \CSIndex{if@fcolmade}.  Then for each
+% $c\In\Cfrom\Cto$, being $c'$ or $\C-1-c'$ for the $c'$-th iteration
+% determined by \!\pcol@swapcolumn! according to the effectiveness of
+% \cswap{} and the parity of \!\c@page!, we put an inner \!\hbox! of
+% $\!\columnwidth!=\w_c$ wide preceded by \!\pcol@@hfil! being \!\relax! at
+% initial or $\!\pcol@hfil!\<c_g\>$ otherwise for a \csepgap{} and
+% \cseprule{}, where $c_g\in\{c,c{-}1\}$ without or with \cswap{}
+% respectively.  That is, at first we obtain $c$'s \cctext{} including
+% $\cc_c(\dl)$ by \!\pcol@getcurrcol!  and pass $\cc_c(\dl)$ to
+% \!\@makefcolumn! to produce a \fcolumn{} in \!\@outputbox!  to be put into
+% the inner \!\hbox!.  Then we do $f\gets f\lor(\cc_d(\dl)\neq\emptyset)$
+% with $\cc_d(\dl)$ shrunk by \!\@makefcolumn! to let $f$ have
+% $\exists{}c\In0\Cto:(\cc_c(\dl)\neq\emptyset)$ at the end of the loop for
+% $c$, and then save the \cctext{} into $\cc_c$ by \!\pcol@setcurrcolnf!
+% because we have no footnotes in $c$.
+% 
+% After the end of the loop, we move $f$ to \CSIndex{if@fcolmade} for
+% the termination check of the loop in \!\pcol@flushfloats!.
+% 

+%    \begin{macrocode}
+\def\pcol@flushfloats{%
+  \global\@colht\textheight
+  \@whilesw\if@fcolmade\fi{%
+    \global\@fcolmadefalse
+    \ifnum\pcol@ncolleft<\pcol@ncol
+      \pcol@iflushfloats\pcol@ncolleft\pcol@ncol\pcol@rightpage
+    \else
+      \setbox\pcol@rightpage\box\voidb@x
+    \fi
+    \pcol@iflushfloats\z@\pcol@ncolleft\@outputbox
+    \@outputpage}}
+\def\pcol@iflushfloats#1#2#3{\setbox#3\vbox{%
+  \ifpcol@paired\else\ifnum#1=\z@\else \advance\c@page\@ne \fi\fi
+  \pcol@buildcolseprule\@colht#1#2\@maxdepth \unvbox\@tempboxa
+  \hb@xt@\textwidth{%
+    \let\pcol@@hfil\relax
+    \if@fcolmade \@tempswatrue \else \@tempswafalse \fi
+    \@tempcntb#1\@whilenum\@tempcntb<#2\do{%
+      \pcol@swapcolumn\@tempcntb\pcol@currcol#1#2\relax
+      \pcol@getcurrcol
+      \@makefcolumn\@deferlist
+      \pcol@@hfil \hb@xt@\columnwidth{%
+        \if@fcolmade \box\@outputbox \else \vbox to\@colht{}\fi \hss}%
+      \ifx\@deferlist\@empty\else \@tempswatrue \fi
+      \edef\pcol@@hfil{\noexpand\pcol@hfil{\pcol@colsepid}}%
+      \pcol@setcurrcolnf
+     \advance\@tempcntb\@ne}%
+    \if@tempswa \global\@fcolmadetrue \else \global\@fcolmadefalse \fi}}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@freshpage}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}

+% \changes{v1.0}{2011/10/10}
+%	{Add save and restore of \cs{@currbox}.}

+% \changes{v1.0}{2011/10/10}
+%	{Remove unnecessary assignment of \cs{pcol@currcol}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add argument 0 for the invocations of \cs{pcol@startcolumn} to
+%	 inhibit inserting deferred page-wise footnotes.}

+% 

+% The macro \!\pcol@freshpage! is invoked from \!\pcol@output@flush! and
+% \!\pcol@output@clear! to start a new page after column flushing.  At
+% first, we let $p=\pbase=\ptop=0$ and $\PP=\emptyset$ because we know no
+% pages are kept.  Then we invoke \!\pcol@startpage! to start a new page
+% with a \!\def!inition of $\!\pcol@currpage!=|{}|$ to indicate the invoker
+% is this macro (i.e., not \!\pcol@opcol!).  Then after keeping \!\@colht!
+% in $h=\!\pcol@colht!$, we do the followings for each column $c\In0\C$.
+% 
+% First we obtain $c$'s \cctext{} in $\cc_c$ by \!\pcol@getcurrcol! but let
+% $p=0$ and $\!\@colroom!=h$, which can be modified by $c'<c$, without
+% referring to $\cc_c(\vb^p)$ nor $\cc_c(\vb^r)$ because they are obsolete.
+% We also save \!\@currbox! to \Midx{\!\pcol@currboxsave!} because it may be
+% modified by \!\pcol@opcol! if we make \fcolumn{}s afterward.  Then we invoke
+% \!\pcol@getcurrpage! to have the \pctext{} of $p=0$, because it might be
+% modified by a column $c'<c$ by producing \fcolumn{}s.  After that and the
+% invocation of \!\pcol@floatplacement! for setting float parametners, we
+% invoke \!\pcol@startcolumn! for $c$'s \colpage{} at $p=0$, and iterate
+% \!\pcol@opcol! and \!\pcol@startcolumn! while a \fcolumn{} is made by the
+% latter\footnote{

+% 

+% Each column can have deferred floats on the invocation from
+% \!\pcol@output@flush!.}.
+% 

+% Note that we give the argument 0 to each invocation of
+% \!\pcol@startcolumn! to keep it from inserting deferred \Scfnote{}s, which
+% will be taken care of by \!\pcol@restartcolumn! if any.  At last in the
+% loop, we restore \!\@currbox! from \!\pcol@currboxsave!, let
+% $\cc_c(\vb^b)$ be an empty \!\vbox! because the main vertical list is
+% empty, and save the \cctext{} into $\cc_c$ by \!\pcol@setcurrcolnf!
+% because of no footnotes obviously, after saving $p$ and \!\@colroom!,
+% which might be modified by the \fcolumn{} production, into $\cc_c(\vb^p)$
+% and $\cc_c(\vb^r)$.
+% 
+% After the loop above, finally we invoke \!\pcol@restartcolumn! to return
+% to the column in which \!\flushpage! or \!\clearpage! was issued.
+% 

+%    \begin{macrocode}
+\def\pcol@freshpage{%
+  \global\pcol@page\z@ \global\pcol@toppage\z@ \global\pcol@basepage\z@
+  \global\let\pcol@pages\@empty \global\let\pcol@currpage\@empty
+  \pcol@startpage \pcol@colht\@colht
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \pcol@getcurrcol \pcol@page\z@ \@colroom\pcol@colht
+    \let\pcol@currboxsave\@currbox
+    \pcol@getcurrpage
+    \pcol@floatplacement
+    \pcol@startcolumn\z@
+    \@whilesw\if@fcolmade\fi{\pcol@opcol \pcol@startcolumn\z@}%
+    \let\@currbox\pcol@currboxsave
+    \global\setbox\@currbox\vbox{}%
+    \global\count\@currbox\pcol@page \global\dimen\@currbox\@colroom
+    \pcol@setcurrcolnf
+   \advance\pcol@currcol\@ne}%
+  \pcol@restartcolumn}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \subsection{Last Page}
+% \label{sec:imp-sout-end}
+% 
+% \begin{macro}{\pcol@output@end}
+% \changes{v1.0}{2011/10/10}
+%	{Drastically changed to take special care of float columns in the
+%	 last page, to deal with the empty last page with and without
+%	 deferred floats, and to try to make post-environment float pages.}
 
+% \changes{v1.2-2}{2013/05/11}
+%	{Add incorporation of page-wise footnotes in the last ordinary
+%	 pages followed by float-pages.}
+% \changes{v1.2-7}{2013/05/11}
+%	{Add \cs{pcol@outputfalse} to solve the \cs{output} request sneaking.}
+% \changes{v1.2-7}{2013/05/11}
+%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping knowing
+%	 it is redundant.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add parallel-paging operations.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add background painting of page-wise footnotes and setting
+%	 of \cs{pcol@preposttop}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add opeartios to pass $\string\cal{M}$ to the next
+%	 \string\texttt{paracol} environment and \cs{@mparbottom} to post
+%	 environment typesetting.}

+% 

+% The macro \!\pcol@output@end! is invoked solely from
+% \!\pcol@specialoutput! to process the \!\output! request made by
+% \!\endparacol!.  We invoke \!\pcol@makeflushedpage! for the \lpage{}
+% production as the setting $\CSIndex{ifpcol@lastpage}=\true$ done by
+% \!\endparacol! indicates, giving it $h=\!\pcol@colht!$ in which
+% \!\pcol@sync! sets the height of the tallest \colpage{} to have the
+% ship-out image of the \tpage{} in \!\@outputbox!.
+% 
+% Next, we define $\mpbout=\!\pcol@mparbottom@out!$ as follows.  First, we
+% invoke \!\pcol@getmparbottom@last! giving it $y=\VPP-\!\ht!\!\@outputbox!$
+% being the negative counterpart of
+% the height of \spanning{} in the \lpage, to let $\mpbout$ have the occupancy
+% information of the bottom marginal note in each margin if any, or
+% $\mpar(y,y)$ otherwise.  Then we transform $y$-coordinates in $\mpbout$
+% from those for columns to those for text area by
+% $\!\pcol@bias@mpbout!\Arg{-y}$ to have the final result.  Then to pass
+% \!\@mparbottom! for post-environment typesetting,
+% 

+% \Index{post-environment stuff}
+% 

+% we invoke \!\pcol@do@mpbout! \!\def!ining \!\pcol@do@mpbout@whole! to do
+% nothing and \!\pcol@do@mpbout@elem! to let $\!\@mparbottom!=b$ where
+% $\mpb_L^x=(\mpar(t,b))$ and $x\in\{l,r\}$ according to the margin which
+% post-environment marginal notes go to.
+% 

+% \Index{post-environment stuff}
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Last Page
+
+\def\pcol@output@end{%
+  \pcol@Logstart\pcol@output@end
+  \pcol@makeflushedpage\pcol@colht
+  \@tempdima\pcol@colht \ifdim\pcol@colht<\z@ \@tempdima\z@ \fi
+  \advance\@tempdima-\ht\@outputbox
+  \pcol@getmparbottom@last\@tempdima
+  \pcol@bias@mpbout{-\@tempdima}
+  \def\pcol@do@mpbout@whole##1##2##3##4{\setbox\@tempboxa\hbox{##1##2##3##4}}%
+  \def\pcol@do@mpbout@elem\@elt##1##2{\global\@mparbottom##2sp}%
+  \pcol@do@mpbout
+%    \end{macrocode}
+% 
+% Next we process one of the following cases.
+% 
+% The first case is for $\CSIndex{ifpcol@dfloats}=\true$ to mean the
+% \lpage{} is followed by one or more pages having deferred \cwise{}
+% floats and thus \!\pcol@makeflushedpage! builds the ship-out image of the
+% \lpage{} in {\em full size} in \!\@outputbox! unless the page has nothing
+% perfectly.  Therefore, we ship the image out by \!\@outputbox! unless it
+% is $\bot$ for perfectly empty case.  Then we invoke \!\pcol@flushfloats!
+% to produce and ship out \fpage{}s, lettinng $\CSIndex{if@fcolmade}={\true}$
+% to tell the macro that at least we will have one \fpage{}.  Now we have
+% shipped out everyting in the closing environment and thus we let
+% $\CSIndex{ifpcol@output}=\false$ to tell \!\output! routine to work
+% ordinarily.  Then we let $\CSIndex{if@tempswa}=f_{\it sp}=\true$ to
+% remember we will start a new page and thus $\!\@pagedp!=\pd=\DP=1000$ to
+% mimic \TeX's \!\prevdepth! mechanism.  Finally we let
+% $\CSIndex{@mparbottom}=0$ and $\mpbout=\mpboutz$ because no marginal notes
+% are carried over to post-environment typesetting.
+% 

+% \Index{post-environment stuff}

+% 

+% \changes{v1.3-6}{2013/09/17}
+%	{Simplify the case with deferred floats thanks to
+%	 \cs{ifpcol@dfloats} and redesign of \cs{pcol@makeflushedpage}.}

+% 

+%    \begin{macrocode}
+  \@tempswafalse
+  \ifpcol@dfloats
+    \ifvoid\@outputbox\else \@outputpage \fi
+    \global\@fcolmadetrue \pcol@flushfloats
+    \global\pcol@outputfalse
+    \@tempswatrue \@pagedp\@m\p@ \global\@mparbottom\z@
+    \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
+%    \end{macrocode}
+% 
+% Before proceeding to the second and third cases, we let
+% $\CSIndex{ifpcol@output}=\false$ because we have nothing to ship out.
+% 
+% Then the second case is for $h=-\infty$ without deferred \cwise{}
+% floats to mean all columns in the \lpage{} are empty and the page does not
+% have non-merged \Scfnote{}s.  In this case, we examine if
+% $\Midx{\!\pcol@firstprevdepth!}=\!\relax!$ to mean we have had at least
+% one new page in \env{paracol} environment, i.e., \!\pcol@startpage! have
+% been invoked at least once.  If so, we let $f_{\it sp}=\true$, $\pd=1000$,
+% $\!\@mparbottom!=0$ and $\mpbout=\mpboutz$ again and put nothing to the
+% main vertical list so that the \postenv{} starts from the top of the page.
+% However, we have to take care of the case that $f_{\it ns}=\false$ and
+% thus \!\@outputbox!  has \spanning.  If so, we acquire an \!\insert! from
+% \!\@freelist! by \!\@next! to let it have the \spanning, i.e., the
+% contents of \!\@outputbox!\footnote{

+% 

+% It does not have \!\dbltextfloatsep! at its tail because the skip has been
+% removed by \!\pcol@makeflushedpage!.}.
+% 

+% Then the \!\insert! is added to the head of \!\@dbldeferlist! with the
+% float placement code 10 to force \LaTeX's float placement mechanism to put
+% it to the page to be started shortly.
+% 
+% On the other hand, $\!\pcol@firstprevdepth!\neq\!\relax!$ means that it
+% has $\!\prevdepth!=\pd'$ just before \beginparacol{} in decimal integer
+% representation.  Since we have not started any pages in the environment,
+% and all columns in the \lpage{} is empty, we have almost nothing in the
+% environment.  Note that the environment can have \pwise{} floats but they
+% have not yet put into any pages but are kept in \!\@dbldeferlist!, or
+% \Mgfnote{}s but they are merged to those in \postenv.  Therefore, the
+% \preenv{} and \postenv{} must be {\em connected} naturally and thus we put
+% the \preenv{} kept in \!\@outputbox! to the main vertical list by
+% \!\unvbox!, letting $\pd=\pd'$ and keeping $f_{\it sp}=\false$\footnote{

+% 

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

+% In this case, the setting of \!\@mparbottom! and $\mpbout$ done at the
+% beginning of this macro is correct because they describe the marginal
+% notes in \preenv{} including \env{paracol} enviroments preceeding it even
+% if any.
+% 

+% \changes{v1.3-3}{2013/09/17}
+%	{Add settings for background painting of post-environment stuff.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add letting $\cs{@mparbottom}\EQ0$ and
+%	 ${\string\cal{M}}\EQ{\string\cal{M}}_0$ for the simple empty page
+%	 case.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Remove \cs{unskip} from the operation to let page-wise floats be 
+%	 ordinary ones because \cs{pcol@makeflushedpage} does it.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \else
+    \global\pcol@outputfalse
+    \ifdim\pcol@colht=-\maxdimen
+      \ifx\pcol@firstprevdepth\relax
+        \@tempswatrue \@pagedp\@m\p@ \global\@mparbottom\z@
+        \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
+        \ifpcol@nospan\else
+          \pcol@Fb
+          \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}%
+            \pcol@ovf
+          \pcol@Fe{output@end(spanning)}%
+          \count\@currbox10\relax
+          {\let\@elt\relax \xdef\@dbldeferlist{\@elt\@currbox\@dbldeferlist}}%
+          \global\setbox\pcol@rightpage\box\voidb@x
+        \fi
+      \else \unvbox\@outputbox \@pagedp\pcol@firstprevdepth sp\relax
+      \fi
+%    \end{macrocode}
+% 
+% The last case without deferred floats and with some non-empty columns or
+% non-merged \Scfnote{}s is
+% most usual.  In this case, we may simply put \!\@outputbox! letting
+% $\!\topskip!=0$ because \!\topskip! has already been inserted in
+% \colpage{}s or \preenv{} in the box\footnote{

+% 

+% If the \lpage{} has non-merged \Scfnote{}s without any other items,
+% \cs{topskip} has not been inserted, but this inconsistency without
+% \cs{topskip} is acceptable.}.
+% 
+% However before putting the box back to the main vertical list, we have to
+% take care of the \bgpaint{} as follows.  First we let
+% $\CSIndex{ifpcol@havelastpage}=\true$ to let \!\@outputpage! paint the
+% \bground{} of the \postenv{} when the page having the \lpage{} completes.
+% Second, we let \!\pcol@bg@preposttop@left! have the height-plus-depth of
+% the \!\@outputbox! having the short \lpage{} because the \bground{} of
+% \postenv{}, or of \preenv{} if we have another \env{paracol} environment
+% in the same page, to be painted is just below the box.  We also
+% \!\pcol@bg@preposttop@right! have the same value but only if $\CL<\C$,
+% because otherwise we have to keep this macro unchanged so that the
+% non-existent right \parapag{}e of the closing environment can be the
+% \postenv{} of a preceding environment and/or the \preenv{} of a succeeding
+% one with \parapag{}ing.  Note that in the aforementioned {\em fresh page}
+% cases and the perfectly empty case, we may be unaware of these macros
+% because it should have been made 0 by the last invocation of
+% \!\@outputpage! in the fresh page case or the \preenv{} and \postenv{} are
+% contiguous in the empty case.
+% 
+% Third and finally, we have to paint the \bground{} of non-merged
+% \Scfnote{}s because the painting is left by \!\pcol@makeflushedpage! for
+% this macro.  Therefore, if $\!\pcol@fnheight@lpage!>0$ to mean we have
+% footnotes whose total height-plus-depth is in the macro, we paint their
+% \bground{} by \!\pcol@bg@paintbox! \!\def!ining \!\pcol@bg@footnoteheight!
+% with the size and temporarily re\!\def!ining \!\pcol@bg@textheight! to be
+% the height-plus-depth of \!\@outputbox!  because the foontnotes are at the
+% bottom of the box instead of the page.  Note that the order of painting is
+% right first and then left second if we have \parapag{}es because we refer
+% the height-plus-depth of \!\@outputbox! being put into the main vertical
+% list making the box $\bot$.  Also note that if the right \parapag{}e is
+% \npaired, we temporarily increment \!\c@page! in \!\pcol@rightpage! to let
+% \!\pcol@bg@paintbox! handle \bginfext{} to side margins correctly.
+% Another remark is that we don't modify $\pd=\!\@pagedp!$ and thus it keeps
+% $\DP$ in this case, and $f_{sp}$ is kept $\false$.
+% 

+% \changes{v1.3-3}{2013/09/17}
+%	{Add background painting of page-wise footnotes.}

+% 

+%    \begin{macrocode}
+    \else
+      \global\pcol@havelastpagetrue
+      \@tempdima\ht\@outputbox \advance\@tempdima\dp\@outputbox
+      \xdef\pcol@bg@preposttop@left{\number\@tempdima sp}%
+      \ifnum\pcol@ncolleft<\pcol@ncol
+        \global\let\pcol@bg@preposttop@right\pcol@bg@preposttop@left
+      \fi
+      \def\pcol@bg@textheight{\@elt{\ht\@outputbox}\@elt{\dp\@outputbox}}%
+      \def\reserved@a{%
+        \ifdim\pcol@fnheight@lpage>\z@
+          \def\pcol@bg@footnoteheight{\@elt\pcol@fnheight@lpage}%
+          \pcol@bg@paintbox{Nn}%
+        \fi}%
+      \ifnum\pcol@ncolleft<\pcol@ncol
+        \global\setbox\pcol@rightpage\vbox{%
+          \ifpcol@paired\else \advance\c@page\@ne \fi
+          \reserved@a \unvbox\pcol@rightpage}%
+      \fi
+      \topskip\z@ \vbox{\reserved@a \unvbox\@outputbox}%
+    \fi
+  \fi
+%    \end{macrocode}
+% 
+% Now we have put almost everything in the \lpage{} but we may still have
+% \Scfnote{}s in $\pp^f(\ptop)$ to be merged with those in \postenv.
+% Therefore, we \!\insert! them through \!\footins! as a part of \postenv,
+% and then do that for deferred footnotes in $\df=\!\pcol@topfnotes!$
+% without using \!\pcol@deferredfootins! because we don't need the height
+% capping.
+% 

+% \changes{v1.2-2}{2013/05/11}
+%	{Add insertion of page-wise footnotes to be merged.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% 

+%    \begin{macrocode}
+  \ifvoid\pcol@footins\else
+    \pcol@Log\pcol@output@end{insert}\pcol@footins
+    \pcol@Fb
+    \insert\footins{\unvbox\pcol@footins}\@cons\@freelist\pcol@footins
+    \pcol@Fe{output@end(pagefn)}%
+  \fi
+  \ifvoid\pcol@topfnotes\else \insert\footins{\unvbox\pcol@topfnotes}\fi
+%    \end{macrocode}
+% 
+% The following operationss are for clean-up and set-up for the \postenv;
+% for all c, return $\cc_c(\vb)$ obtained by \!\pcol@getcurrcol! and
+% $\Celt^c\neq\bot$ letting it $\bot$ to \!\@freelist!; reestablish the
+% \colorstack{} by \!\pcol@restorecolorstack! for column-0\footnote{

+% 

+% It can be any other column.}
+% 

+% so that the \colorstack{} is just $\cst$ and is rewinded at \Endparacol,
+% and let $\cst=\bot$; reload $\cc_d$ for $d=\!\pcol@lastcol!$ being the
+% column in which \Endparacol{} occurs to let $\!\everypar!=\cc_d(\ep)$ and
+% to let \CSIndex{if@nobreak} and \CSIndex{if@afterindent} have the value
+% represented by $\cc_d(\sw)$, so that the first paragraph of the \postenv{}
+% is typeset following them\footnote{

+% 

+% For rare cases that the last item of the closing environment is a
+% sectioning command, but a user has such very unusual usage.};
+% 

+% let $\!\pcol@prevdepth!=\pd$ so that it is set to \!\prevdepth! by
+% \!\pcol@invokeoutput!; let $\!\@colht!=\!\@colroom!=\!\textheight!$ to
+% mean the single-column page does not have any floats so far because those
+% produced in or before the environment have already been shipped out, are
+% put to the main vertical list packed in \!\@outputbox!, or are in
+% \!\@dbldeferlist!.
+% 
+% As for deferred \pwise{} floats produced in the environment, including
+% those once put in the \lpage{} but returned to the list by the operation
+% described above, we move them to \!\@deferlist! because they are now
+% \cwise{} floats.  Then we invoke \!\pcol@floatplacement! to
+% reinitialize float placement parameters.  Finally, if $f_{\it sp}=\true$,
+% we invoke \!\@startcolumn! and then repeat invocations of \!\@opcol! and
+% \!\@startcolumn! while \fpage{}s are produced, after letting
+% $\CSIndex{ifpcol@lastpage}=\false$ to make \!\@combinefloats! work as
+% \LaTeX's original\footnote{

+% 

+% Letting $\!\pcol@textfloatsep!=\infty$ is done by \!\pcol@floatplacement!.}.
+% 

+% \changes{v1.2-1}{2013/05/11}
+% 	{Add color resetting.}

+% \changes{v1.31}{2013/10/10}
+%	{Add \cs{pcol@getcurrcol} for the column specified by
+%	 \cs{pcol@lastcol} to pass \cs{if@nobreak}, \cs{if@afterindent} and
+%	 \cs{everypar} of the column to post-environment stuff.}

+% \changes{v1.32-2}{2015/10/10}
+% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}

+% \changes{v1.34}{2018/05/07}
+%	{Remove nullification of $\gamma_0^0$ because it is not meaningless
+%	 now, add release of $\gamma_0^c\NEQ\bot$ and then nullification of
+%	 it for all $c$, move color stack reestablishment down to the loop
+%	 with $c$ to ensure $\gamma_0^0\EQ\bot$, and add nullification of
+%	 $\mathit{\Gamma}$.}

+% 

+%    \begin{macrocode}
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \pcol@Fb
+    \pcol@getcurrcol \@cons\@freelist\@currbox
+    \ifvoid\pcol@ccuse{@box}\else
+      \@cons\@freelist{\pcol@ccuse{@box}}%
+      \pcol@ccxdef{\voidb@x}%
+    \fi
+    \pcol@Fe{output@end(col)}%
+   \advance\pcol@currcol\@ne}%
+  \pcol@currcol\z@ \pcol@restorecolorstack
+  \global\setbox\pcol@colorins\box\voidb@x
+  \pcol@currcol\pcol@lastcol\relax \pcol@getcurrcol
+  \global\pcol@prevdepth\@pagedp
+  \global\@colht\textheight
+  \global\@colroom\textheight
+  \global\let\@deferlist\@dbldeferlist \gdef\@dbldeferlist{}%
+  \pcol@floatplacement
+  \pcol@lastpagefalse
+  \if@tempswa
+    \@startcolumn \@whilesw\if@fcolmade\fi{\@opcol\@startcolumn}%
+  \fi
+  \pcol@Logend\pcol@output@end
+}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Starting Environment}
+% \label{sec:imp-startenv}
+% 
+% \begin{macro}{\pcol@invokeoutput}
+% \changes{v1.0}{2011/10/10}
+%	{Let \cs{pcol@prevdepth} have \cs{prevdepth} directly instead of via
+%	 \cs{tempdima}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add logging.}

+% \changes{v1.2-5}{2013/05/11}
+%	{Move the setting of \cs{linewidth} and \cs{hsize} from
+%	 \cs{pcol@getcurrcol} to this macro and add \cs{parshape}.}

+% \changes{v1.21}{2013/06/06}
+%	{Add zero-clearing of \cs{deadcycles}.}
+% 

+% Before giving the definition of \env{paracol} environment and commands
+% used in it, we define the macro $\!\pcol@invokeoutput!\arg{pen}$ invoked
+% from them to make an \!\output!-request with \!\penalty! of
+% $\arg{pen}=|\pcol@op@|{\cdot}f$.  The macro's structure is similar to that
+% for the request sequence in \!\end@float! as follows; insert a \!\penalty!
+% of $-10004$ to save the main vertical list in \!\@holdpg!; save
+% \!\prevdepth!; insert a \!\vbox! to make it sure the following \!\penalty!
+% of $\arg{pen}$ is kept even when we are at the top of a page; and finally
+% restore \!\prevdepth!.
+% 
+% A difference is that we zero-clear \!\deadcycles! because it can be reach
+% $\!\maxdeadcycles!=100$ easily if a page has many \sync{}ations and many
+% columns.  Another and more important difference is in the save\slash
+% restore of \!\prevdepth!.  First, the value of the register is saved in
+% our own \!\pcol@prevdepth! instead of \!\@tempdima! by a \!\global!
+% assignment so that \!\output!-routine refers to it\footnote{

+% 

+% The assignment is not necessary to be done \!\global!ly but we dare to do
+% it to make all assignments to \!\pcol@prevdepth! being \!\global!
+% consistently.}.
+% 

+% Second, the value restored to \!\prevdepth! may be different from that we
+% just have saved because \!\output!-routine may update \!\pcol@prevdepth!
+% to have, for example, the value saved in $\cc_c(\pd)$ when we left from
+% $c$ which we are now restarting.
+% 
+% In addition to above, after the invocatoin of \!\output!-routine, we let
+% $\!\linewidth!=\w_c-\lrm$ so that the register is shrunk from $\w_c$ by the
+% total width of left and right margins of the \env{list}-like environment
+% surrounding \env{paracol} if $\lrm=\!\pcol@lrmargin!>0$ to mean that.
+% Then if so, we set \!\parshape! to let every line of paragraphs in the
+% column $c$ is indented by \!\@totalleftmargin! and has width of
+% \!\linewidth!, as \LaTeX's \!\list!  does.  We also let $\!\hsize!=\w_c$
+% because it should have the width of the column even in a \env{list}-like
+% environment.
+% 
+% The macro is invoked from \!\pcol@zparacol! ($f=|start|$),
+% \!\pcol@switchcol! for \!\switch~column! and \csenv{}s ($f=|switch|$),
+% \!\pcol@visitallcols! for \cscan{} prior to \sync{}ed \cswitch{} and page
+% flushing ($f=|switch|$), \!\pcol@flushclear! for \pfcheck{}
+% ($f=|switch|$), \!\pcol@com@flushpage!  for \!\flushpage! ($f=|flush|$),
+% \!\pcol@com@clearpage! for \!\clearpage!  ($f=|clear|$), and
+% \!\endparacol!  ($f=|end|$).
+% \SpecialIndex{\pcol@op@start}

+% \SpecialIndex{\pcol@op@switch}

+% \SpecialIndex{\pcol@op@flush}

+% \SpecialIndex{\pcol@op@clear}

+% \SpecialIndex{\pcol@op@end}

+% 

+%    \begin{macrocode}
+%% Starting Environment
+
+\def\pcol@invokeoutput#1{\deadcycles\z@
+  \pcol@Logstart{\pcol@invokeoutput
+    {#1:\the\pcol@currcol/\the\pcol@nextcol%
+     \ifnum#1=-10011:\ifpcol@sync s\fi \ifpcol@clear c\fi\fi}}%
+  \penalty-\@Miv \global\pcol@prevdepth\prevdepth \vbox{}%
+  \penalty#1\relax \prevdepth\pcol@prevdepth
+  \linewidth\columnwidth \advance\linewidth-\pcol@lrmargin
+  \ifdim\pcol@lrmargin>\z@ \parshape\@ne\@totalleftmargin\linewidth \fi
+  \hsize\columnwidth
+  \pcol@Logend{\pcol@invokeoutput{#1}}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\paracol}
+% \changes{v1.0}{2011/10/10}
+%	{Change the order of operations for sake of clarity.}

+% \changes{v1.0}{2011/10/10}
+%	{Add the mechanism of inter-environment local counter conservation.}

+% \changes{v1.0}{2011/10/10}
+%	{Let $\cs{col@number}\EQ1$ instead of $C$ to keep \cs{maketitle} from
+%	 producing title with \cs{twocolumn}.}

+% \changes{v1.0}{2011/10/10}
+%	{Add initialization of \cs{pcol@textfloatsep}, \cs{ifpcol@lastpage},
+%	 \cs{pcol@firstprevdepth} and \cs{@combinefloats}.}

+% \changes{v1.0}{2011/10/10}
+%	{Make API commands environment-local and inhibit nesting of
+%	 \texttt{paracol}.}
 
+% \changes{v1.3-2}{2013/09/17}
+%	{Modify to add the optinal argument $C_L$ and optional
+%	 `\string\texttt{*}' for parallel-paging.}

+% \begin{macro}{\pcol@xparacol}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to let $C_L\EQ C$ if the optional argument $C_L$ is not
+%	 given to \cs{paracol}.}

+% \begin{macro}{\pcol@yparacol}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to process the optional `\string\texttt{*}' given with
+%	 the optioal argument $C_L$ of \cs{paracol}.}

+% \begin{macro}{\pcol@zparacol}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to add the optinal argument $C_L$ and optional
+%	 `\string\texttt{*}' to \cs{paracol} for parallel-paging and to do
+%	 what had done by \cs{paracol}.}

+% 

+% The API macro $\!\paracol!|[|\CL|][*]|\Arg{\C}$\oarg{text} is invoked by
+% \beginparacol{} to start a \Midx{\env{paracol}} environment.  The macro
+% sipmly examines the existence of the optional argument $\CL$, whose
+% default value $\C$ is given by \!\pcol@xparacol!, to decide the
+% number of columns in left \parapag{}es.  Then if the optional argument is
+% given, \!\pcol@yparacol! examines the existence of `|*|' following it for
+% \npaired{} \parapag{}ing to let $\CSIndex{ifpcol@paired}=\false$, while
+% \!\paracol! gave the default $\true$ for \paired{} one to the switch.
+% Then the all other operations to start the environment is doen by
+% \!\pcol@zparacol!.
+% 

+%    \begin{macrocode}
+\def\paracol{\global\pcol@pairedtrue \@ifnextchar[%]
+  \pcol@yparacol\pcol@xparacol}
+\def\pcol@xparacol#1{\pcol@zparacol[#1]{#1}}
+\def\pcol@yparacol[#1]{%
+  \@ifstar{\global\pcol@pairedfalse \pcol@zparacol[#1]}%
+          {\pcol@zparacol[#1]}}
+%    \end{macrocode}
+% 
+% In \!\pcol@zparacol!, after making it sure to be in vertical mode by
+% \CSIndex{par}, at first we examine if we are neither in a box by
+% \CSIndex{ifinner} nor with ordinary two-column typesetting by
+% \CSIndex{if@twocolumn}, and complain about inappropriateness unless our
+% expectation is satisfied.  Then we let $\CL$ and $\C$ have the value given
+% through the corresponding arguments, unless $\CL>\C$ to let us make
+% $\CL=\C$ silently.  Next we examine $\CL<\C$, and if not we let
+% $\CSIndex{ifpcol@paired}=\true$ regardless the setting in
+% \!\pcol@yparacol! because \npaired{} typesetting is meaningless without
+% \parapag{}ing.  On the other hand, if \npaired{} typesetting is specified,
+% we let $\CSIndex{ifpcol@swapcolumn}={\false}$ but {\em not} \!\global!ly
+% because \cswap{} is meaningless in \npaired{} mode in the environment now
+% starting.
+% 
+% Second, we perform the operations done by \!\item! if
+% $\CSIndex{if@newlist}=\true$ and $\CSIndex{if@inlabel}\~=\false$ to mean
+% the first one in a \env{list}-like environment will appear at the very
+% first line of the leftmost column.  That is, we invoke \!\@nbitem! if
+% $\CSIndex{if@nobreak}=\true$, or add a penalty \!\@beginparpenalty! and a
+% vertical skip $\!\@topsep!-\!\parskip!-\!\itemsep!$ so that the first
+% \!\item! is \!\@topsep! apart from the last line above the environment,
+% and then let $\CSIndex{if@newlist}=\false$.  The reason why we do these
+% operations here is that, if the \env{paracol} environment is enclosed in a
+% \env{list}-like environment without anything between two \!\begin! for
+% environments, we have to align all first \!\item!s in all columns.  That
+% is, if we did not do that, the {\em literally first} \!\item! would do
+% that resulting in the column having the \!\item! led by the vertical skip
+% of \!\@topsep! while others should have ordinary inter-\!\item! skips.
+% Therefore, we perform the operations on behalf of all first \!\item!s in
+% all columns to have the skip of \!\@topsep! {\em above} the \env{paracol}
+% environment we are opening.  Note that if \beginparacol{} immediately
+% follows a \!\begin! for a \env{trivlist}-like environment,
+% $\CSIndex{if@inlabel}=\true$ because the first \!\item! was given in the
+% opening macro and thus the operations shown above has already been
+% performed.
+% 

+% \changes{v1.3-6}{2013/09/17}
+%	{Add operations for the vertical skips at the beginning of a
+%	 \texttt{list}-like environment.}

+% \changes{v1.35-6}{2018/12/31}
+% 	{Add error check with \cs{ifinner} and \cs{if@twocolumn}.}

+% \changes{v1.35-2}{2018/12/31}
+% 	{Add $\lnot$\cs{if@inlabel} to the condition to perform operations
+%	 for first \cs{item}.}

+% 

+%    \begin{macrocode}
+\def\pcol@zparacol[#1]#2{\par
+  \ifinner \@parmoderr \fi
+  \if@twocolumn \PackageError{paracol}{%
+    Environment paracol cannot work with ordinary two-column
+    typesetting.}\@ehb\fi
+  \global\pcol@ncolleft#1\relax \global\pcol@ncol#2\relax
+  \ifnum\pcol@ncolleft>\pcol@ncol \global\pcol@ncolleft\pcol@ncol \fi
+  \ifnum\pcol@ncolleft<\pcol@ncol\else \global\pcol@pairedtrue \fi
+  \ifpcol@paired\else \pcol@swapcolumnfalse \fi
+  \if@newlist \if@inlabel\else
+    \if@nobreak \@nbitem
+    \else
+      \addpenalty\@beginparpenalty
+      \addvspace\@topsep
+      \addvspace{-\parskip}\addvspace{-\itemsep}%
+    \fi
+    \global\@newlistfalse
+  \fi\fi
+%    \end{macrocode}
+% 
+% The third operation group is to set up lists for counters as follows.
+% First we obtain $\CC=\!\cl@@ckpt!$ to have all counters defined by
+% \!\newcounter! and \counter{page}.  Then we scan $\CG=\!\pcol@gcounters!$
+% applying \!\pcol@remctrelt! to each element to have
+% $\CTL=\!\pcol@counters!$ for all \lcounter{}s by removing all $\cg\in\CG$
+% from $\CC$, and to move $\clist(\cg)=|\cl@|{\cdot}\cg$ to
+% $|\pcol@cl@|{\cdot}\cg$ redefining
+% $|\cl@|{\cdot}\cg=\!\pcol@stepcounter!\Arg{\cg}$
+% 

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

+% 

+% to clear descendant \lcounter{}s of $\cg$, i.e., those in $\clist(\cg)$.
+% 
+% Next we scan $\CTL$ applying \!\pcol@thectrelt! to each element $\cl\in\CTL$
+% to let $|\pcol@thectr@|{\cdot}\~\cl=|\the|{\cdot}\cl$
+% 

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

+% \SpecialArrayIndex{\theta}{\the}

+% 

+% so that the former has the {\em default} \lrep{} of $\cl$.  The macro
+% \!\pcol@thectrelt! also lets
+% $|\the|{\cdot}\cl=|\pcol@thectr@|{\cdot}\cl{\cdot}0$
+% 

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

+% \SpecialArrayIndex{\theta}{\the}

+% 

+% if the \lrep{} for $\cl$ and $c=0$ has been defined by
+% \!\definethecounter!.  This is necessary because in the first visit to the
+% leftmost column 0 we will neither invoke \!\pcol@switchcol! nor thus scan
+% $\CTL$ with \!\pcol@setctrelt! which defines \lrep{}s, unless a \mctext{}
+% is specified with \beginparacol.
+% 
+% Next we give the initial value of $\val_c(\cl)$ for each column $c$ and
+% \lcounter{} $\cl\in\CTL$ by the followings enclosed in a group.  First we
+% scan $\Cc_0$ applying \!\pcol@loadctrelt! to each
+% $\cl\in\Cc'_0=\Set{\theta}{\<\theta,\val_0(\theta)\>\in\Cc_0}$ to have
+% the value $\val_0(\cl)$ in $|\pcol@ctr@|{\cdot}\cl$
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 

+% temporarily.  Next we scan $\CTL$ to pick \lcounter{}s $\theta$ such that
+% $\Uidx\Val(\theta)\neq\val_0(\theta)$ where $\Val(\theta)$ is the value of
+% $\theta$ outside \env{paracol} environment, or $\theta\notin\Cc'_0$, to
+% let them be listed in \!\@gtempa!.  That is, we pick \lcounter{}s which
+% have been updated or defined after the closing of the previous
+% \env{paracol}, or everything in $\CTL$ at the first \beginparacol{} because
+% $\Cc_0=\emptyset$\footnote{

+% 

+% Undefined in fact.}.
+% 

+% Finally, we invoke \!\pcol@synccounter! giving it \!\@gtempa! as its
+% argument to let $\val_c(\theta)=\Val(\theta)$ for all $c$ and for each
+% $\theta$ in \!\@gtempa!.  That is, when \env{paracol} environment appears
+% two or more times, the value of a \lcounter{} at the beginning of the
+% second or succeeding environment is kept unchanged from that at the end of
+% the previous environment, unless it has been updated between them.  Note
+% that these scans above are enclosed in a group in order to make
+% $|\pcol@ctr@|{\cdot}\cl$
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 

+% local and thus collected as a garbage at \!\endgroup!.
+% 

+%    \begin{macrocode}
+  \global\let\pcol@counters\cl@@ckpt
+  \let\@elt\pcol@remctrelt \pcol@gcounters
+  \let\@elt\pcol@thectrelt \pcol@counters
+  \begingroup
+    \let\@elt\pcol@loadctrelt \csname pcol@counters0\endcsname
+    \let\@elt\pcol@cmpctrelt \global\let\@gtempa\@empty \pcol@counters
+    \pcol@synccounter\@gtempa
+  \endgroup
+%    \end{macrocode}
+% 

+% Fourth, we set up a few \LaTeX's typesetting parameters which should have
+% appropriate values in the environment.  We let
+% $\CSIndex{if@twocolumn}=\true$ so that \textit{float}|*| environments work
+% for \pwise{} floats and LaTeX's \!\@addmarginpar! determine the margin
+% for marginal notes by \CSIndex{if@firstcolumn} whose truth value is
+% determined by our own \!\@addmarginpar!.  We also let $\!\col@number!=1$
+% instead of $\C$ so that its (almost surely) sole user \!\maketitle! will
+% not produce the title with \!\twocolumn! which cannot be in the
+% environment.
+% 
+% Then we invoke $\!\pcol@setcolumnwidth!\<\Cfrom\>\<\Cto\>\<r\>\<s\>$ once
+% or twice with
+% $(\Cfrom,\Cto,r,s)=(0,\CL,\!\pcol@columnratioleft!,\!\pcol@colwidthspecleft!)$
+% always for left \parapag{}e, and with
+% $(\CL,\C,\!\pcol@columnratioright!,\!\pcol@colwidthspecright!)$ for right
+% one if $\CL<\C$ to define column widths $\w_c=|\pcol@columnwidth|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}
+% 

+% and that of \csepgap{}s $\gap_c=|\pcol@columnsep|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}
+% 

+% for all $c\In0\C=\LBRP0\CL\cup\LBRP\CL\C$.
+% 
+% Then we initialize other variables as follows;
+% $\lrm=\!\pcol@lrmargin!=\!\textwidth!-\!\linewidth!$ so that, if $\lrm>0$,
+% \!\linewidth! for $c$ has $\w_c-\lrm$ reflecting the paragraph shape of the
+% \env{list}-like environment surrounding \env{paracol} environment;
+% $\!\pcol@topskip!=\!\topskip!$ for the second and succeeding pages;
+% $\!\pcol@textfloatsep!=\infty$ to mean we don't have any \sync{}ation
+% points so far; $\CSIndex{ifpcol@lastpage}=\false$ because the \spage{} is
+% not the last so far; and $\!\pcol@firstprevdepth!=\!\prevdepth!$ in
+% decimal integer form for the extreme empty case.
+% 
+% We also make the macro \!\@combinefloats! \!\let!-equal to our own
+% \!\pcol@combinefloats!  throughout the environment, after saving its
+% original definition into \Midx{\!\pcol@@combinefloats!} for processing
+% \!\output! request sneaked from outsied of environment, so that our
+% customization is in effect for any invocations including those from
+% \LaTeX's own macros.  Similarly, \!\@addmarginpar! is made \!\let!-equal
+% to our own \!\pcol@addmarginpar!  while its orginal definition is saved
+% into \!\pcol@@addmarginpar! but in this case we need the original for the
+% implementaion of our own.  On the other hand, \!\end@dblfloat! is simply
+% replaced with our own \!\pcol@end@dblfloat! being what \LaTeX{} had had until
+% 2014 as discussed in item-(\ref{item:ovv-float-end@dblfloat}) of
+% \secref{sec:imp-ovv-float}.
+% 

+% \changes{v1.1}{2012/05/11}
+% 	{Replace the calculation of \cs{columnwidth} with the call of
+%	 \cs{pcol@setcolumnwidth} and the assignment of $w_0$ to it.}

+% \changes{v1.2-4}{2013/05/11}
+%	{Modify the setting of \cs{if@firstcolumn} according to
+%	 column-swapping.}

+% \changes{v1.2-5}{2013/05/11}
+%	{Remove the setting \cs{columnwidth}, \cs{hsize} and \cs{linewidth}
+%	 because they are properly set in and after \cs{pcol@output@start}.}

+% \changes{v1.2-5}{2013/05/11}
+%	{Add the setting of \cs{pcol@lrmargin}.}

+% \changes{v1.2-7}{2013/05/11}
+%	{Add the saving of \cs{@combinefloats}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Revise the mechanism to define the width of columns and
+%	 column-separating gaps, and add local overriding definition of
+%	 \cs{@addmarginpar}.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add operations to define the width of columns and column-separating
+%	 gaps in right parallel-pages.}

+% \changes{v1.32-3}{2015/10/10}
+% 	{Add replacement of \cs{end@dblfloat} with \cs{pcol@end@dblfloat}.}
+% 

+%    \begin{macrocode}
+  \global\@twocolumntrue \col@number\@ne
+  \pcol@setcolumnwidth\z@\pcol@ncolleft
+    \pcol@columnratioleft\pcol@colwidthspecleft
+  \ifnum\pcol@ncolleft<\pcol@ncol
+    \pcol@setcolumnwidth\pcol@ncolleft\pcol@ncol
+      \pcol@columnratioright\pcol@colwidthspecright
+  \fi
+  \pcol@lrmargin\textwidth \advance\pcol@lrmargin-\linewidth
+  \global\pcol@topskip\topskip
+  \global\pcol@textfloatsep\maxdimen
+  \pcol@lastpagefalse \xdef\pcol@firstprevdepth{\number\prevdepth}%
+  \let\pcol@@combinefloats\@combinefloats \let\@combinefloats\pcol@combinefloats
+  \let\pcol@@addmarginpar\@addmarginpar \let\@addmarginpar\pcol@addmarginpar
+  \let\end@dblfloat\pcol@end@dblfloat
+%    \end{macrocode}
+%
+% Fifth, we save the original definition of \!\set@color! into
+% \!\pcol@set@color!, and then examine if $\!\set@color!\neq\!\relax!$
+% meaning some coloring package is loaded.  If any coloring packages are not
+% loaded, we make macros for \bgpaint{}, namely \!\pcol@bg@paintpage!,
+% \!\pcol@bg@paintcolumns! and \!\pcol@bg@paintbox!, \!\let!-equal to
+% \!\relax! for the first two and to \!\@gobble! for the last so that they do
+% nothing without coloring package.
+% 
+% If the coloring is enabled, on the other hand, we redefine \LaTeX's
+% \!\set@color!  so that it works as \!\pcol@set@color@push!  with
+% \colorstack.  We also prepare the text colring mechanism to let
+% $\CSIndex{ifpcol@inner}=\true$ in every \!\vbox! in the \env{paracol}
+% environment as follows.  First, we let $\CSIndex{ifpcol@inner}=\false$
+% because we are not in any \!\vbox!es obviously.  Then, to use
+% \!\everyvbox! for our own pupose, we do the followings; (1) \!\global!ly
+% assign a token \Midx{\!\pcol@dummytoken!}, which should never occurs, to
+% \!\pcol@everyvbox!; (2) save \!\everyvbox!  into \!\pcol@everyvbox!
+% locally; (3) let \!\everyvbox! have a \!\the!-reference to
+% \!\pcol@everyvbox! and |\pcol@innerture| to let
+% $\CSIndex{ifpcol@inner}={\true}$; and then (4) make \!\everyvbox!
+% \!\let!-equal to \!\pcol@everyvbox!.  By the last operation (4), any
+% \!\everyvbox! appearing in the \env{paracol} environment is replaced with
+% \!\pcol@everyvbox! to keep the real \!\everyvbox! from modified nullifying
+% our own operation |\pcol@innertrue|.  On the other hand, since both
+% \!\everyvbox!  and \!\pcol@everyvbox! are registers to hold tokens and
+% thus any operations applicable to \!\everyvbox! are also applicable to
+% \!\pcol@everyvbox!, any updates on \!\everyvbox! and explicit references
+% to it are simulated by \!\pcol@everyvbox!.  Then the initial tokens given
+% to \!\pcol@everyvbox!  by the saving operation (2) or tokens given inside
+% the environment are correctly processed whenever a \!\vbox! is opened,
+% toghether with |\pcol@innertrue| to fulfill our own purpose, because the
+% real \!\everyvbox! is let have a \!\the!-reference to \!\pcol@everyvbox!
+% by (3).  We also reserve the invocation of \!\pcol@restoreeveryvbox! by
+% \!\aftergroup! so that the macro is invoked just after \Endparacol{} to
+% examine if any \!\global! assignments to \!\everyvbox! has been made in
+% the environment.  The funny \!\global!  assignment (1) is done for this
+% examination so that we detect global assignments done in the environment
+% having been closed because they should have changed the global value of
+% \!\pcol@everyvbox! to something different from \!\pcol@dummytoken!.
+% 
+% Then we continue the case having some coloring package to make \bgpaint{}
+% macros \!\pcol@bg@paintpage!, \!\pcol@bg@paintbox! and
+% \!\pcol@bg@paintcolumns! activated by making them \!\let!-equal to thier
+% |@@| counterparts namely \!\pcol@bg@@paintpage!, \!\pcol@bg@@paintbox! and
+% \!\pcol@bg@@paintcolumns! which implement \bgpaint{}.
+% 
+% Finally we empty the shadow \colorstack{}
+% $\cstshadow={}$\!\pcol@colorstack@shadow!  to give it initial value
+% regardless of the availability of coloring package.
+% 

+% \changes{v1.2-1}{2013/05/11}
+% 	{Add redefinitions of \cs{set@color} and \cs{reset@color}.}

+% \changes{v1.22}{2013/06/30}
+% 	{Add a trick with \cs{everyvbox} to turn on \cs{ifpcol@inner} in
+%	 every \cs{vbox}.}

+% \changes{v1.22}{2013/06/30}
+% 	{Move initial emptying of $\string\mathit{\Gamma}$ from
+%	 \cs{pcol@output@start} to \cs{pcol@zparacol}.}

+% \changes{v1.22}{2013/06/30}
+% 	{Add initial emptying of $\string\hat{\mathit{\Gamma}}$ and $\chi$.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add definition of painting macros dependent to the availability of
+%	 a coloring package.}

+% \changes{v1.34}{2018/05/07}
+%	{Remove the initializations of \cs{pcol@colorstack} and
+%	 \cs{pcol@colorstack@buf} because they no longer exist.}
+% 

+%    \begin{macrocode}
+  \global\let\pcol@set@color\set@color
+  \ifx\set@color\relax
+    \let\pcol@bg@paintpage\relax \let\pcol@bg@paintbox\@gobble
+    \let\pcol@bg@paintcolumns\relax
+  \else
+    \let\set@color\pcol@set@color@push
+    \pcol@innerfalse
+    \global\pcol@everyvbox{\pcol@dummytoken}%
+    \pcol@everyvbox\everyvbox
+    \everyvbox{\the\pcol@everyvbox \pcol@innertrue}
+    \let\everyvbox\pcol@everyvbox
+    \aftergroup\pcol@restoreeveryvbox
+    \let\pcol@bg@paintpage\pcol@bg@@paintpage
+    \let\pcol@bg@paintbox\pcol@bg@@paintbox
+    \let\pcol@bg@paintcolumns\pcol@bg@@paintcolumns
+  \fi
+  \gdef\pcol@colorstack@shadow{}%
+%    \end{macrocode}
+% 

+% \changes{v1.2-2}{2013/05/11}
+% 	{Add initialization of \cs{pcol@footnotebase} and
+%	 \cs{pcol@nfootnotes}, and redefinitions of \cs{footnote},
+%	 \cs{footnotemark}, \cs{footnotetext} and \cs{@footnotetext}.}

+% 
+% The sixth settings are for (mainly \mcfnote) footnotes.  We initialize two
+% footnote-related count registers letting $\bf=\!\pcol@footnotebase!$ have
+% \!\c@footnote! and zero-clearing $\nf=\!\pcol@nfootnotes!$.  Then we
+% redefine \LaTeX's API macros \!\footnote!, \!\footnotemark! and
+% \!\footnotetext! to let them be our own \!\pcol@footnote!,
+% \!\pcol@footnotemark! and \!\pcol@footnotetext! so that they have
+% starred-versions.  The other API macro to be redefined, if \Scfnote{}
+% typesetting is in effect, is \!\footnoterule!  which lets
+% $\!\columnwidth!=\!\textwidth!$ before invoking its original version saved
+% in \!\pcol@footnoterule! so that it acts as in single-columned typesetting
+% rateher than multi-columned.  Then we redefine \LaTeX's internal macro
+% \!\@footnotetext! letting it be our own \!\pcol@fntext! for encapsulating
+% a footnote in a \!\vbox! and for deferred \!\insert!ion with \Scfnote{}
+% typesetting.
+% 

+%    \begin{macrocode}
+  \pcol@footnotebase\c@footnote \global\pcol@nfootnotes\z@
+  \let\footnote\pcol@footnote
+  \let\footnotemark\pcol@footnotemark
+  \let\footnotetext\pcol@footnotetext
+  \ifpcol@scfnote
+    \def\footnoterule{{\columnwidth\textwidth \pcol@footnoterule}}%
+  \fi
+  \let\@footnotetext\pcol@fntext
+%    \end{macrocode}
+% 
+% Seventh, we let \!\marginpar!, \!\@mn@@marginnote! and \!\@xympar! be our
+% own versions \!\pcol@marginpar!, \!\pcol@marginnote! and \!\pcol@xympar!
+% respectively for the emulation of \!\marginnote!, saving the original
+% version of the first and third into \!\pcol@@marginpar! and
+% \!\pcol@@xympar!.  Then we inactivate API macros \!\twosided! and
+% \!\footnotelayout!  together with their backward-compatible macros
+% \!\swapcolumninevenpages!, \!\noswapcolumnineven~pages!,
+% \!\multi~columnfootnotes!, \!\singlecolumnfootnotes! and
+% \!\mergedfootnotes!, so that they commonly invoke \!\pcol@ignore! because
+% their inherent operations turning corresponding switches are harmful in
+% \env{paracol} environment.  Note that the inactivation of \!\twosided! is
+% done by redefinition of \!\pcol@twosided! because we need optional
+% argument processing by \!\twosided! even when it is inactivated.
+% 

+% \changes{v1.2-4}{2013/05/11}
+%	{Add nullificaion of \cs{[no]swapcolumninevenpages}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add nullificaton of API macros of footnote typesetting definition.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add new API inactivation for \cs{pcol@twosided}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add new API inactivation for \cs{pcol@twosided}.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Add new API inactivation for \cs{footnotelayout}.}

+% \changes{v1.35-3}{2018/12/31}
+% 	{Add local modifications of \cs{marginpar}, \cs{@mn@@marginnote} and
+%	 \cs{@xympar} for the emulation of \cs{marginnote}.}

+% 

+%    \begin{macrocode}
+  \let\pcol@@marginpar\marginpar \let\marginpar\pcol@marginpar
+  \let\@mn@@marginnote\pcol@marginnote
+  \let\pcol@@xympar\@xympar \let\@xympar\pcol@xympar
+  \def\pcol@twosided[#1]{\pcol@ignore\twosided}%
+  \def\swapcolumninevenpages{\pcol@ignore\swapcolumninevenpages}%
+  \def\noswapcolumninevenpages{\pcol@ignore\noswapcolumninevenpages}%
+  \def\footnotelayout#1{\pcol@ignore\footnotelayout}%
+  \def\multicolumnfootnotes{\pcol@ignore\multicolumnfootnotes}%
+  \def\singlecolumnfootnotes{\pcol@ignore\singlecolumnfootnotes}%
+  \def\mergedfootnotes{\pcol@ignore\mergedfootnotes}%
+%    \end{macrocode}
+% 
+% Eigth, we scan the list \!\pcol@localcommands! of $\arg{com}$ being the
+% name of commands, e.g., |switchcolumn|, available only in the environment
+% or customized for the environment, applying \!\pcol@defcomelt! to each
+% $\arg{com}$ to let $|\|\arg{com}=|\pcol@com@|{\cdot}\arg{com}$
+% 

+% \SpecialArrayMainIndex{\<\string\mathit{com}\>}{\pcol@com@}

+% 

+% the latter of which is the real implementation of the former.  Note that
+% the list does not have all \elocal{} API commands but we omit
+% \!\column!(|*|) for \env{column}(|*|) environments because their
+% implementations \!\pcol@com@column!(|*|) are modified after the first
+% invocation.  Therefore, we \!\def!ine \!\column!(|*|) to have
+% \!\pcol@com@column!(|*|) in their bodies\footnote{

+% 

+% We can do this for other commands instead of adhearing to \cs{let} to
+% eliminate the execption, but the author loves to use \cs{let} as much as
+% possible.}.
+% 

+% We also give the first \!\def!initions of
+% \!\pcol@com@column!(|*|) to let them do nothing but re\!\def!ine
+% themselves by \!\pcol@defcolumn! unless
+% \!\pcol@com@column*! is given an optional \mctext{} argument which is
+% directly processed by \!\pcol@sptext!, if they appear as the first
+% \cswitch{} command\slash environment after \beginparacol.  Then we
+% re\!\def!ine \!\paracol! itself so that it will complain of illegal
+% nesting by \!\PackageError!.
+% 

+%    \begin{macrocode}
+  \let\@elt\pcol@defcomelt \pcol@localcommands
+  \def\column{\pcol@com@column}%
+  \@namedef{column*}{\@nameuse{pcol@com@column*}}%
+  \global\let\pcol@com@column\pcol@defcolumn
+  \global\@namedef{pcol@com@column*}{\pcol@defcolumn
+    \@ifnextchar[%]
+     \pcol@sptext\relax}%
+  \def\paracol##1{\PackageError{paracol}{%
+    Environment paracol cannot be nested.}\@eha}%
+%    \end{macrocode}
+% 
+% Ninth, we let \!\output! have our output routine \!\pcol@output! as its sole
+% token, and then make \!\output! request with
+% $\!\penalty!=\!\pcol@op@start!$ by \!\pcol@invokeoutput! to invoke
+% \!\pcol@output@start! for initialization, after letting
+% $\!\@elt!=\!\relax!$ to make it sure that any lists can be manipulated
+% without unexpected application of a macro to their elements.
+% 

+%    \begin{macrocode}
+  \output{\pcol@output}%
+  \let\@elt\relax
+  \pcol@invokeoutput\pcol@op@start
+%    \end{macrocode}
+% 
+% Tenth and finally, we let $\!\pcol@nextcol!=0$ in case \beginparacol{} has
+% the optional argument for \mctext{}, and invoke \!\pcol@sptext! if it has.
+% Otherwise, we invoke $|\pcol@colpream|{\cdot}0$ being the \colpream{} of
+% the first column 0, which will be invoked by \!\pcol@switchcol! if
+% \mctext{} is given.
+% 

+% \SpecialArrayIndex{c}{\pcol@colpream}

+% 

+% \changes{v1.35-5}{2018/12/31}
+% 	{Add the invocation of $\cs{pcol@colpream}{\cdot}0$.}

+% 

+%    \begin{macrocode}
+  \pcol@nextcol\z@
+  \@ifnextchar[%]
+    \pcol@sptext{\@nameuse{pcol@colpream0}}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@paracol}
+% The macro \!\pcol@paracol! has the definition of \!\paracol!, which is
+% redefined in the macro itself, so that the only referrer
+% \!\pcol@icolumncolor! examines if it appears in \env{paracol}, i.e.,
+% $\!\pcol@paracol!\neq\!\paracol!$.
+% 

+%    \begin{macrocode}
+\let\pcol@paracol\paracol
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\thecolumn}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to let users know which column they are working in.}

+% 

+% The API macro \!\thecolumn! gives the value of \!\pcol@currcol! to users
+% to let them know which column they are working in so that, for example,
+% they do some column-dependent opreations.
+% 

+%    \begin{macrocode}
+\def\thecolumn{\number\pcol@currcol}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@ignore}
+% \changes{v1.2-4}{2013/05/11}
+%	{Introduced for nullificaion of \cs{[no]swapcolumninevenpages}.}
+% \changes{v1.2-2}{2013/05/11}
+%	{Introduced for nullificaton of API macros of footnote typesetting
+%	 definition.}
+% 

+% The macro \!\pcol@ignore!$\arg{macro}$ is to complain that the
+% $\arg{macro}$ being one of the followings appears in \env{paracol}
+% environment.
+% 

+% \begin{itemize}\raggedright\item[]
+% \!\twosided!,
+% \!\swapcolumninevenpages!,
+% \!\noswapcolumninevenpages!,
+% \!\footnotelayout!,
+% \!\multicolumnfootnotes!,
+% \!\singlecolumnfootnotes!,
+% \!\mergedfootnotes!
+% \end{itemize}
+% 

+% That is, these macros, except for \!\twosided!, are re\!\def!ined in
+% \!\pcol@zparacol! to invoke this macro with the argument identifying
+% themselves, which is shown in the warning message given by
+% \!\PackageWarning!.  As for \!\twosided!, the target of the
+% re\!\def!inition is \!\pcol@twosided! so that its optional argument is
+% captured before the complaint.
+% 

+%    \begin{macrocode}
+\def\pcol@ignore#1{\PackageWarning{paracol}{The command \string#1 is not
+  effective in paracol environment and thus ignored}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@localcommands}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to make API commands environment-local.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Add \cs{@elt}\string\texttt{\char`\{cleardoublepage\char`\}} for
+%	 \cs{cleardoublepage}.} 

+% 

+% The macro \!\pcol@localcommands! is the list of the names of the following
+% {\em\Uidx\elocal} API commands (or {\em\Uidx\lcommand{}s} in short) and is
+% solely referred to by \!\pcol@zparacol!.
+% 

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

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

+%    \begin{macrocode}
+\def\pcol@localcommands{%
+  \@elt{switchcolumn}%
+  \@elt{endcolumn}\@elt{endcolumn*}%
+  \@elt{nthcolumn}\@elt{endnthcolumn}\@elt{nthcolumn*}\@elt{endnthcolumn*}%
+  \@elt{leftcolumn}\@elt{endleftcolumn}\@elt{leftcolumn*}\@elt{endleftcolumn*}%
+  \@elt{rightcolumn}\@elt{endrightcolumn}%
+    \@elt{rightcolumn*}\@elt{endrightcolumn*}%
+  \@elt{flushpage}\@elt{clearpage}\@elt{cleardoublepage}%
+  \@elt{synccounter}\@elt{syncallcounters}}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@defcomelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to make API commands environment-local.}

+% 

+% The macro \!\pcol@defcomelt! is invoked solely from \!\pcol@zparacol! to be
+% applied to each element $\arg{com}$ in \!\pcol@localcommands!.  Two
+% lengthy \!\let!s with \!\expandafter!s are for doing
+% $\!\let!|\|\arg{com}|=\pcol@com@|{\cdot}\arg{com}$ to bind the \elocal{}
+% API command $|\|\arg{com}$ and its implementation
+% $|\pcol@com@|{\cdot}\arg{com}$.
+% 

+% \SpecialArrayIndex{\<\string\mathit{com}\>}{\pcol@com@}

+% 

+%    \begin{macrocode}
+\def\pcol@defcomelt#1{%
+  \expandafter\let\expandafter\reserved@a\csname pcol@com@#1\endcsname
+  \expandafter\let\csname #1\endcsname\reserved@a}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\@dbldeferlist}
+% \changes{v1.32-3}{2015/10/10}
+% 	{Add top-level definition in case that future \LaTeX{} removes it at
+%	 all.}
+% \begin{macro}{\pcol@end@dblfloat}
+% \changes{v1.32-3}{2015/10/10}
+% 	{Added to go back to old mechanism.}
+% As discussed in \secref{sec:imp-ovv-float}, 2015 version of \LaTeX{}
+% no longer uses \!\@dbldeferlist! but the macro itself is still kept in
+% \LaTeX{}.  However it will be removed in future to make the first
+% \!\@cons! with it resulting in an error.  Therefore, here we have its top
+% level definition with empty duplicatedly in case of its future
+% elimination.  The macro \!\end@dblfloat!, on the other hand, is replaced
+% with a new definition in the new \LaTeX{} of course, and thus we define
+% \!\pcol@end@dblfloat! here to keep its old definition and to replace the
+% new one in \env{paracol} environment as discussed in
+% item-(\ref{item:ovv-float-end@dblfloat}) of \secref{sec:imp-ovv-float}.
+% 

+%    \begin{macrocode}
+\gdef\@dbldeferlist{}
+\def\pcol@end@dblfloat{%
+  \if@twocolumn
+    \@endfloatbox
+    \ifnum\@floatpenalty <\z@
+      \@largefloatcheck
+      \@cons\@dbldeferlist\@currbox
+    \fi
+    \ifnum \@floatpenalty =-\@Mii \@Esphack\fi
+  \else
+    \end@float
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% 
+% 
+% \KeepSpace{6}
+% \section{Column Width Setting}
+% \label{sec:imp-cwidth}
+% \changes{v1.3-4}{2013/09/17}
+%	{Add the secion ``Column Width Setting'' mainly to discuss the new
+%	 API \cs{setcolumnwidth}.}

+% 
+% \begin{macro}{\columnratio}
+% \changes{v1.1}{2012/05/11}
+% 	{Introduced to specify column width fractions.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add optional second argument for fractions in right
+%	 parallel-pages.}
 
+% \begin{macro}{\pcol@icolumnratio}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to process the optional second argument of
+%	 \cs{columnratio}.}

+% \begin{macro}{\pcol@columnratioleft}
+% \changes{v1.1}{2012/05/11}
+% 	{Introduced to keep column width fractions.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Renamed from \cs{pcol@columnratio} to clarify it has fractions for
+%	 left parallel-pages.}

+% \begin{macro}{\pcol@columnratioright}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduced to keep column width fractions for right
+%	 parallel-pages.}

+% 

+% The API macro $\!\columnratio!
+% \Arg{r^l_0,r^l_1,\cdots,r^l_{k^l-1}}|[|r^r_0,r^r_1,\cdots,r^r_{k^r-1}|]|$
+% defines the column width fraction $r^l_c$ for column $c$ in left
+% \parapag{}es and optionally $r^r_c$ for those in right \parapag{}es.  This
+% macro and its callee \!\pcol@icolumnratio! just \!\global!y \!\def!ine
+% macros \!\pcol@columnratioleft! and \!\pcol@columnratioright!  whose
+% bodies have the first and second arguments respectively, or commonly have
+% the first if the second optional one is not given, so that they are given
+% to \!\pcol@setcolwidth@r! as its third argument through
+% \!\pcol@setcolumnwidth! invoked in \!\pcol@zparacol!.  Both of
+% \!\pcol@columnratioleft! and \!\pcol@columnratioright! are initialized to
+% be empty so that all columns have same width and are separated by
+% \!\columnsep! as default.  Note that \!\pcol@columnratioleft! can be made
+% \!\let!-equial to \!\relax! by the related API macro \!\setcolumnwidth! so
+% that \!\pcol@setcolumnwidth! knows which of specifications given by two
+% API macros is effective and chooses \!\pcol@setcolwidth@r! or
+% \!\pcol@setcolwidth@s!.
+% 

+%    \begin{macrocode}
+%% Column Width Setting
+
+\def\columnratio#1{\global\let\pcol@colwidthspecleft\relax
+  \gdef\pcol@columnratioleft{#1}%
+  \@ifnextchar[%]
+    \pcol@icolumnratio{\gdef\pcol@columnratioright{#1}}}
+\def\pcol@icolumnratio[#1]{\gdef\pcol@columnratioright{#1}}
+\columnratio{}\relax
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\setcolumnwidth}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to specify column widths and column-separating gaps more
+%	 detailedly.}

+% \begin{macro}{\pcol@isetcolumnwidth}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to process the optional second argument of
+%	 \cs{setcolumnwidth}.}

+% \begin{macro}{\pcol@colwidthspecleft}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to keep column width specifications for left
+%	 parallel-pages.}

+% \begin{macro}{\pcol@colwidthspecright}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to keep column width specifications for right
+%	 parallel-pages.}

+% 

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

+%    \begin{macrocode}
+\def\setcolumnwidth#1{\global\let\pcol@columnratioleft\relax
+  \gdef\pcol@colwidthspecleft{#1}%
+  \@ifnextchar[%]
+    \pcol@isetcolumnwidth{\gdef\pcol@colwidthspecright{#1}}}
+\def\pcol@isetcolumnwidth[#1]{\gdef\pcol@colwidthspecright{#1}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@setcolumnwidth}
+% \changes{v1.3-4}{2013/09/17}
+%	{Move original functions to \cs{pcol@setcolumnwidth@r} and redefine
+%	 this macro to switch \cs{pcol@setcolumnwidth@r} and
+%	 \cs{pcol@setcolumnwidth@s}.}

+% 

+% \begin{Sloppy}{1500}
+% The macro $\!\pcol@setcolumnwidth!\<\Cfrom\>\<\Cto\>\arg{ratio}\arg{spec}$
+% is invoked solely from \!\pcol@zparacol! but can be twice, with;
+% $$
+% (\Cfrom,\Cto,\arg{ratio},\arg{spec})=
+%   (0,\CL,\!\pcol@columnratioleft!,\!\pcol@colwidthspecleft!)
+% $$
+% always and with;
+% $$
+% (\Cfrom,\Cto,\arg{ratio},\arg{spec})=
+%   (\CL,\C,\!\pcol@columnratioright!,\!\pcol@colwidthspecright!)
+% $$
+% if $\CL<\C$ for \parapag{}ing.  The macro simply invokes
+% \!\pcol@setcolwidth@s! if $\!\pcol@columnratioleft!=\!\relax!$ because
+% \!\setcolumnwidth! did so, or \!\pcol@setcolwidth@r! otherwise, with all
+% arguments given by \!\pcol@zparacol!.
+% \end{Sloppy}
+% 

+%    \begin{macrocode}
+\def\pcol@setcolumnwidth{%
+  \ifx\pcol@columnratioleft\relax \let\reserved@a\pcol@setcolwidth@s
+  \else                           \let\reserved@a\pcol@setcolwidth@r
+  \fi
+  \reserved@a}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@setcolwidth@r}
+% \changes{v1.1}{2012/05/11}
+% 	{Introduced to calculate $w_c$.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Renamed from \cs{pcol@setcolumnwidth} to make it clear what the
+%	 marco works for.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add arguments $C^0$, $C^1$, $\langle\string\mathit{ratio}\rangle$
+%	 and $\langle\string\mathit{spec}\rangle$ for columns in right
+%	 parallel-pages.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add setting of $g_c\EQ\cs{pcol@columnsep}{\cdot}c=\cs{columnsep}.}
+% 

+% \begin{Hfuzz}{0.3pt}%
+% The macro $\!\pcol@setcolwidth@r!\<\Cfrom\>\<\Cto\>\arg{ratio}\arg{spec}$
+% is invoked solely from \!\pcol@zparacol! through \!\pcol@setcolumnwidth!
+% once or twice with the arguments described in the explanation of the
+% latter macro.  The macro calculates $\w_c=|\pcol@columnwidth|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% 

+% for all $c\In\Cfrom\Cto$, from the fractions $r_0$, $r_1$, \ldots,
+% $r_{k-1}$ given through the third argument $\arg{ratio}$, which was given
+% to \!\columnratio! and then kept in \!\pcol@columnratioleft! or
+% \!\pcol@columnratioright!.  The macro also lets
+% $\gap_c=|\pcol@columnsep|{\cdot}c=\!\columnsep!$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% for all $c\In\Cfrom\Cto$.
+% \end{Hfuzz}
+% 
+% First, we calculate $W=\!\textwidth!-(\Cto-\Cfrom-1)\times\!\columnsep!$
+% being the sum of $\w_c$ for all $c\In\Cfrom\Cto$.  Then we let
+% $\w_c=r_d{}W$ and $\gap_c=\!\columnsep!$ for all $c\In\Cfrom{k'}$ where
+% $k'=\min(k,\Cto-1)$, in the \!\@for! loop scanning $r_d$ for all
+% $d=c-\Cfrom\In0k$.  Finally, we let
+% $\w_c=(W-\sum_{d=\Cfrom}^{k'-1}w_d)/(\Cto-\Cfrom-k')$ and
+% $\gap_c=\!\columnsep!$ for all $c\In{k'}\Cto$.  Note that
+% $|\pcol@columnwidth|{\cdot}c$ and $|\pcol@columnsep|{\cdot}c$ are macros
+% having the integer representations of $\w_c$ and $\gap_c$ with the unit
+% |sp|.
+% 

+%    \begin{macrocode}
+\def\pcol@setcolwidth@r#1#2#3#4{%
+  \@tempcntb#2\advance\@tempcntb-#1\advance\@tempcntb\m@ne
+  \@tempdima-\columnsep \multiply\@tempdima\@tempcntb
+  \advance\@tempdima\textwidth \@tempdimb\@tempdima
+  \@tempcnta#1\relax\@tempcntb#2\advance\@tempcntb\m@ne
+  \@for\reserved@a:=#3\do{%
+    \ifnum\@tempcnta<\@tempcntb
+      \@tempdimc\reserved@a\@tempdima
+      \expandafter\xdef\csname pcol@columnwidth\number\@tempcnta\endcsname{%
+        \number\@tempdimc sp}%
+      \global\@namedef{pcol@columnsep\number\@tempcnta}{\columnsep}%
+      \advance\@tempdimb-\@tempdimc
+      \advance\@tempcnta\@ne
+    \fi}%
+  \@tempcntb#2\advance\@tempcntb-\@tempcnta
+  \divide\@tempdimb\@tempcntb
+  \@whilenum\@tempcnta<#2\do{%
+    \expandafter\xdef\csname pcol@columnwidth\number\@tempcnta\endcsname{%
+      \number\@tempdimb sp}%
+    \global\@namedef{pcol@columnsep\number\@tempcnta}{\columnsep}%
+    \advance\@tempcnta\@ne}%
+}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{3}
+% \begin{macro}{\pcol@setcolwidth@s}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to calculate $w_c$ and $g_c$.}

+% \begin{macro}{\pcol@setcw@c}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to process column width components in the argument
+%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}

+% \begin{macro}{\pcol@setcw@s}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to process column-separating gap components in the
+%	 argument $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}

+% \begin{macro}{\pcol@setcw@filunit}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to define the unit of infinite stretch factors in the
+%	 argument $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}

+% 

+% \begin{Hfuzz}{0.3pt}%
+% The macro $\!\pcol@setcolwidth@s!\<\Cfrom\>\<\Cto\>\arg{ratio}\arg{spec}$
+% is invoked solely from \!\pcol@zparacol! through \!\pcol@setcolumnwidth!
+% once or twice with the arguments described in the explanation of the
+% latter macro.  The macro calculates $\w_c=|\pcol@columnwidth|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}

+% 

+% for all $c\In\Cfrom\Cto$ and $\gap_c=|\pcol@columnsep|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@columnsep}

+% 

+% for all $c\In\Cfrom{\Cto{-}1}$, from the column\slash gap specifications
+% $s_0$, $s_1$, \ldots, $s_{k-1}$ given through the fourth argument
+% $\arg{spec}$, which was given to \!\setcolumnwidth! and then kept in
+% \!\pcol@colwidthspecleft! or \!\pcol@colwidthspecright!.
+% \end{Hfuzz}
+% 
+% Each specification $s_d$ for $\w_c$ and $\gap_c$ where $c=\Cfrom+d$ has
+% the form $|[|w'_d|][/[|g'_d|]]|$ to specify the natural width $w^n_d$ and
+% $g^n_d$ and inifite stretch factor $w^f_d$ and $g^f_d$ of column\slash gap
+% sepcfication as follows;
+% 

+% \begin{eqnarray*}
+% w^n_d&=&\cases{0&$w'_d=\emptyset$\cr
+%                0&$w'_d=f\!\fill!$\cr
+%                \mathit{natural}(w'_d)&otherwise}\qquad
+% w^f_d = \cases{1&$w'_d=\emptyset$\cr
+%                f&$w'_d=f\!\fill!$\cr
+%                \mathit{stretch}(w'_d)&otherwise}\\[1ex]
+% g^n_d&=&\cases{\!\columnsep!&$g'_d=\emptyset$\cr
+%                0&$g'_d=f\!\fill!$\cr
+%                \mathit{natural}(g'_d)&otherwise}\qquad
+% g^f_d = \cases{0&$g'_d=\emptyset$\cr
+%                f&$g'_d=f\!\fill!$\cr
+%                \mathit{stretch}(g'_d)&otherwise}
+% \end{eqnarray*}
+% 

+% where $\mathit{natural}(x)$ is the natural width of the skip $x$ and
+% $\mathit{stretch}(x)$ is the infinite stretch factor of $x$.  Note that
+% any finite stretch factors or any shirnk factors do not affect them, and
+% infinite strech units |fil|, |fill| and |filll| are not distinguished.
+% From factors above, we determine $w_c$ and $\gap_c$ as follows;
+% 

+% \begin{eqnarray*}
+% W&=&\sum_{d=0}^{m-2}(w^n_d+g^n_d)+w^n_{m-1}\\
+% F&=&\sum_{d=0}^{m-2}(w^f_d+g^f_d)+w^f_{m-1}\\
+% x_c&=&\cases{(\WT/W)x^n_{c-\Cfrom}&$W\geq\WT\;\lor\;F\leq0$\cr
+%              x^n_{c-\Cfrom}+(x^f_{c-\Cfrom}/F)(\WT-W)&$W<\WT\;\land\;F>0$}
+%     \qquad(x\in{\w,\gap})
+% \end{eqnarray*}
+% where $\WT=\!\textwidth!$ and $m=\Cto-\Cfrom$.
+% 
+% To perform the assignments above, the macro at first invoke
+% $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\~\ARg{spec}$ letting
+% $\!\pcol@setcw@c!=\!\pcol@setcw@s!=\!\pcol@setcw@accumwd!$ and
+% \!\pcol@setcw@filunit!${}=1$\,pt to scan $s_d$ for all $d\In0{m}$ and to
+% accumulate $W+g^n_{m-1}$ and $F+g^f_{m-1}$ in \!\dimen@! and \!\dimen@ii!
+% and then subtract $g^n_{m-1}$ and $g^f_{m-1}$ from them to have $W$ and
+% $F$.  Note that $F$ is represented by a dimension with the unit of pt by
+% the definition of \!\pcol@setcw@filunit!.  Then we invoke
+% \!\pcol@setcw@calcfactors! to calculate $(\WT/W)=\!\pcol@setcw@scale!$ and
+% $(\WT-W)/F=\!\@tempdimb!$.  Finally we scan $s_d$ again but in this case
+% we let $\!\pcol@setcw@c!=\!\pcol@setcw@set!|{width}|$,
+% $\!\pcol@setcw@s!=\!\pcol@setcw@set!|{sep}|$ and
+% $\!\pcol@setcw@filunit!=\!\@tempdimb!=(\WT-W)/F$ to let $w_c$ and $\gap_c$
+% have the values shown above.
+% 

+%    \begin{macrocode}
+\def\pcol@setcolwidth@s#1#2#3#4{\begingroup
+  \dimen@\z@ \dimen@ii\z@ \def\pcol@setcw@filunit{\@ne\p@}%
+  \let\pcol@setcw@c\pcol@setcw@accumwd \let\pcol@setcw@s\pcol@setcw@accumwd
+  \pcol@setcw@scan#1#2{#4}%
+  \advance\dimen@-\@tempdima \advance\dimen@ii-\@tempdimb
+  \pcol@setcw@calcfactors
+  \def\pcol@setcw@c{\pcol@setcw@set{width}}%
+  \def\pcol@setcw@s{\pcol@setcw@set{sep}}%
+  \let\pcol@setcw@filunit\dimen@ii
+  \pcol@setcw@scan#1#2{#4}%
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@setcw@scan}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to scan the argument
+%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}

+% 

+% The macro $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\~\ARg{spec}$ is to scan
+% first $m=\Cto-\Cfrom$ elements in $\arg{spec}=s_0,s_1,\ldots$ being the
+% column\slash gap specifications given to \!\setcolumnwidth!.  At first we
+% add `,' as many as $m$ to the tail of $\arg{spec}$ to make it sure the
+% resulting $\arg{spec}$ has $m$ or more elements.  Then we scan all
+% elements in the extended $\arg{spec}$ by a \!\@for! loop having many
+% \!\expandafter! but equivalent to;
+% 

+% \begin{quote}
+% |\@for\reserved@a:=|$s_0,s_1,\ldots$|\do{|\textit{body}|}|
+% \end{quote}
+% 

+% In the \textit{body} above, we invoke
+% $\!\pcol@setcw@getspec!\;s_i|//|\!\@nil!$ to parse $s_i$ to have $w^n_i$,
+% $w^f_i$ to be processed by \!\pcol@setcw@c! and $g^n_i$ and $g^f_i$ by
+% \!\pcol@setcw@s!, for all $i\In0m$.
+% 

+%    \begin{macrocode}
+\def\pcol@setcw@scan#1#2#3{\def\reserved@a{#3}%
+  \@tempcnta#1\relax \@whilenum\@tempcnta<#2\do{
+    \edef\reserved@a{\reserved@a,}\advance\@tempcnta\@ne}%
+  \@tempcnta#1\relax
+  \expandafter\@for\expandafter\reserved@a\expandafter:\expandafter=\reserved@a
+    \do{%
+      \ifnum\@tempcnta<#2\relax
+        \expandafter\pcol@setcw@getspec\reserved@a//\@nil
+      \fi
+      \advance\@tempcnta\@ne}}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \KeepSpace{1}
+% \begin{macro}{\pcol@setcw@getspec}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to parse an element in the argument
+%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}

+% \begin{macro}{\pcol@setcw@getspec@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to parse an element in the argument
+%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}

+% \begin{macro}{\pcol@setcw@fill}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to extract \cs{fill} factor from an element in the
+%	 argument  $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}

+% 

+% The macro
+% $\!\pcol@setcw@getspec!\<w'_d\>|/|\<g'_d\>|/|\arg{garbage}\!\@nil!$ is
+% used solely in \!\pcol@setcw@scan! to parse a column\slash gap
+% specification $s_d=|[|w'_d|][/[|g'_d|]]|$, to extract factors $w_d^n$,
+% $w_d^f$, $g_d^n$ and $g_d^f$, and to process width factors by
+% \!\pcol@setcw@c! and gap factors by \!\pcol@setcw@s!.  Since the macro is
+% invoked with arguments in the form of $s_d|//|\!\@nil!$, if $s_d$ has
+% `|/|' in it $w'_d$ and $g'_d$ should have everything preceeding and
+% following the `|/|' respectively while $\arg{garbage}$ should have the
+% redundant `|/|'.   Otherwise, i.e., if $s_d$ does not have `|/|',
+% $w'_d=s_d$ and $g'_d=\emptyset$ while $\arg{garbage}=\emptyset$\footnote{

+% 

+% If $s_d$ have two or more `|/|', everything following the second one is
+% thrown away into $\arg{garbage}$ together with `|//|'.  Therefore we could
+% check if $s_d$ has at most one `|/|' by examining $\arg{garbage}$ but we
+% abandon it simply ingoring $\arg{garbage}$.}.
+% 

+% Therefore, we invoke $\!\pcol@setcw@getspec@i!\arg{default}\Arg{x'_d}$ twice
+% with $(\arg{default},x'_d)=(\!\fill!,w'_d)$ for a column and
+% $(\arg{default},x'_d)=(\!\columnsep!,g'_d)$ for a gap, and \!\pcol@setcw@c!
+% and \!\pcol@setcw@s! after each invocation respectively.
+% 
+% In this macro, at first we scan all tokens in $x'_d$ by \!\@tfor! to
+% remove all space tokens in it\footnote{

+% 

+% A proper skip specification and ``$f\!\fill!$'' is always proper without
+% space tokens in them.}.
+% 

+% Then if $x'_d$ after the space removal has nothing, we let
+% $x'_d=\arg{default}$.  Next we examine if $x'_d=f\!\fill!$ in a trickey
+% way by temporarily \!\let!ting $\!\@gtempa!=\!\relax!$, defining \!\fill!
+% as ``|1pt|\!\gdef!\!\@gtempa!|{}|'' and making an assignment
+% ``\!\@tempskipa!  $x'_d$''.  That is, if $x'_d=f\!\fill!$, \!\@tempskipa!
+% will have $f{\cdot}|1pt|$ being a proper dimension and \!\@gtempa! is made
+% empty.  Otherwise, \!\@tempskipa! should have $x'_d$ which must be a
+% proper skip and \!\@gtempa! remains unchanged from \!\relax!.  Therefore,
+% if $\!\@gtempa!=\!\relax!$ we let $\!\@tempskipa!=x'_d$ again\footnote{

+% 

+% Because the first assignment is done in a group.}.
+% 

+% Otherwise, we invoke $\!\pcol@setcw@fill!\;x'_d$ to let
+% \!\@tempskipa! have $0\,|pt|\ |plus|\ f\,|fil|$ where $f$ is replaced by 1
+% if $f=\emptyset$.
+% 
+% Now \!\@tempskipa! has $x_d^n$ as its natural component and may have some
+% infinite strectch component $x_d^f$ specified explicitly or with \!\fill!.
+% Therefore, we assign \!\@tempskipa! to \!\@tempdima! so that it has
+% $x_d^n$, and then, after adding 0\,|pt| |plus| 1000\,|pt| |minus|
+% 1000\,|pt| to \!\@tempskipa! to make it sure it has both strech and shrink
+% components\footnote{

+% 

+% Almost sure becaues they could be $-1000$\,pt, but we ignore the
+% possibility.}
+% 

+% keeping infinite stretch factor if any, invoke \!\pcol@extract@fil! giving
+% it \!\the!-expansion of \!\@tempskipa! as the argument to let
+% $\!\@tempdimb!=x_d^f\times\!\pcol@setcw@filunit!$.
+% 

+%    \begin{macrocode}
+\def\pcol@setcw@getspec#1/#2/#3\@nil{%
+  \pcol@setcw@getspec@i\fill{#1}\pcol@setcw@c
+  \pcol@setcw@getspec@i\columnsep{#2}\pcol@setcw@s}
+\def\pcol@setcw@getspec@i#1#2{%
+  \def\reserved@a{}%
+  \@tfor\reserved@b:=#2\do{\edef\reserved@a{\reserved@a\reserved@b}}
+  \ifx\reserved@a\@empty \let\reserved@a#1\fi
+  \let\@gtempa\relax
+  {\def\fill{1\p@\gdef\@gtempa{}}\@tempskipa\reserved@a}%
+  \ifx\@gtempa\relax \@tempskipa\reserved@a\relax
+  \else \expandafter\pcol@setcw@fill\reserved@a
+  \fi
+  \@tempdima\@tempskipa
+  \advance\@tempskipa0\p@\@plus\@m\p@\@minus\@m\p@\relax
+  \expandafter\pcol@extract@fil\the\@tempskipa\@nil}
+\def\pcol@setcw@fill#1\fill{\def\reserved@b{#1}%
+  \ifx\reserved@b\@empty \let\reserved@b\@ne \fi
+  \@tempskipa0\p@\@plus\reserved@b fil\relax}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@setcw@accumwd}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to accumulate natural and fill factors of the element in
+%	 the argument $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}
 
+% 

+% The macro \!\pcol@setcw@accumwd! is made \!\let!-equal to \!\pcol@setcw@c!
+% and \!\pcol@setcw@s! commonly and thus invoked from \!\pcol@setcw@getspec!
+% with setting $\!\@tempdima!=x_d^n$ and $\!\@tempdimb!=x_d^f\times1\,|pt|$,
+% where $x\in\{w,g\}$.  The macro simply add them to \!\dimen@! and
+% \!\dimen@ii! repsectively to accumurate $x_d^n$ and $x_d^f$ in them.
+% 

+%    \begin{macrocode}
+\def\pcol@setcw@accumwd{\advance\dimen@\@tempdima \advance\dimen@ii\@tempdimb}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@setcw@set}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to define $w_c$ and $g_c$ according to the element in
+%	 the argument $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}
 
+% 

+% The macro $\!\pcol@setcw@set!\ARg{wors}$ is made the body of
+% \!\pcol@setcw@c! with $\arg{wors}=|width|$ and of
+% \!\pcol@setcw@s! with $\arg{wors}=|sep|$ and thus invoked from
+% \!\pcol@setcw@getspec!  with setting $\!\@tempdima!=x_d^n$ and
+% $$
+% (\!\pcol@setcw@scale!,\!\@tempdimb!)
+% \in\{(\emptyset,\,(x_d^f/F)(\WT-W)),\;(\WT/W,\,0)\}
+% $$
+% Therefore, we calculate
+% $x_c=\!\pcol@setcw@scale!\times\!\@tempdima!+\!\@tempdimb!$ and
+% \!\xdef!ine $|\pcol@column|{\cdot}\<wors\>{\cdot}c$ to let it have the
+% integer representation of $x_c$ with the unit |sp|.
+% 

+% \SpecialArrayIndex{c}{\pcol@columnwidth}
+% \SpecialArrayIndex{c}{\pcol@columnsep}
+% 

+%    \begin{macrocode}
+\def\pcol@setcw@set#1{%
+  \@tempdima\pcol@setcw@scale\@tempdima \advance\@tempdima\@tempdimb
+  \expandafter\xdef\csname pcol@column#1\number\@tempcnta\endcsname{%
+    \number\@tempdima sp}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@setcw@calcfactors}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to caclulate scaling and stretch factors from
+%	 the argument $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}
 
+% \begin{macro}{\pcol@setcw@calcf}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to caclulate scaling or stretch factor from
+%	 the argument $\langle\string\mathit{spec}\rangle$ of
+%	 \cs{pcol@setcolwidth@s}.}
 
+% \changes{v1.31}{2013/10/10}
+%	{Capitalize the first word of the error message for consistency.}

+% \begin{macro}{\pcol@setcw@scale}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to have the scaling factor of $w_c$ and $g_c$.}

+% 

+% The macro \!\pcol@setcw@calcfactors! is used solely in
+% \!\pcol@setcolwidth@s! to calculate $\phi_s=\!\pcol@setcw@scale!$ and
+% $\phi_f=\!\dimen@ii!$ as follows
+% $$
+% (\phi_s,\phi_f)=\cases{(\WT/\W,\;0)& $W\geq\WT\;\lor\;F\leq0$\cr
+%                        (1,\;(\WT-W)/F)&$W<\WT\;\land\;F>0$}
+% $$
+% where $W=\!\dimen@!$, $F\times1\,|pt|=\!\dimen@ii!$ and $\WT=\!\textwidth!$,
+% and $\phi_s=1$ is represented by empty body of \!\pcol@setcw@scale!.
+% First we deal with the special and trivial case of $W=\WT$ to let
+% $\phi_s=1$ and $\phi_f=0$ so as to avoid arithmetic error in the
+% calculation of $\WT/W$.  If $W\neq\WT$ on the other hand, we calculate
+% $\WT/W$ by $\!\pcol@setcw@calcf!\<\WT\>\<W\>\<\phi_s\>$ to have a
+% provisional result.  Then if $W<\WT$ and $F>0$, we let $\phi_s=1$ and
+% invoke \!\pcol@setcw@calcf! again giving it $(\WT-W)$ and $F\times1\,|pt|$
+% but throw away the result $(\WT-W)/(F\times1\,|pt|)$ because \!\@tempdimb!
+% should have $(\WT-W)/F$ which is then set into $\phi_f=\!\dimen@ii!$.
+% Otherwise, we keep the provisional result of $\phi_s$ as the final one and
+% let $\phi_f=\!\dimen@ii!=0$.
+% 
+% The macro $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ caclulates $z\approx x/y$
+% and let $\!\@tempdimb!=Z=z\times1\,|pt|$ as follows.  First we find the
+% following three parameters.
+% 

+% \begin{eqnarray*}
+% k_1&=&\min\Set{k}{k\geq0,\;x\cdot2^k\geq2^{13}\,|pt|}\\
+% k_2&=&\max\Set{k}{y\bmod2^k=0}\\
+% k_3&=&\min\Set{k}{k\geq0,\;\lceil y/2^{k_2+k}\rceil\leq2^{15}}
+% \end{eqnarray*}
+% 

+% With these parameters, we calculate $z'=\lfloor(x\cdot2^{k_1})/\lceil
+% y/2^{k_2+k_3}\rceil\rfloor$ to have a good approximation of
+% $(x/y)\cdot2^{k}$ where $k=k_1+k_2+k_3$ without arithmetic overflow.  Then
+% if $z'/2^k\geq2^{14}$ or in other words $Z$ is larger than \!\maxdimen!,
+% we complain that by \!\PackageError! and, in case a user dare to
+% continue the typesetting process, we let $Z=10000\,|pt|$.  Otherwise, we
+% calculate $Z=(z'/2^k)\cdot2^{16}=z'\cdot2^{16-k}$ to have it in
+% \!\@tempdimb! by $Z=z'\times2^{16-k}$ if $k<16$, or by $Z=z'/2^{k-16}$
+% otherwise.  Finally we invoke \!\pcol@extract@pt! giving it
+% \!\the!-representaion of $Z$ to have $z$.
+% 
+% Note that it is assured $z\leq x/y$ regardless of successfulness of the
+% calculation and thus the scaling $\phi_s x_d^n$ and strething
+% $x_d^n+\phi_f x_d^f$ cannot exceed their exact value to make it also sure
+% that $\sum_{c=\Cfrom}^{\Cto-2}(\w_c+\gap_c)+\w_{\Cto-1}\leq\WT$ and thus
+% the series of columns and \csepgap{}s should not cause overfull when a
+% page is shipped out with \!\hfil! added to each \csepgap{} for underfull
+% avoidance.
+% 

+%    \begin{macrocode}
+\def\pcol@setcw@calcfactors{%
+  \ifdim\dimen@=\textwidth \def\pcol@setcw@scale{}\dimen@ii\z@
+  \else
+    \pcol@setcw@calcf\textwidth\dimen@\pcol@setcw@scale
+    \ifdim\dimen@<\textwidth \ifdim\dimen@ii>\z@
+      \def\pcol@setcw@scale{}%
+      \@tempdimc\textwidth \advance\@tempdimc-\dimen@
+      \pcol@setcw@calcf\@tempdimc\dimen@ii\reserved@a \dimen@ii\@tempdimb
+    \else \dimen@ii\z@ \fi
+    \else \dimen@ii\z@ \fi
+  \fi}
+\def\pcol@setcw@calcf#1#2#3{%
+  \@tempdimb#1\@tempdima#2\@tempcnta\z@
+  \ifdim\@tempdima=\z@ \@tempdima1sp\relax\fi
+  \@whiledim\@tempdimb<8192\p@\do{%
+    \multiply\@tempdimb\tw@ \advance\@tempcnta\@ne}%
+  \@tempdimc\@tempdima
+  \@whiledim\@tempdima=\@tempdimc\do{%
+    \divide\@tempdimc\tw@ \multiply\@tempdimc\tw@
+    \ifdim\@tempdima=\@tempdimc
+      \divide\@tempdima\tw@ \divide\@tempdimc\tw@ \advance\@tempcnta\@ne
+    \fi}
+  \advance\@tempdima-1sp\relax
+  \@whilenum\@tempdima>32768\do{\divide\@tempdima\tw@ \advance\@tempcnta\@ne}%
+  \advance\@tempdima1sp\relax
+  \divide\@tempdimb\@tempdima \@tempdimc\@tempdimb \@tempcntb\@tempcnta
+  \@whilenum\@tempcntb>\z@\do{\divide\@tempdimc\tw@ \advance\@tempcntb\m@ne}
+  \ifnum\@tempdimc>16383\relax
+    \PackageError{%
+      Scaling/filling factor for column/gap width is too large.}\@eha
+    \@tempdimb\@M\p@
+  \else
+    \@tempcntb\sixt@@n \advance\@tempcntb-\@tempcnta
+    \ifnum\@tempcntb<\z@
+      \@whilenum\@tempcntb<\z@\do{\divide\@tempdimb\tw@ \advance\@tempcntb\@ne}%
+    \else
+      \@whilenum\@tempcntb>\z@\do{%
+        \multiply\@tempdimb\tw@ \advance\@tempcntb\m@ne}%
+    \fi
+  \fi
+  \expandafter\pcol@extract@pt\the\@tempdimb#3}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{3}
+% \begin{macro}{\pcol@defkw}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to define $\cs{pcol@kw@}{\cdot}k$ where
+%	 $k\in\{\string\texttt{pt},\string\texttt{plus},\string\texttt{minus},
+% 	 \string\texttt{fil}\}$.}
+% \begin{macro}{\pcol@kw@pt}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to have the keyword \string\texttt{pt}.}
+% \begin{macro}{\pcol@kw@plus}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to have the keyword \string\texttt{plus}.}
+% \begin{macro}{\pcol@kw@minus}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to have the keyword \string\texttt{minus}.}
+% \begin{macro}{\pcol@kw@fil}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to have the keyword \string\texttt{fil}.}
+% 

+% The macro
+% $\!\pcol@defkw!|1.0|\arg{pt}\verb*| |\arg{plus}\verb*| 1.0|\arg{fil}
+% \verb*| |\arg{minus}\verb*| 1.0|\arg{garbage}\!\@nil!$ is used just once at
+% the top level to \!\def!ine \!\pcol@kw@pt!, \!\pcol@kw@plus!,
+% \!\pcol@kw@minus! and \!\pcol@kw@fil! letting them have $\arg{pt}=|pt|$,
+% $\arg{plus}=|plus|$, $\arg{minus}=|minus|$ and $\arg{fil}=|fil|$ in their
+% body respectively but with $\!\catcode!=12$ (other) which is used in
+% \!\the!-representation of glues.  For the definition, we invoke
+% \!\pcol@defkw! giving it \!\the!-representation of \!\@tempskipa! letting
+% it have $1\,|pt|\ |plus|\ 1\,|fil|\ |minus|\ 1\,|fil|$ having all keywards
+% we need to have\footnote{

+% 

+% We can do what \!\pcol@defkw! does by temporarily giving $\!\catcode!=12$
+% to the characters for the keywords of course, but this method is much
+% easier.}.
+% 

+% The macro \!\pcol@kw@pt! is used in
+% $\!\pcol@extract@fil@ii!\arg{unit}\!\@nil!$ to examine if
+% $\arg{unit}=|pt|$, and in \!\pcol@def@extract@pt! to \!\def!ine
+% \!\pcol@extract@pt! having |pt| in its argument specification.  The macros
+% \!\pcol@kw@plus! and \!\pcol@kw@minus! are used only in
+% \!\pcol@def@extract@fil!, and
+% \!\pcol@kw@fil! only in \!\pcol@def@extract@fil@iii!, to \!\def!ine
+% \!\pcol@extract@fil! having |plus| and |minus|, and
+% \!\pcol@extract@fil@iii! having |fil|, in their argument specifications
+% respectively.
+% 

+%    \begin{macrocode}
+\@tempskipa 1\p@\@plus1fil\@minus1fil\relax
+\def\pcol@defkw1.0#1 #2 1.0#3 #4 1.0#5\@nil{%
+  \def\pcol@kw@pt{#1}\def\pcol@kw@plus{#2}\def\pcol@kw@fil{#3}%
+  \def\pcol@kw@minus{#4}}
+\expandafter\pcol@defkw\the\@tempskipa\@nil
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \KeepSpace{4}
+% \begin{macro}{\pcol@def@extract@fil}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to define \cs{pcol@extract@fil}.}

+% \begin{macro}{\pcol@extract@fil}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to extract infinite stretch factor from a skip if any.}

+% \begin{macro}{\pcol@extract@fil@i}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to extract the factor of \string\texttt{fil} from the
+% 	 stretch factor in a skip if any.}
 
+% \begin{macro}{\pcol@extract@fil@ii}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to extract the factor of \string\texttt{fil} from the
+% 	 stretch factor in a skip if any.}
 
+% \begin{macro}{\pcol@def@extract@fil@iii}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to define \cs{pcol@extract@fil@iii}.}

+% \begin{macro}{\pcol@extract@fil@iii}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to extract the factor of \string\texttt{fil} from the
+% 	 stretch factor in a skip.}
 
+% 

+% The macro
+% $\!\pcol@extract@fil!\<\mathit{garbge}_1\>\verb*| plus |\<s\>\verb*| minus|
+% \<\mathit{garbage}_2\>\!\@nil!$ is used solely in \!\pcol@setcw@getspec@i!
+% to extract the infinite stretch factor $f$ in the stretch component $s$ of
+% a column\slash gap specification $x'_d$ and to let
+% $\!\@tempdimb!=f\cdot{}u$ where
+% $u=\!\pcol@setcw@filunit!\in\{1\,|pt|,\;\phi_f=\!\dimen@ii!\}$ if $f$
+% exist or $\!\@tempdimb!=0$ otherwise.  First of all, since the macro has
+% keywords |plus| and |minus| in $\!\catcode!=12$ in its argument
+% specification, we \!\def!ine it using \!\pcol@def@extract@fil!, whose body
+% is equivalent to
+% 

+% \begin{itemize}\item[]
+% \let\@sverb\latex@sverb
+% \verb*|\def\pcol@extract@fil#1 plus #2 minus#3\@nil|

+% |{\pcol@extract@fil@i#2\@nil}|
+% \end{itemize}
+% 

+% just once at the top level.  Then since $s$ should have the form
+% $\<n\>|.|\<m\>\arg{unit}$ where $n$ and $m$ are decimal digit sequences and
+% $\arg{unit}\in\{|pt|,|fil|,|fill|,|filll|\}$, we examine if
+% $\arg{unit}=|pt|$ or not by a trickey way in
+% $\!\pcol@extract@fil@i!\<n\>|.|\<m{\cdot}\mathit{unit}\>\!\@nil!$.  That
+% is, we do $\!\count@!\<m{\cdot}\mathit{unit}\>\!\@nil!$ with
+% \!\afterassignment! to invoke $\!\pcol@extract@fil@ii!\arg{unit}\!\@nil!$
+% after $m$ is assigned to \!\count@! to capture $\arg{unit}$.  Then if it
+% is |pt| we let $\!\@tempdimb!=0$, or otherwise invoke
+% $\!\pcol@extract@fil@iii!\<f\>|fil|\arg{garbage}\!\@nil!$ giving it $s$
+% because it should have a postfix being |fil|, |fill| or |filll|, to have
+% $\!\@tempdimb!=f\cdot u$ finally.  Note that since
+% \!\pcol@extract@fil@iii!  also has the keyword |fil| in its argument
+% specification, we \!\def!ine it using \!\pcol@def@extract@fil@iii!, whose
+% body is equivalent to
+% 

+% \begin{quote}
+% \let\@sverb\latex@sverb
+% \verb*|\def\pcol@extract@fil@iii#1fil#2\@nil{%|\\
+% |    \@tempdimb\pcol@setcw@filunit\relax \@tempdimb#1\@tempdimb}|
+% \end{quote}
+% 

+% just once at the top level too.
+% 

+%    \begin{macrocode}
+\edef\pcol@def@extract@fil{%
+  \def\noexpand\pcol@extract@fil
+  ##1\space\pcol@kw@plus\space##2\space\pcol@kw@minus##3\noexpand\@nil{%
+    \noexpand\pcol@extract@fil@i##2\noexpand\@nil}}
+\pcol@def@extract@fil
+\def\pcol@extract@fil@i#1.#2\@nil{\def\reserved@a{#1.#2}%
+  \afterassignment\pcol@extract@fil@ii\count@#2\@nil}
+\def\pcol@extract@fil@ii#1\@nil{\def\reserved@b{#1}%
+  \ifx\reserved@b\pcol@kw@pt \@tempdimb\z@
+  \else \expandafter\pcol@extract@fil@iii\reserved@a\@nil
+  \fi}
+\edef\pcol@def@extract@fil@iii{%
+  \def\noexpand\pcol@extract@fil@iii##1\pcol@kw@fil##2\noexpand\@nil{%
+    \@tempdimb\noexpand\pcol@setcw@filunit\relax \@tempdimb##1\@tempdimb}}
+\pcol@def@extract@fil@iii
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@def@extract@pt}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to define \cs{pcol@extract@pt}.}

+% \begin{macro}{\pcol@extract@pt}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to extract the factor of \string\texttt{pt} from the
+%	 \cs{the} representaion of a dimension.}

+% 

+% The macro $\!\pcol@extract@pt!\<f\>|pt|\<scale\>$ is solely used in
+% \!\pcol@setcw@calcf! to extract $f$ from a dimension in the form of
+% $f|pt|$ and to let the macro $\<scale\>$ have $f$.  Since this macro has
+% the keyword |pt| in its argument specification, we \!\def!ine it using
+% \!\pcol@def@extract@pt!, whose body is equivalent to
+% 

+% \begin{quote}
+% \let\@sverb\latex@sverb
+% |\def\pcol@extract@pt#1pt#2{\def#2{#1}}|
+% \end{quote}
+% just once at the top level again.
+% 

+%    \begin{macrocode}
+\edef\pcol@def@extract@pt{%
+  \def\noexpand\pcol@extract@pt##1\pcol@kw@pt##2{\def##2{##1}}}
+\pcol@def@extract@pt
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% 
+% 
+% \section{Counter Operations}
+% \label{sec:imp-counter}
+% 
+% \begin{macro}{\globalcounter}
+% \changes{v1.2-7}{2013/05/11}
+% 	{Examine if the argument counter is already in
+%	 $\string\mathit{\Theta}^g$ to avoid the duplicatoin in the list
+%	 which caused a bug.}

+% \changes{v1.32-1}{2015/10/10}
+% 	{Modified according to the introduction of \cs{globalcounter*}.}

+% \begin{macro}{\pcol@globalcounter@s}
+% \changes{v1.32-1}{2015/10/10}
+% 	{Added for \cs{globalcounter*}.}

+% \begin{macro}{\pcol@globalcounter}
+% \changes{v1.32-1}{2015/10/10}
+% 	{Renamed from \cs{globalcounter} according to the introduction of
+%	 \cs{globalcounter*}.}

+% \begin{macro}{\pcol@gcounters}
+% The API macro $\!\globalcounter!\ARg{ctr}$, implemented by
+% \!\pcol@globalcounter! and also used in \!\pcol@fnlayout@p! to globalize the
+% counter \counter{footnote}, defines that $\arg{ctr}$ is a \gcounter, and
+% thus adds it to $\CG=\Midx{\!\pcol@gcounters!}$, which has \counter{page}
+% at initial.  Note that we examines if $\arg{ctr}\in\CG$ prior to the
+% addition to avoid the duplication in $\CG$.  Also note that initial
+% definition of \!\pcol@gcounters! is done by \!\gdef! just for consistent
+% \!\global!  assignments to it.  On the other hand \!\globalcounter!|*|,
+% implemented by \!\pcol@globalcounter@s!, makes all counters kept in
+% \!\cl@@ckpt! global by letting \!\pcol@gcounters! have the list.
+% Switching these two functionality is done by \!\globalcounter! examining
+% if it is followed by a |*| by \!\@ifstar!.
+% 

+%    \begin{macrocode}
+%% Counter Operations
+
+\def\globalcounter{\@ifstar\pcol@globalcounter@s\pcol@globalcounter}
+\def\pcol@globalcounter@s{\global\let\pcol@gcounters\cl@@ckpt}
+\def\pcol@globalcounter#1{{%
+  \@tempswafalse \def\reserved@a{#1}%
+  \def\@elt##1{\def\reserved@b{##1}%
+    \ifx\reserved@a\reserved@b \@tempswatrue \fi}%
+  \pcol@gcounters
+  \if@tempswa\else \@cons\pcol@gcounters{{#1}}\fi}}
+\gdef\pcol@gcounters{\@elt{page}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\localcounter}
+% \changes{v1.2-6}{2013/05/11}
+%	{Introduced to remove the argument counter from
+%	 $\string\mathit{\Theta}^g$.}

+% 

+% The API macro \!\localcounter!\marg{ctr}, also used in
+% \!\pcol@fnlayout@c! to localize the counter \counter{footnote},
+% declares that $\arg{ctr}$ is a \lcounter, and thus removes it from $\CG$
+% by \!\pcol@removecounter! if $\arg{ctr}\neq\counter{page}$.
+% 

+%    \begin{macrocode}
+\def\localcounter#1{%
+  \expandafter\ifx\csname c@#1\endcsname\c@page\else
+    \pcol@removecounter\pcol@gcounters{#1}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \KeepSpace{1}
+% \begin{macro}{\pcol@remctrelt}
+% \changes{v1.2-6}{2013/05/11}
+%	{Recode to use newly introduced \cs{pcol@removecounter}.}

+% \begin{macro}{\pcol@removecounter}
+% \changes{v1.2-6}{2013/05/11}
+%	{Introduced for the counter removal operation in
+%	 \cs{localcounter} and \cs{pcol@remctrelt}.}

+% \begin{macro}{\pcol@iremctrelt}
+% \changes{v1.2-6}{2013/05/11}
+%	{Add the first argument $\string\mathit{\Theta}'$ as the counter
+%	 list from which the second argument $\theta$ is removed.}

+% 

+% The macro $\!\pcol@remctrelt!\Arg\cg$ is invoked solely from
+% \!\pcol@zparacol!  and is applied to each \gcounter{} $\cg\in\CG$ to
+% remove it from $\CC=\!\pcol@counters!$ in which we have $\CTL$ finally.
+% The macro also moves $|\cl@|{\cdot}\cg=\clist(\cg)$
+% 

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

+% 

+% to $|\pcol@cl@|{\cdot}\cg$
+% 

+% \SpecialArrayMainIndex{\theta}{\pcol@cl@}

+% 

+% to keep the list of the descendant \lcounter{}s of $\cg$ in it, and then
+% re\!\def!ines $|\cl@|{\cdot}\cg=\!\pcol@stepcounter!\Arg\cg$
+% 

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

+% 

+% so that it is invoked on $\!\stepcounter!\Arg\cg$ to let $\val_c(\cl)=0$
+% for all $c\In0\C$ and $\cl\in\clist(\cg)$, if $\cg\neq\counter{page}$.
+% These operations are performed by a lengthy sequence with many occurrences
+% of \!\expandafter!, \!\csname! and \!\endcsname! but the sequence is
+% equivalent to the following.
+% 

+% \begin{quote}
+% $\!\let!|\pcol@cl@|{\cdot}\cg|=\cl@|{\cdot}\cg$\\
+% $\CSIndex{ifx}|\c@|{\cdot}\cg\!\c@page!|\else |

+%     |\def\cl@|{\cdot}\cg|{|\!\pcol@stepcounter!|{|\cg|}}\fi|$
+% \end{quote}
+% 

+% As for the removal of $\cg$ from $\CC$, we invoke
+% $\!\pcol@removecounter!\<\mathit{\Theta}'\>\Arg{\theta}$ giving it
+% $\mathit{\Theta}'=\CC$ and $\theta=\cg$.  This macro, also invoked from
+% $\!\localcounter!\Arg\cl$ with $\mathit{\Theta}'=\CG$ and $\theta=\cl$,
+% does $\mathit{\Theta}''\gets\mathit{\Theta}'$,
+% $\mathit{\Theta}'=\emptyset$, and then apply
+% $\!\pcol@iremctrelt!\arg{\mathit{\Theta}'}$ to each
+% $\theta'\in\mathit{\Theta}''$ to let
+% $\mathit{\Theta}'\gets\mathit{\Theta}'\cup\{\theta'\}$ by \!\@cons! if
+% $\theta'\neq\theta$.
+% 

+%    \begin{macrocode}
+\def\pcol@remctrelt#1{%
+  \expandafter\let\expandafter\reserved@a\csname cl@#1\endcsname
+  \expandafter\let\csname pcol@cl@#1\endcsname\reserved@a
+  \expandafter\ifx\csname c@#1\endcsname\c@page\else
+    \@namedef{cl@#1}{\pcol@stepcounter{#1}}%
+  \fi
+  \pcol@removecounter\pcol@counters{#1}}
+\def\pcol@removecounter#1#2{%
+  \def\reserved@a{#2}\let\reserved@b#1\relax \global\let#1\@empty
+  {\def\@elt{\pcol@iremctrelt#1}\reserved@b}}
+\def\pcol@iremctrelt#1#2{%
+  \def\reserved@b{#2}%
+  \ifx\reserved@a\reserved@b\else \@cons#1{{#2}}\fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\definethecounter}
+% The API macro $\!\definethecounter!\<\cl\>\<c\>\arg{rep}$ define the
+% \lrep{} $\arg{rep}$ for a \lcounter{} $\cl$ in a column $c$.  It
+% \!\def!ines $|\pcol@thectr@|{\cdot}\cl{\cdot}c$
+% 

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

+% 

+% to have $\arg{rep}$ in its  body.
+% 

+%    \begin{macrocode}
+\def\definethecounter#1#2#3{\@namedef{pcol@thectr@#1#2}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@thectrelt}
+% The macro $\!\pcol@thectrelt!\<\cl\>$ is invoked solely in \!\pcol@zparacol!
+% and is applied to each $\cl\in\CTL$ to define its \lrep{} of
+% default and that of the leftmost column 0.  It performs a lengthy sequence
+% with many occurrences of \!\expandafter!, \!\csname! and \!\endcsname! but
+% the sequence is equivalent to the followings.
+% 

+% \begin{quote}
+% $\!\let!|\pcol@thectr@|{\cdot}\cl|=\the|{\cdot}\cl$\\
+% $\CSIndex{ifx}|\pcol@thectr@|{\cdot}\cl{\cdot}0\!\relax!|\else |

+%     \!\let!|\the|{\cdot}\cl|=\pcol@thectr@|{\cdot}\cl{\cdot}0| \fi|$
+% \end{quote}
+% 

+% \SpecialArrayMainIndex{\theta}{\pcol@thectr@}

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

+% \SpecialArrayMainIndex{\theta}{\the}

+% 

+%    \begin{macrocode}
+\def\pcol@thectrelt#1{%
+  \expandafter\let\expandafter\reserved@a\csname the#1\endcsname
+  \expandafter\let\csname pcol@thectr@#1\endcsname\reserved@a
+  \expandafter\let\expandafter\reserved@a\csname pcol@thectr@#10\endcsname
+  \ifx\reserved@a\relax\else
+    \expandafter\let\csname the#1\endcsname\reserved@a
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@loadctrelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for inter-environment local counter conservation.}

+% \begin{macro}{\pcol@storecounters}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for inter-environment local counter conservation.}

+% \begin{macro}{\pcol@storectrelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for inter-environment local counter conservation.}

+% 

+% The macro $\!\pcol@loadctrelt!\<\cl\>\<\val_c(\cl)\>$ is invoked from
+% \!\pcol@zparacol! and \!\pcol@synccounter! and is applied to each element
+% $\<\cl,\val_c(\cl)\>\in\Cc_c$ for a column $c$ to define a macro
+% $|\pcol@ctr@|{\cdot}\cl=v(\cl)$
+% 

+% \SpecialArrayMainIndex{\theta}{\pcol@ctr@}

+% 

+% having $\val_c(\cl)$ in its body for a temporary use.  This macro or its
+% redefined version is then referred to by $\!\pcol@cmpctrelt!\<\cl\>$ or
+% $\!\pcol@storectrelt!\<\cl\>$.  The latter is invoked from
+% \!\pcol@storecounters! via \!\pcol@sscounters! to add $\<\cl,v(\cl)\>$ to
+% \!\@gtempa! by \!\@cons! to rebuild $\CC_c$ for a column $c$ in
+% \!\@gtempa!.
+% 
+% The macro \!\pcol@storecounters! is invoked solely from
+% $\!\pcol@synccounter!\<\theta\>$ to update a \lcounter{} $\theta$ with
+% $\Val(\theta)$ for \csync.  That is, \!\pcol@storecounters! is used to add
+% $\<\cl,v(\cl)\>$ to \!\@gtempa! for all $\cl\in\CTL$ by \!\pcol@sscounters!
+% giving it \!\pcol@storectrelt! as its argument, where $v(\cl)$ is modified
+% if $\cl=\theta$ or unmodifed otherwise after it is defined by
+% \!\pcol@loadctrelt!.
+% 

+%    \begin{macrocode}
+\def\pcol@loadctrelt#1#2{\@namedef{pcol@ctr@#1}{#2}}
+\def\pcol@storecounters{\pcol@sscounters\pcol@storectrelt}
+\def\pcol@storectrelt#1{\@cons\@gtempa{{#1}{\@nameuse{pcol@ctr@#1}}}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@savecounters}
+% \changes{v1.0}{2011/10/10}
+%	{Move the body to \cs{pcol@sscounters}.}

+% 

+% \begin{macro}{\pcol@savectrelt}
+% The macro \!\pcol@savecounters! is invoked from
+% \!\pcol@com@syncallcounters!, \!\pcol@stepcounter! and \!\pcol@switchcol!
+% to let $\CC_c$ for a column $c$ have the list of $\<\cl,\val_c(\cl)\>$
+% where $\val_c(\cl)$ is the value of $|\c@|{\cdot}\cl$ to be saved in
+% the list.
+% 

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

+% 

+% It does this operation invoking \!\pcol@sscounters! giving it
+% \!\pcol@savectrelt! as its argument.
+% 
+% The macro $\!\pcol@savectrelt!\<\cl\>$ adds $\<\cl,\val_c(\cl)\>$ to
+% \!\@gtempa! by \!\@cons! to rebuild $\CC_c$ for a column $c$ in
+% \!\@gtempa!.
+% 

+%    \begin{macrocode}
+\def\pcol@savecounters{\pcol@sscounters\pcol@savectrelt}
+\def\pcol@savectrelt#1{\@cons\@gtempa{{#1}{\number\csname c@#1\endcsname}}}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@sscounters}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to implement the common operations of
+%	 \cs{pcol@storecounters} and \cs{pcol@savecounters}.}

+% 

+% The macro $\!\pcol@sscounters!\arg{elt}$ is invoked from
+% \!\pcol@storecounters! with $\arg{elt}=\!\pcol@storectrelt!$ or
+% \!\pcol@savecounters! with $\arg{elt}=\!\pcol@savectrelt!$ to build
+% $\CC_c=|\pcol@counters|{\cdot}c$ for a column $c$.
+% 

+% \SpecialArrayMainIndex{c}{\pcol@counters}

+% 

+% To do that, it lets $\!\@gtempa!=()$ and then apply $\arg{elt}$ to all
+% $\cl\in\CTL=\!\pcol@counters!$ to have updated $\CC_c$ in \!\@gtempa!.
+% Then finally, \!\@gtempa! is moved into $\CC_c$ by \!\xdef!\footnote{

+% 

+% It can be done by \cs{global}\cs{let} more efficiently but it is lengthy
+% due to two \cs{expandafter}.}.
+% 

+%    \begin{macrocode}
+\def\pcol@sscounters#1{\begingroup
+  \global\let\@gtempa\@empty
+  \let\@elt#1\relax \pcol@counters
+  \let\@elt\relax
+  \expandafter\xdef\csname pcol@counters\number\pcol@currcol\endcsname{%
+    \@gtempa}%
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@cmpctrelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for inter-environment local counter conservation.}

+% 

+% The macro $\!\pcol@cmpctrelt!\<\theta\>$ is invoked solely from
+% \!\pcol@zparacol!  and is applied to each $\theta\in\CC$ to examine if
+% $\val_0(\theta)=\Val(\theta)$ where $\val_0(\theta)$ is in
+% $|\pcol@ctr@|{\cdot}\theta$.
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 

+% If the examination fails including due to that $|\pcol@ctr@|{\cdot}\theta$
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 

+% is undefined, we add $\theta$ to the list \!\@gtempa! by \!\@cons!.
+% 

+%    \begin{macrocode}
+\def\pcol@cmpctrelt#1{\@tempswafalse \@tempcnta\@nameuse{c@#1}%
+  \expandafter\ifx\csname pcol@ctr@#1\endcsname\relax \@tempswatrue
+  \else\ifnum\@nameuse{pcol@ctr@#1}=\@tempcnta\else \@tempswatrue
+  \fi\fi
+  \if@tempswa \@cons\@gtempa{{#1}}\fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\synccounter}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as an environment-local API command.}

+% \begin{macro}{\pcol@com@synccounter}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for the implementation of the new API command
+%	 \cs{synccounter}.}
 
+% 

+% The macro $\!\pcol@com@synccounter!\<\theta\>$, being the implementation
+% of the \elocal{} API macro \!\synccounter!, lets
+% $\val_c(\theta)=\Val(\theta)$ for all $c\In0\C$.  That is, the value of
+% the counter $\theta$ is {\em broadcasted} to all columns for the
+% {\em\Uidx\csync} of $\theta$.  This broadcast is done by
+% \!\pcol@synccounter! with an argument $\!\@elt!|{|\theta|}|$ so that it
+% works only on $\theta$.
+% 

+%    \begin{macrocode}
+\def\pcol@com@synccounter#1{\pcol@synccounter{\@elt{#1}}}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@synccounter}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for \cs{synccounter} and inter-environment local counter
+%	 conservation.}

+% \begin{macro}{\pcol@syncctrelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for \cs{synccounter} and inter-environment local counter
+%	 conservation.}

+% 

+% The macro $\!\pcol@synccounter!\arg{lst}$ is invoked from
+% \!\pcol@zparacol! with $\arg{lst}=\!\@gtempa!$ and from
+% $\!\pcol@com@synccounter!\arg{ctr}$ with $\arg{lst}=\!\@elt!\Arg{ctr}$, to
+% let $\val_c(\theta)=\Val(\theta)$ for all $c\In0\C$ and all $\theta$ in
+% $\arg{lst}$.  To do that, at first we move $\arg{lst}$ into \!\reserved@a!
+% in order to make \!\@gtempa! free so that it can be used in
+% \!\pcol@storecounters!.  Next, for each $c\In0\C$, we let
+% $v(\cl)=\val_c(\cl)$ by applying \!\pcol@loadctrelt! to all
+% $\<\cl,\val_c(\cl)\>\in\Cc_c$, then scan $\arg{lst}$ applying
+% $\!\pcol@syncctrelt!\<\theta\>$ for each $\theta$ in $\arg{lst}$ to let
+% $v(\theta)=\Val(\theta)$, and finally store all $v(\cl)$ back to $\Cc_c$
+% by \!\pcol@storecounters!, where $v(\theta)$ is
+% $|\pcol@ctr@|{\cdot}\theta$.
+% 

+% \SpecialArrayIndex{\theta}{\pcol@ctr@}

+% 

+%    \begin{macrocode}
+\def\pcol@synccounter#1{{%
+  \let\@elt\relax \edef\reserved@a{#1}%
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \let\@elt\pcol@loadctrelt \@nameuse{pcol@counters\number\pcol@currcol}%
+    \let\@elt\pcol@syncctrelt \reserved@a
+    \pcol@storecounters
+    \advance\pcol@currcol\@ne}}}
+\def\pcol@syncctrelt#1{%
+    \expandafter\edef\csname pcol@ctr@#1\endcsname{\number\@nameuse{c@#1}}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\syncallcounters}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as an environment-local API command.}

+% \begin{macro}{\pcol@com@syncallcounters}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for the implementation of the new API command
+%	 \cs{syncallcounters}.}
 
+% 

+% The macro \!\pcol@com@syncallcounters!, being the implementation of the
+% \elocal{} API macro \!\syncallcounters!, makes all \lcounter{}s in all
+% columns have the value in the current column.  That is, for each
+% $c\In0\C$, we invoke \!\pcol@savecounters! to let $\val_c(\cl)={\Val}(\cl)$
+% for all $\cl\in\CTL$.
+% 

+%    \begin{macrocode}
+\def\pcol@com@syncallcounters{{%
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \pcol@savecounters \advance\pcol@currcol\@ne}}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@setctrelt}
+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{setcounter} with direct assignment with \cs{csname} and
+%	 \cs{endcsname}}

+% 

+% The macro $\!\pcol@setctrelt!\<\cl\>\<\val_c(\cl)\>$ is solely inovked
+% from \!\pcol@switchcol! to swich to a column $c$ and is applied to each
+% $\<\cl,\val_c(\cl)\>\in\Cc_c$ to let $\Val(\cl)=\val_c(\cl)$ \!\global!ly.
+% It also define the \lrep{} of $\cl$, being $|\the|{\cdot}\cl$,
+% 

+% \SpecialArrayIndex{\theta}{\the}

+% 

+% to be $|\pcol@thectr@|{\cdot}\cl{\cdot}c$
+% 

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

+% 

+% if it is defined, or otherwise to be $|\pcol@thectr@|{\cdot}\cl$ which keeps
+% the original $|\the|{\cdot}\cl$.
+% 

+% \SpecialArrayIndex{\theta}{\the}

+% 

+% This \lrep{} definition is done by a lengthy sequence with many occurrences
+% of \!\expandafter!, \!\csname! and \!\endcsname!, but it is equivalent to
+% the followings.
+% 

+% \begin{quote}
+% $\CSIndex{ifx}|\pcol@thectr@|{\cdot}\cl{\cdot}c\!\relax!| |

+%     \!\let!|\the|{\cdot}\cl|=\pcol@thectr@|{\cdot}\cl$\\
+% $|\else |\!\let!|\the|{\cdot}\cl|=\pcol@thectr@|{\cdot}\cl{\cdot}c$\\
+% |\fi|
+% \end{quote}
+% % 

+%    \begin{macrocode}
+\def\pcol@setctrelt#1#2{%
+  \global\csname c@#1\endcsname#2\relax
+  \expandafter\ifx\csname pcol@thectr@#1\number\pcol@currcol\endcsname\relax
+    \expandafter\let\expandafter\reserved@a\csname pcol@thectr@#1\endcsname
+  \else
+    \expandafter\let\expandafter\reserved@a
+      \csname pcol@thectr@#1\number\pcol@currcol\endcsname
+  \fi
+  \expandafter\let\csname the#1\endcsname\reserved@a}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@stepcounter}
+% \changes{v1.0}{2011/10/10}
+%	{Change the order of operations.}

+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{csname}/\cs{endcsname} with \cs{@nameuse}.}

+% \begin{macro}{\pcol@stpldelt}
+% \begin{macro}{\pcol@stpclelt}
+% 

+% The macro $\!\pcol@stepcounter!\<\cg\>$ is invoked from
+% $\!\stepcounter!\<\cg\>$ for a \gcounter{} $\cg$ because
+% $|\cl@|{\cdot}\cg$
+% 

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

+% 

+% is modified by \!\pcol@remctrelt! so as to invoke this macro to zero-clear
+% \lcounter{}s $\theta\in\clist(\cg)$.  To do that, we do the followings in
+% a group for each $c\In0\C$.  First we apply
+% $\!\pcol@stpldelt!\<\cl\>\<\val_c(\cl)\>$ to each
+% $\<\cl,\val_c(\cl)\>\in\Cc_c$ to let $\Val(\cl)=\val_c(\cl)$ locally.
+% Then we apply $\!\pcol@stpclelt!\<\theta\>$ to each $\theta\in\clist(\cg)$
+% to let $\Val(\theta)=0$.  Finally, we invoke \!\pcol@savecounters! to let
+% $\val_c(\cl)=\Val(\cl)$ for all $\cl\in\CTL$ to reflect the zero-clear of
+% $\theta\in\clist(\cg)$.
+% 
+% After the operations above, we apply $\!\@stpelt!\<\theta\>$ to each
+% $\theta\in\clist(\cg)$ for \!\global! zero-clearing.
+% 

+%    \begin{macrocode}
+\def\pcol@stepcounter#1{\begingroup
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \let\@elt\pcol@stpldelt \@nameuse{pcol@counters\number\pcol@currcol}%
+    \let\@elt\pcol@stpclelt \@nameuse{pcol@cl@#1}%
+    \pcol@savecounters
+   \advance\pcol@currcol\@ne}%
+  \endgroup
+  \let\@elt\@stpelt \@nameuse{pcol@cl@#1}}
+\def\pcol@stpldelt#1#2{\csname c@#1\endcsname#2\relax}
+\def\pcol@stpclelt#1{\csname c@#1\endcsname\z@}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \section{Column-Switching Commands and Environments}
+% \label{sec:imp-switch}
+% 
+% \begin{macro}{\pcol@par}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for \cs{par}-if-necessary operation.}

+% 

+% Before giving the definition of \cswitch{} commands and environments, we
+% define a commonly used macro \!\pcol@par!, which do \CSIndex{par} if
+% necessary, i.e., we are not in vertical mode.  The reason why we don't
+% simply do \CSIndex{par} is that it may have some definition different from
+% \!\@@par! and thus an incautious repetition of \CSIndex{par} may cause
+% undesirable results.  This macro is used in \!\pcol@com@switchcolumn!,
+% \!\pcol@sptext!, \!\pcol@com@endcolumn!, \!\pcol@flushclear!,
+% and \!\endparacol!.
+% 

+%    \begin{macrocode}
+%% Column-Switching Commands and Environments
+
+\def\pcol@par{\ifvmode\else \par \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\switchcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@switchcolumn} for localization.}

+% \begin{macro}{\pcol@com@switchcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implementation of \cs{switchcolumn}.}

+% \changes{v1.0}{2011/10/10}
+%	{Add \cs{pcol@defcolumn} to clarify the behavior of \texttt{column}.}

+% \begin{macro}{\pcol@switchcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Add the check of $d\geq0$.}

+% \changes{v1.31}{2013/10/10}
+%	{Add a space before the number of columns in the error message.}

+% 

+% \begin{macro}{\pcol@iswitchcolumn}
+% The macro $\!\pcol@com@switchcolumn!|[|d|]|$, being the implementation of the
+% \elocal{} API macro \!\switchcolumn!, switches to the column $d$ if provided
+% through its optional argument, or to $d=(c+1)\bmod\C$ otherwise where $c$
+% is the ordinal of the current column.  After making it sure to be in
+% vertical mode by \!\pcol@par!, it invokes \!\pcol@defcolumn! to give
+% \!\pcol@com@column!(|*|) their
+% \!\def!initions for occurrences not as the very first \cswitch{} command
+% or environment of the current \env{paracol} environment.  Then, after
+% calculating $d=(c+1)\bmod\C$, this macro simply invokes
+% $\!\pcol@switchcol!|[|d|]|$ with or without the calculated $d$ depending
+% on the existance of the optional argument delimitor `|[|'.
+% 
+% The macro $\!\pcol@switchcolumn!|[|d|]|$ lets $\!\pcol@nextcol!=d$ and
+% confirms $0\leq d<\C$ or abort the execution by \!\PackageError! if it
+% does not hold.  Then it invokes \!\pcol@iswitchcolumn! if
+% $\!\switchcolumn!|[|d|]|$ is followed by a `|*|', or \!\pcol@switchcol!
+% othewise.
+% 
+% The macro $\!\pcol@iswitchcolumn!|[|\arg{text}|]|$ invokes
+% $\!\pcol@sptext!|[|\arg{text}|]|$ if the optional argument is provided, or
+% \!\pcol@switchcol! otherwise, after letting $\CSIndex{ifpcol@sync}=\true$
+% for \exsync{}.
+% 

+%    \begin{macrocode}
+\def\pcol@com@switchcolumn{\pcol@par
+  \pcol@defcolumn
+  \@tempcnta\pcol@currcol \advance\@tempcnta\@ne
+  \ifnum\@tempcnta<\pcol@ncol\else \@tempcnta\z@ \fi
+  \@ifnextchar[%]
+    \pcol@switchcolumn{\pcol@switchcolumn[\@tempcnta]}}
+\def\pcol@switchcolumn[#1]{%
+  \pcol@nextcol#1\relax
+  \@tempswafalse
+  \ifnum#1<\z@ \@tempswatrue \fi
+  \ifnum#1<\pcol@ncol\else \@tempswatrue \fi
+  \if@tempswa
+    \PackageError{paracol}{%
+      Column number \number#1 must be less than \number\pcol@ncol}\@eha
+    \pcol@nextcol\z@
+  \fi
+  \@ifstar\pcol@iswitchcolumn\pcol@switchcol}
+\def\pcol@iswitchcolumn{%
+  \global\pcol@synctrue
+  \@ifnextchar[%]
+    \pcol@sptext\pcol@switchcol}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@sptext}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{long} to allow \cs{par} in its argument.}

+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{par} with \cs{pcol@par}.}

+% \changes{v1.0}{2011/10/10}
+%	{Add $\cs{ifpcol@mctext}\EQ\mathit{true}$ for restriction of the
+%	 broadcast of \cs{if@nobreak} and \cs{everypar}.}

+% \changes{v1.2-4}{2013/05/11}
+%	{Add \cs{pcol@swapcolumn} for column-swapping.}

+% \changes{v1.2-5}{2013/05/11}
+% 	{Add setting of \cs{columnwidth}, \cs{linewidth} and \cs{parshape}
+%	 to have indented spanning text with surrounding
+%	 \string\texttt{list}-like environments.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Add $\cs{ifpcol@sptextstart}\EQ\string\mathit{true}$ before first
+% 	 synchronized column-switching to let \cs{pcol@output@switch} save
+%	 pre-spanning-text stuff, move the timing of
+%	 $\cs{ifpcol@sptext}\EQ\string\mathit{true}$ from the end of
+%	 spanning text to the beginning so that \cs{output} routine for a
+%	 page break in the text capture the pre-break portion, and remove
+%	 the invocation of \cs{pcol@swapcolumn} because spanning texts are
+%	 now always put into the column-0.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Add globalization of \cs{@svsechd} and \cs{@svsec}.}
+% 

+% The macro $\!\pcol@sptext!|[|\arg{text}|]|$ is invoked from
+% \!\pcol@zparacol! and \!\pcol@iswitchcolumn! to put a \Uidx\mctext{}
+% $\arg{text}$ given as the optional argument of the former or that of
+% \!\switchcolumn!|*| and its relative envrironment openers for the latter.
+% The macro has \!\long!  attribute because the \mctext{} may have
+% \CSIndex{par}.  Since the text is put in the column-0 regardless of its
+% physical position, we let \!\pcol@nextcol!  have 0 after saving the target
+% column $d=\!\pcol@nextcol!$ in \!\@tempcnta!.  Then we switch to the
+% column by \!\pcol@switchcol!, after turning $\CSIndex{ifpcol@sync}=\true$
+% to set a \sync{}ation point above the text and
+% $\CSIndex{ifpcol@sptextstart}=\true$ to tell \!\pcol@output@switch! to
+% prepare the capture of \mctext{} saveing the \prespan{}.
+% 
+% Next, we let $\CSIndex{ifpcol@sptextstart}=\false$ and
+% $\CSIndex{ifpcol@sptext}=\true$ to indicate the main vertical list
+% contains only the \mctext{} and it is to be captured by \!\output!
+% routine.  Then the $\arg{text}$ is put in a group in which we let
+% $\!\columnwidth!=\!\hsize!=\!\textwidth!$ and
+% $\!\linewidth!=\!\textwidth!-\lrm$ with \!\parshape! to indent lines by
+% \!\@totalleftmargin! if $\lrm>0$, to let \mctext{} span across all columns
+% reflecting the indentation in the \env{list}-like environments surrounding
+% \env{paracol} if any.  We also let $\!\col@number!=1$ to ensure again that
+% \!\maketitle!  produces a title without \!\twocolumn! if it is in the
+% \mctext.
+% 
+% Then, after invoking \!\pcol@par! to ensure to be in vertical
+% mode, we \!\global!ize \!\@svsechd! and \!\@svsec! which may be defined in
+% a lower-level sectioning command such as \!\paragraph! in the \mctext{} so
+% that they are properly expanded in \!\everypar! inserted at the beginning
+% of the first paragraph of the column to which we switch shortly, even when
+% the sectioning command is used inappropriately in the \mctext.
+% We also \!\global!ize \!\everypar! by a sequence with three
+% \!\expandafter! so that \!\pcol@output@switch! for the \sync{}ed
+% \cswitch{} we make shortly broadcasts it to other columns.  Finally after
+% closing the group, we let $\!\pcol@nextcol!=d$ and
+% $\CSIndex{pcol@sync}=\true$ to set another \sync{}ation point below the
+% \mctext{} and to make the captured text combined with \prespan, and then
+% invoke \!\pcol@switchcol!  to switch the coloumn $d$.
+% 

+%    \begin{macrocode}
+\long\def\pcol@sptext[#1]{%
+  \@tempcnta\pcol@nextcol
+  \global\pcol@synctrue \pcol@nextcol\z@
+  \global\pcol@sptextstarttrue
+  \pcol@switchcol
+  \global\pcol@sptextstartfalse \global\pcol@sptexttrue
+  \begingroup
+    \columnwidth\textwidth \hsize\columnwidth
+    \linewidth\columnwidth \advance\linewidth-\pcol@lrmargin
+    \ifdim\pcol@lrmargin>\z@ \parshape\@ne\@totalleftmargin\linewidth \fi
+    \col@number\@ne #1\pcol@par
+    \global\let\@svsechd\@svsechd \global\let\@svsec\@svsec
+    \expandafter\global\expandafter\everypar\expandafter{\the\everypar}%
+  \endgroup
+  \pcol@nextcol\@tempcnta \global\pcol@synctrue \pcol@switchcol}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@switchcol}
+% \changes{v1.0}{2011/10/10}
+%	{Add \cs{pcol@aconly} for disabling \cs{addcontentsline}.}

+% \changes{v1.2-2}{2013/05/11}
+% 	{Add column-scanning and page-overflow check for synchronized
+%	 column-switching.}

+% \changes{v1.2-4}{2013/05/11}
+%	{Add \cs{pcol@swapcolumn} for column-swapping to turn
+%	 \cs{if@firstcolumn}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Remove settig \cs{if@firstcolumn} and the invocation of
+%	 \cs{pcol@swapcolumn} for it because the position of marginal notes
+%	 are now controlled by \cs{pcol@addmarginpar}.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Add setting $V_E\EQ\cs{pcol@@ensurevspace}$ and reinitialization of
+%	 \cs{pcol@ensurevspace} for avoidance of post-synchronization
+%	 inconsistent page break.}

+% \changes{v1.35-5}{2018/12/31}
+% 	{Add the invocation of $\cs{pcol@colpream}\cdot c$.}
+% 

+% The macro \!\pcol@switchcol! is invoked from \!\pcol@switchcolumn!,
+% \!\pcol@iswitchcolumn!, \!\pcol@sptext! and \!\endparacol! to switch the
+% column $d=\!\pcol@nextcol!$.  First, we save \lcounter{}s in the current
+% column $c$ into $\Cc_c$ by \!\pcol@savecounters!.
+%
+% Next, if $\CSIndex{ifpcol@sync}=\true$, we do the followings.  At first we
+% let $\VE={}$\!\pcol@@ensure~vspace! have the natrual component of
+% \!\pcol@ensurevspace! which can have a glue specified by \!\ensurevspace!,
+% so that it is referred to by \!\pcol@sync! as the minimum space required
+% below the \sync{}ation point we are now setting.  Second, we invoke
+% \!\pcol@visitallcols! temporarily turning $\CSIndex{ifpcol@sync}=\false$
+% for \cscan{}ning to visit all columns but current one to give \TeX's page
+% builder the chance to break \colpage{}s in the \tpage{} with \Scfnote{}s
+% which could have not been presented in the last visit of the columns.
+% Third, we make an \!\output! request with $\!\penalty!=\!\pcol@op@switch!$
+% to invoke \!\pcol@output@switch! by \!\pcol@invokeoutput! with
+% $\CSIndex{ifpcol@sync}=\true$ to make \sync{}ed switch to the column $d$.
+% This invocation may result in $\CSIndex{ifpcol@flush}=\true$ to mean the
+% \tpage{} should be broken before setting the \sync{}ation point.
+% Therefore if so, since \!\pcol@output@switch! switched to the tallest
+% column rather than $d$, we put \!\vfil! and \!\penalty!|-10000| to force
+% page break, make \cscan{} with \!\newpage! put into each column to have
+% some floats in the column in the new \tpage{}, and then invoke
+% \!\pcol@output@switch!  again until it returns
+% $\CSIndex{ifpcol@flush}=\false$ telling us it successfully sets the
+% \sync{}ation point switching to the column $d$.  Then as the last operation
+% specific to \sync{}ed \cswitch{}, we invoke \!\ensurevspace! with
+% \!\baselineskip! to give the default of $\VE$ for the next \sync{}ation.
+% 
+% Otherwise, i.e., if $\CSIndex{ifpcol@sync}=\false$, we simply make the
+% \!\output! request for \!\pcol@output@switch! to switch to the column $d$.
+% 
+% Then we scan $\Cc_d$ applying \!\pcol@setctrelt! to each
+% $\<\cl,\val_d(\cl)\>\in\Cc_d$ to let $\Val(\cl)={\val_d(\cl)}$.  We also
+% scan $\T=\!\pcol@aconly!$ applying \!\pcol@aconlyelt! to each
+% $\<t_c,c\>\in T$ to inhibit \!\addcontentsline! to the contents file of
+% type $t_d$ as specified so by $\!\addcontentsonly!\arg{t_d}\~\arg{d}$.
+% After that, we let $\!\@elt!=\!\relax!$ to make it sure that any lists can
+% be manipulated without unexpected application of a macro to their
+% elements.
+% 
+% Finally, we invoke $|\pcol@colpream|{\cdot}c$, where $c=-1$ if
+% $\CSIndex{ifpcol@sptextstart}=\true$ to mean the \cswitch{} is for a
+% \sptext{}, or $c=d$ otherwise.
+% 

+% \SpecialArrayIndex{c}{\pcol@colpream}

+% 

+%    \begin{macrocode}
+\def\pcol@switchcol{%
+  \pcol@savecounters
+  \ifpcol@sync
+    \@tempdima\pcol@ensurevspace\relax
+    \edef\pcol@@ensurevspace{\number\@tempdima sp\relax}%
+    \global\pcol@syncfalse \pcol@visitallcols\@@par \global\pcol@synctrue
+    \pcol@invokeoutput\pcol@op@switch
+    \@whilesw\ifpcol@flush\fi{%
+      \vfil \penalty-\@M
+      \global\pcol@syncfalse \pcol@visitallcols\newpage \global\pcol@synctrue
+      \pcol@invokeoutput\pcol@op@switch}%
+    \ensurevspace{\baselineskip}%
+  \else
+    \pcol@invokeoutput\pcol@op@switch
+  \fi
+  \let\@elt\pcol@setctrelt
+  \csname pcol@counters\number\pcol@currcol\endcsname
+  \let\@elt\pcol@aconlyelt \pcol@aconly \let\@elt\relax
+  \@nameuse{pcol@colpream\ifpcol@sptextstart-1\else\number\pcol@currcol\fi}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@visitallcols}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for column-scanning in synchronized column-switching and
+%	 page flushing.}

+% 

+% The macro $\!\pcol@visitallcols!\arg{cs}$, invoked from \!\pcol@switchcol!
+% and \!\pcol@flushclear!, performs \cscan{}ning putting $\arg{cs}$ into the
+% visited columns.  That is, we repeat the invocation of
+% \!\pcol@output@switch! to visit $d$ through \!\pcol@invokeoutput! with
+% $\!\penalty!=\!\pcol@op@switch!$ for all $d\In0\C-\{c\}$.  In each visit,
+% we put $\arg{cs}\in\{\!\@@par!,\!\newpage!\}$ to have a chance of or to
+% force page break in each visited \colpage{}.  Finally we go back to $c$ to
+% restore its \cctext{} especially when we are leaving the column 0 for
+% \mctext.  That is, $\cc_c(\sw)$ and $\cc_c(\ep)$ should be presented to
+% \!\pcol@output@switch! to broadcast them to other columns.
+% 

+%    \begin{macrocode}
+\def\pcol@visitallcols#1{\begingroup
+  \@tempcnta\z@ \@tempcntb\pcol@currcol
+  \@whilenum\@tempcnta<\pcol@ncol\do{%
+    \ifnum\@tempcnta=\@tempcntb\else
+      \pcol@nextcol\@tempcnta \pcol@invokeoutput\pcol@op@switch #1%
+    \fi
+    \advance\@tempcnta\@ne}%
+  \pcol@nextcol\@tempcntb \pcol@invokeoutput\pcol@op@switch
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{3}
+% \begin{macro}{\column}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@column} for localization.}

+% \begin{macro}{\column*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@column*} for localization.}

+% \begin{macro}{\pcol@com@column}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{column}.}

+% \begin{macro}{\pcol@com@column*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{column*}.}

+% \begin{macro}{\pcol@defcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{column} with \cs{pcol@com@column} and \cs{switchcolumn}
+%	 with \cs{pcol@switchenv}.}

+% 

+% The macros \!\pcol@com@column!(|*|), the implementations of the \elocal{}
+% API commands \!\column!(*), starts the environment |column(*)|.
+% 

+% \Midx{\EnvIndex{column}}\Midx{\EnvIndex{column*}}

+% 

+% Basically, the macros do \!\switch~column!\~(|*|), but if the environment
+% starts just after \beginparacol{} the macro have to switch to the column
+% 0.  Therefore, the definitions for this very-beginning appearance are
+% given in \!\pcol@zparacol! to do (almost) nothing, and then those for
+% other ones are given by \!\pcol@defcolumn! invoked in
+% \!\pcol@com@switchcolumn!  to invoke
+% \!\pcol@switchenv!|{column|(|*|)|}|(|*|) which then invokes
+% \!\switchcolumn!.  Note that the definition of non-starred
+% \!\pcol@com@column! has \!\relax!  after the invocatoin of
+% \!\pcol@switchenv!  so that \!\@ifnextchar! and \!\@ifstar! to examine the
+% existence of `|[|' and `|*|' definitely tells us no even if the body of the
+% environment starts with a `|[|' or `|*|'.
+% 

+%    \begin{macrocode}
+\def\pcol@defcolumn{%
+  \gdef\pcol@com@column{\pcol@switchenv{column}\relax}%
+  \global\@namedef{pcol@com@column*}{\pcol@switchenv{column*}*}}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{10}
+% \begin{macro}{\nthcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@nthcolumn} for localization.}

+% \begin{macro}{\nthcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@nthcolumn*} for localization.}

+% \begin{macro}{\pcol@com@nthcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{nthcolumn} with the
+%	 inhibition of column-switching in the environment.}

+% \begin{macro}{\pcol@com@nthcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{nthcolumn*} with the
+%	 inhibition of column-switching in the environment.}

+% \begin{macro}{\leftcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@leftcolumn} for localization.}

+% \begin{macro}{\leftcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@leftcolumn*} for localization.}

+% \begin{macro}{\pcol@com@leftcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{leftcolumn} with the
+%	 inhibition of column-switching in the environment.}

+% \begin{macro}{\pcol@com@leftcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{leftcolumn*} with the
+%	 inhibition of column-switching in the environment.}

+% \begin{macro}{\rightcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@rightcolumn} for localization.}

+% \begin{macro}{\rightcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@rightcolumn*} for localization.}

+% \begin{macro}{\pcol@com@rightcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{rightcolumn} with the
+%	 inhibition of column-switching in the environment.}

+% \begin{macro}{\pcol@com@rightcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{rightcolumn*} with the
+%	 inhibition of column-switching in the environment.}

+% 

+% The macros $\!\pcol@com@nthcolumn!(|*|)\arg{d}$,
+% \!\pcol@com@leftcolumn!(|*|) and |\pcol@com@right|\~|column|(|*|) are the
+% implementations of \elocal{} API macros \!\nthcolumn!(|*|)$\arg{d}$,
+% \!\leftcolumn!(|*|) and \!\rightcolumn!(|*|) respectively.  They start
+% corresponding environments |nthcolumn|(|*|), |leftcolumn|(|*|), and
+% |rightcolumn|(|*|)
+% 

+% \Midx{\EnvIndex{nthcolumn}}\Midx{\EnvIndex{nthcolumn*}}

+% \Midx{\EnvIndex{leftcolumn}}\Midx{\EnvIndex{leftcolumn*}}

+% \Midx{\EnvIndex{rightcolumn}}\Midx{\EnvIndex{rightcolumn*}}

+% 

+% simply invoking \!\pcol@switchenv!$\Arg{env}$\~(|*|), where $\arg{env}$ is
+% the name of each environment, giving it $d$, 0 and 1 repectively as its
+% optional argument for the target column.
+% 

+%    \begin{macrocode}
+\def\pcol@com@nthcolumn#1{\pcol@switchenv{nthcolumn}[#1]\relax}
+\@namedef{pcol@com@nthcolumn*}#1{\pcol@switchenv{nthcolumn*}[#1]*}
+\def\pcol@com@leftcolumn{\pcol@switchenv{leftcolumn}[0]\relax}
+\@namedef{pcol@com@leftcolumn*}{\pcol@switchenv{leftcolumn*}[0]*}
+\def\pcol@com@rightcolumn{\pcol@switchenv{rightcolumn}[1]\relax}
+\@namedef{pcol@com@rightcolumn*}{\pcol@switchenv{rightcolumn*}[1]*}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@switchenv}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to inhibit column-switching in the environment.}

+% \changes{v1.31}{2013/10/10}
+%	{Fix the misspell ``swicthing'' in the error message.}

+% 

+% The macro $\!\pcol@switchenv!\arg{env}$ is invoked from
+% $|\pcol@com@|{\cdot}\arg{env}$ where $\arg{env}\in
+% \{\env{column}\~(|*|),\env{nthcolumn}(|*|),\env{leftcolumn}(|*|),
+% \env{rightcolumn}(|*|)\}$ to invoke \!\switchcolumn! with the arguments
+% following $\arg{env}$ given by the invoker macros.  Before invoking
+% \!\switchcolumn!, we save it in \!\reserved@a! for the invocation and
+% re\!\def!ine it so that it will complain the illegal usage of \cswitch{}
+% commands\slash environments in the environment $\arg{env}$ by
+% \!\PackageError!.
+% 

+%    \begin{macrocode}
+\def\pcol@switchenv#1{\let\reserved@a\switchcolumn
+  \def\switchcolumn{\PackageError{paracol}{%
+    Column switching commands and environments cannot be used in #1}\@eha}
+  \reserved@a}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \KeepSpace{14}
+% \begin{macro}{\endcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endcolumn} for localization.}

+% \begin{macro}{\endcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endcolumn*} for localization.}

+% \begin{macro}{\pcol@com@endcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endcolumn} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\pcol@com@endcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endcolumn*} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\endnthcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endnthcolumn} for localization.}

+% \begin{macro}{\endnthcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endnthcolumn*} for
+%	 localization.}

+% \begin{macro}{\pcol@com@endnthcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endnthcolumn} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\pcol@com@endnthcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endnthcolumn*} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\endleftcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endleftcolumn} for
+%	 localization.}
 
+% \begin{macro}{\endleftcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endleftcolumn*} for
+%	 localization.}

+% \begin{macro}{\pcol@com@endleftcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endleftcolumn} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\pcol@com@endleftcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endleftcolumn*} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\endrightcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endrightcolumn} for
+%	 localization.}

+% \begin{macro}{\endrightcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@endrightcolumn*} for
+%	 localization.}

+% \begin{macro}{\pcol@com@endrightcolumn}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endrightcolumn} with the
+%	 globalizatoin of \cs{everypar}.}

+% \begin{macro}{\pcol@com@endrightcolumn*}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{endrightcolumn*} with the
+%	 globalizatoin of \cs{everypar}.}

+% 

+% The macro \!\pcol@com@endcolumn! is the implementation of the \elocal{}
+% API macro \!\endcolumn! to close \env{column} environment.  The macro
+% makes it sure we are in vertical mode by \!\pcol@par! and \!\global!ize
+% \!\everypar! so that it is saved in $\cc_c(\ep)$ of the current column
+% $c$ on the switch to another column.  The macro also gives the commmon
+% definition of \!\pcol@com@endcolumn*!  for \!\endcolumn*!,
+% \!\pcol@com@endnthcolumn!(|*|) for \!\endnthcolumn!(|*|),
+% \!\pcol@com@endleftcolumn!(|*|) for \!\endleftcolumn!(|*|), and
+% \!\pcol@com@endrightcolumn!(|*|) for \!\endrightcolumn!(|*|).
+% 

+%    \begin{macrocode}
+\def\pcol@com@endcolumn{\pcol@par
+  \expandafter\global\expandafter\everypar\expandafter{\the\everypar}}
+\expandafter\let\csname pcol@com@endcolumn*\endcsname\pcol@com@endcolumn
+\let\pcol@com@endnthcolumn\pcol@com@endcolumn
+\expandafter\let\csname pcol@com@endnthcolumn*\endcsname\pcol@com@endcolumn
+\let\pcol@com@endleftcolumn\pcol@com@endcolumn
+\expandafter\let\csname pcol@com@endleftcolumn*\endcsname\pcol@com@endcolumn
+\let\pcol@com@endrightcolumn\pcol@com@endcolumn
+\expandafter\let\csname pcol@com@endrightcolumn*\endcsname\pcol@com@endcolumn
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\definecolumnpreamble}
+% \changes{v1.35-5}{2018/12/31}
+% 	{Introduced to define a column preamble.}

+% 

+% The API macro \!\definecolumnpreamble!\marg{c}\marg{pream} is to define
+% the \colpream{} $\arg{pream}$ for the column $c$ or that for \sptext{}s if
+% $c=-1$.  After assiging $c$ to \!\@tempcnta! to ensure $c$ is a number,
+% the macro $|\pcol@colpream|{\cdot}c$ is |\def|ined to have $\arg{pream}$.
+% 

+% \SpecialArrayMainIndex{c}{\pcol@colpream}

+% 

+%    \begin{macrocode}
+\def\definecolumnpreamble#1#2{\@tempcnta#1\relax
+  \expandafter\gdef\csname pcol@colpream\number\@tempcnta\endcsname{#2}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% \begin{macro}{\ensurevspace}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to declare the minimum space $V_E$ below a
+%	 synchronization point to let it stay in a page.}

+% \begin{macro}{\pcol@ensurevspace}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to keep $V_E$ declared by \cs{ensurevspace}.}

+% \begin{macro}{\pcol@@ensurevspace}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to pass $V_E$ declared by \cs{ensurevspace} to
+%	 \cs{output} routine.}

+% 

+% The API macro $\!\ensurevspace!\ARg{space}$ is to declare that the
+% \sync{}ation point following it must be thrown to the next page unless the
+% page has the vertical $\arg{space}$ below the \sync{}ation point.  The
+% macro makes a dummy assignment of $\arg{space}$ to \!\@tempdima! to ensure
+% the argument is a dimension including forced one, or in other words to
+% raise an error if not in this macro rather than at the time $\arg{space}$
+% is {\em evaluated} in \!\pcol@switchcol!.  Then $\arg{space}$ is kept in
+% \!\pcol@ensurevspace! so that $\arg{space}$ is evaluated in
+% \!\pcol@switchcol! for the \sync{}ation in question to pass the value to
+% \!\pcol@sync!  through the macro $\!\pcol@@ensurevspace!=\Uidx\VE$,
+% especially when it has register references, for example to
+% \!\baselineskip!.  To give the default of \!\pcol@ensurevspace!, we invoke
+% \!\ensurevspace! at the top level with \!\baselineskip!.
+% 

+%    \begin{macrocode}
+\def\ensurevspace#1{{\@tempdima#1\relax \gdef\pcol@ensurevspace{#1}}}
+\ensurevspace{\baselineskip}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \section{Disabling \cs{addcontentsline}}
+% \label{sec:imp-aconly}
+% 
+% \begin{macro}{\addcontentsonly}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@aconly}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% 

+% The API macro $\!\addcontentsonly!\arg{t}\arg{c}$ makes the type $t$
+% contents file written by commands appearing only in the column $c$.  The
+% macro simply add the pair $\<t,c\>$ to the list $\Uidx\T=\!\pcol@aconly!$
+% being empty at initial, after confirming we know the type $t$, one of
+% |toc|, |lof| and |lot| so far, by the fact $|\pcol@ac@def|{\cdot}t$ is
+% defined, or abort execution by \!\PackageError!.
+% 

+%    \begin{macrocode}
+%% Disabling \addcontentsline
+
+\def\addcontentsonly#1#2{%
+  \@ifundefined{pcol@ac@def@#1}
+    {\PackageError{paracol}{Unknown contents type #1}\@eha}\relax
+  \@cons\pcol@aconly{{#1}{#2}}}
+\gdef\pcol@aconly{}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@aconlyelt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% 

+% The macro $\!\pcol@aconlyelt!\arg{t_d}\arg{d}$ is invoked solely in
+% \!\pcol@switchcol!  for the \cswitch{} to column $c$, and is applied to
+% each $\<t_d,d\>\in\T$ to enable \!\addcontentsline! for $t_d$ if $d=c$ by
+% the invocation of $|\pcol@ac@def@|{\cdot}t_d$
+% 

+% \SpecialArrayMainIndex{t}{\pcol@ac@def@}
+% 

+% with an argument |enable|, or to disable if $d\neq c$ with |disable|.
+% 

+%    \begin{macrocode}
+\def\pcol@aconlyelt#1#2{%
+  \ifnum#2=\pcol@currcol \@nameuse{pcol@ac@def@#1}{enable}%
+  \else \@nameuse{pcol@ac@def@#1}{disable}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@gobblethree}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@addcontentsline}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% 

+% \hfuzz0.39pt
+% The macro $\!\pcol@gobblethree!\arg{file}\arg{sec}\arg{entry}$ is used in
+% \!\pcol@ac@disable@toc! and \!\pcol@ac@caption! to make
+% \!\addcontentsline! \!\let!-equal to this macro, which does nothing but
+% discarding three arguments, for disabling.  The macro
+% \!\pcol@addcontentsline! is the \LaTeX's original \!\addcontentsline! and
+% is used in the macros mentioned above to let \!\addcontentsline! act as
+% original.
+% 

+%    \begin{macrocode}
+\def\pcol@gobblethree#1#2#3{}
+\let\pcol@addcontentsline\addcontentsline
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@ac@def@toc}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@enable@toc}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@disable@toc}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% 

+% The macro $\!\pcol@ac@def@toc!\arg{eord}$ is invoked solely in
+% $\!\pcol@aconlyelt!|{toc}|\arg{c}$ to enable or disable
+% \!\addcontentsline! according to $\arg{eord}$ by making \!\@sect!
+% \!\let!-equal to \!\pcol@ac@enable@toc! which is the \LaTeX's original
+% \!\@sect!, or to \!\pcol@ac@disable@toc! respectively.  The macro
+% $\!\pcol@ac@disable@toc!
+% \<a_1\>\<a_2\>\<a_3\>\<a_4\>\<a_5\>\<a_6\>|[|\<a_7\>|]|\<a_8\>$ at first
+% disables \!\addcontentsline! by making it \!\let!-equal to
+% \!\pcol@gobblethree!, then invokes the original \!\@sect! saved in
+% \!\pcol@ac@enable@toc! ginving it all arguments $a_1$ to $a_8$, and
+% finally enables it by making it \!\let!-equal to \!\pcol@addcontentsline!.
+% Note that the argument $a_7$ is surrounded by |{| and |}| on the
+% invocation of \!\@sect! to conceal `|]|' in $a_7$.
+% 

+%    \begin{macrocode}
+\def\pcol@ac@def@toc#1{%
+  \expandafter\let\expandafter\@sect\csname pcol@ac@#1@toc\endcsname}
+\let\pcol@ac@enable@toc\@sect
+\def\pcol@ac@disable@toc#1#2#3#4#5#6[#7]#8{%
+  \let\addcontentsline\pcol@gobblethree
+  \pcol@ac@enable@toc{#1}{#2}{#3}{#4}{#5}{#6}[{#7}]{#8}%
+  \let\addcontentsline\pcol@addcontentsline}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{5}
+% \begin{macro}{\pcol@ac@def@lof}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@def@lot}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@caption@enable}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@caption@disable}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@caption@def}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@caption@if@lof}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@caption@if@lot}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% 

+% The macro $\!\pcol@ac@def@lof!\arg{eord}$ and
+% $\!\pcol@ac@def@lot!\arg{eord}$ are invoked solely in
+% $\!\pcol@aconlyelt!\<t\>\<c\>$ when $t$ is |lof| or |lot|
+% respectively.  They invoke \!\pcol@ac@caption@enable!$\<t\>$ or
+% $\!\pcol@ac@caption@disable!\<t\>$ according to $\arg{eord}$, and then
+% these macros invoke $\!\pcol@ac@caption@def!\<s\>\<t\>$ where
+% $s=\!\@tempswatrue!$ or $s=\!\@tempswafalse!$ respectievely to let
+% $\!\@caption!=\!\pcol@ac@caption!$ and $|\pcol@ac@caption@if@|{\cdot}t=s$
+% which are \!\let!-equal to \!\@tempswatrue! in default.  That is,
+% $|\pcol@ac@catption@if@|{\cdot}t$ lets $\CSIndex{if@tempswa}={}\true$ iff
+% \!\addcontentsline! for $t$ is to be enable.
+% 

+%    \begin{macrocode}
+\def\pcol@ac@def@lof#1{\@nameuse{pcol@ac@caption@#1}{lof}}
+\def\pcol@ac@def@lot#1{\@nameuse{pcol@ac@caption@#1}{lot}}
+\def\pcol@ac@caption@enable{\pcol@ac@caption@def\@tempswatrue}
+\def\pcol@ac@caption@disable{\pcol@ac@caption@def\@tempswafalse}
+\def\pcol@ac@caption@def#1#2{\let\@caption\pcol@ac@caption
+ \expandafter\let\csname pcol@ac@caption@if@#2\endcsname#1}
+\let\pcol@ac@caption@if@lof\@tempswatrue
+\let\pcol@ac@caption@if@lot\@tempswatrue
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@ac@caption}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% \begin{macro}{\pcol@ac@caption@latex}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for disabling \cs{addcontentsline}.}

+% 

+% The macro $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\<cap\>$ is made
+% \!\let!-equal to \!\@caption! by \!\pcol@ac@caption@def! to do what
+% \!\@caption! do but with enabling\slash disabling \!\addcontentsline!.  At
+% first, it invokes $|\pcol@ac@cation@if@|{\cdot}t$ where
+% $t=|\ext@|{\cdot}\arg{type}$
+% 

+% \SpecialIndex{\ext@figure}\SpecialIndex{\ext@table}

+% 

+% to let \CSIndex{if@tempswa} be $\true$ or $\false$ according to the
+% enable\slash disable status of $t$.  Then, after letting
+% $\!\addcontentsline!=\!\pcol@gobblethree!$ for disabling if $\false$, we
+% invoke \!\pcol@ac@caption@latex!, being the \LaTeX's orignial \!\@caption!,
+% giving all three arguments of \!\pcol@ac@caption! itself surrounding
+% $\arg{lcap}$ with |{| and |}| for the concealment of `|]|'.  Finally, we
+% let $\!\addcontentsline!=\!\pcol@addcontentsline!$ so that other macros
+% uses it with its original definition.
+% 

+%    \begin{macrocode}
+\long\def\pcol@ac@caption#1[#2]#3{%
+  \@nameuse{pcol@ac@caption@if@\@nameuse{ext@#1}}%
+  \if@tempswa\else \let\addcontentsline\pcol@gobblethree \fi
+  \pcol@ac@caption@latex{#1}[{#2}]{#3}%
+  \let\addcontentsline\pcol@addcontentsline}
+\let\pcol@ac@caption@latex\@caption
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% 
+% 
+% \KeepSpace{7}
+% \section{Page Flushing Commands}
+% \label{sec:imp-flush}
+% 
+% \begin{macro}{\flushpage}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@flushpage} for
+%	 localization.}

+% \begin{macro}{\pcol@com@flushpage}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{flushpage} with the
+%	 replacement of \cs{par} with \cs{pcol@par}.}

+% \begin{macro}{\clearpage}
+% \changes{v1.0}{2011/10/10}
+%	{Made \cs{let}-equal to \cs{pcol@com@clearpage} for
+%	 localization.}

+% \begin{macro}{\pcol@com@clearpage}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced as the implemenatation of \cs{clearpage} with the
+%	 replacement of \cs{par} with \cs{pcol@par}.}

+% \begin{macro}{\cleardoublepage}
+% \changes{v1.3-5}{2013/09/17}
+%	{Added as a member of local commands and made \cs{let}-equal to
+%	 \cs{pcol@com@cleardoublepage}.}

+% \begin{macro}{\pcol@com@cleardoublepage}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced as the implemenatation of \cs{cleardoulbepage}.}

+% 

+% The macros \!\pcol@com@flushpage!, \!\pcol@com@clearpage! and
+% \!\pcol@com@cleardoublepage! are the implementations of \elocal{} API
+% macro \!\flushpage!, \!\clearpage! and \!\cleardoublepage!  respectively.
+% The first two have a common structure in which we at first invoke
+% \!\pcol@flushclear! for \cscan{} and \pfcheck, and then make an \!\output!
+% request by \!\pcol@invokeoutput! with \!\penalty! being \!\pcol@op@flush!
+% or \!\pcol@op@clear! according to the commands.  On the other hand the
+% last one simply invokes \!\pcol@com@clearpage! unconditionally, and then
+% \!\pcol@com@flushpage!\footnote{

+% 

+% Unlike \LaTeX's \!\cleardoublepage!, it is unnecessary to put an empty
+% \!\hbox! before \!\flushpage! because it is active even at the top of a
+% page.}
+% 

+% if two-sided paging is enabled by $\CSIndex{if@twoside}=\true$, we are
+% in an even-numbered page, and $\CSIndex{ifpcol@paired}=\false$ to mean we
+% are not doing \npaired{} \parapag{}ing.
+% 

+%    \begin{macrocode}
+%% Page Flushing Commands
+
+\def\pcol@com@flushpage{\pcol@flushclear\voidb@x
+  \pcol@invokeoutput\pcol@op@flush}
+\def\pcol@com@clearpage{\pcol@flushclear\voidb@x
+  \pcol@invokeoutput\pcol@op@clear}
+\def\pcol@com@cleardoublepage{\pcol@com@clearpage
+  \if@twoside \ifodd\c@page\else \ifpcol@paired\else \pcol@com@flushpage
+  \fi\fi\fi}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@flushclear}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for column-scanning in synchronized column-switching and
+%	 page flushing.}

+% 

+% The macro $\!\pcol@flushclear!\arg{box}$, invoked from
+% \!\pcol@com@flushpage!, \!\pcol@com@clear~page! and \!\endparacol!,
+% performs \cscan{} and \pfcheck{} prior to page flushing or environment
+% closing.  After confirming we are in vertical mode by \!\pcol@par! and
+% letting $d=\!\pcol@nextcol!$ be $c=\!\pcol@currcol!$ to stay in $c$, we
+% invoke \!\pcol@visitallcols! for \cscan{} to give \TeX's page builder the
+% chance to break the \tpage{} prior to flushing it.
+% 
+% Then we repeat \pfcheck{} invoking \!\pcol@output@switch! through
+% \!\pcol@invokeoutput! with $\!\penalty!=\!\pcol@op@switch!$ and
+% $\CSIndex{ifpcol@clear}=|\ifpcol@|\~|sync|=\true$

+% 

+% \SpecialIndex{\ifpcol@sync}
+% 

+% until the special \!\output! routine finishes with
+% $\CSIndex{ifpcol@flush}=\false$ and $\arg{box}=\bot$, where
+% $\arg{box}=\df=\!\pcol@topfnotes!$ if this macro is invoked from
+% \!\endparacol! with non-merged \Scfnote{} typesetting.  In the repetition,
+% we put \!\vfil! and \!\penalty!|-10000| to force page break into the
+% tallest column, temporarily turning $\CSIndex{ifpcol@lastpage}=\false$
+% using \!\ifpcol@lastpagesave!  because the broken page is not last one,
+% each time the \pfcheck{} tells us to do it.  That is, we repeat the check
+% while we have too tall columns due to \Scfnote{}s or, when closing
+% \env{paracol} environment, deferred non-merged \Scfnote{}s.
+% 
+% Finally we let $\CSIndex{ifpcol@clear}$ have its default setting, i.e.,
+% $\false$.
+% 

+%    \begin{macrocode}
+\def\pcol@flushclear#1{\pcol@par
+  \pcol@nextcol\pcol@currcol
+  \pcol@visitallcols\@@par
+  \pcol@cleartrue \global\pcol@synctrue
+  \ifpcol@lastpage \pcol@lastpagesavetrue \else \pcol@lastpagesavefalse \fi
+  \pcol@invokeoutput\pcol@op@switch \ifvoid#1\else \global\pcol@flushtrue \fi
+  \@whilesw\ifpcol@flush\fi{%
+    \pcol@lastpagefalse
+    \vfil \penalty-\@M \pcol@cleartrue \global\pcol@synctrue
+    \ifpcol@lastpagesave \pcol@lastpagetrue \fi
+    \pcol@invokeoutput\pcol@op@switch
+    \ifvoid#1\else \global\pcol@flushtrue \fi}%
+  \pcol@clearfalse}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% 
+% \KeepSpace{8}
+% \section{Commands for Footnotes}
+% \label{sec:imp-fnote}
+% \changes{v1.2-2}{2013/05/11}
+%	{Add the subsection ``Commands for Footnotes'' to describe newly
+%	 introduced macros for page-wise footnotes.}

+% 
+% \begin{macro}{\footnotelayout}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced for easier declaration of footnote layout.}

+% \begin{macro}{\pcol@fnlayout@c}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced for easier declaration of column-wise footnotes.}

+% \begin{macro}{\pcol@fnlayout@p}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced for easier declaration of page-wise footnotes.}

+% \begin{macro}{\pcol@fnlayout@m}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced for easier declaration of merged footnotes.}

+% \begin{macro}{\multicolumnfootnotes}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to delclare the defalut column-wise footnote
+%	 typesetting explicitly.}

+% \begin{macro}{\singlecolumnfootnotes}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to delclare the page-wise but non-merged footnote
+%	 typesetting.}

+% \begin{macro}{\mergedfootnotes}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to delclare the page-wise and merged footnote
+%	 typesetting.}

+% 

+% The API macros $\!\footnotelayout!\Arg{l}$ is to determine that footnotes
+% are \mcfnote{} ($l=|c|$), \scfnote{} without merging ($l=|p|$), or
+% \mgfnote{} and \scfnote{} ($l=m$).  The macro examines if
+% $l\in\{|c|,|p|,|m|\}$ by the existence of the corresponding macro
+% $|\pcol@fnlayout@|{\cdot}l$
+% 

+% \SpecialArrayIndex{l}{\pcol@fnlayout@}
+% 

+% and invokes it, or complains if not by \!\PackageError!.
+% 
+% The macros \!\pcol@fnlayout@c!, \!\pcol@fnlayout@p! and
+% \!\pcol@fnlayout@m! turn switches $f_s=\CSIndex{ifpcol@scfnote}$,
+% $f_m=\CSIndex{ifpcol@mgfnote}$ and
+% $f_a=\CSIndex{ifpcol@fncounteradjustment}$ and make the counter
+% \counter{footnote} global or local as follows.
+% $$
+% \nosv\begin{array}{l|llll}
+% l&f_s&f_m&f_a&\counter{footnote}\\\hline
+% \verb|c|&\false&\false&\false&\hbox{local}\\
+% \verb|p|&\true&\false&\true&\hbox{global}\\
+% \verb|m|&\true&\true&\true&\hbox{global}
+% \end{array}
+% $$
+% Note that turning \CSIndex{ifpcol@fncounteradjustment} is done by
+% \!\fncounteradjustment! ($\true$) or \!\nofncounteradjustment! ($\false$).
+% Also note that the setting of |\ifpcol@fncounter|\~|adjustment|

+% 

+% \SpecialIndex{\ifpcol@fncounteradjustment}
+% 

+% and the globalization\slash localization of \counter{footnote} are just to
+% give defaults and thus can be overridden by API macros giving non-default
+% settings.  Another remark is that backward-compatible macros
+% \!\multicolumnfootnotes!, \!\singlecolumnfootnotes! and
+% \!\mergedfootnotes! are \!\let!-equal to \!\pcol@fnlayout@c!,
+% \!\pcol@fnlayout@p! and \!\pcol@fnlayout@m! respectively.
+% 

+%    \begin{macrocode}
+%% Commands for Footnotes
+
+\def\footnotelayout#1{\@ifundefined{pcol@fnlayout@#1}%
+  {\PackageError{paracol}{Unknown footnote layout specifier #1}}%
+  {\@nameuse{pcol@fnlayout@#1}}}
+\def\pcol@fnlayout@c{\global\pcol@scfnotefalse \global\pcol@mgfnotefalse
+  \localcounter{footnote}\nofncounteradjustment}
+\def\pcol@fnlayout@p{\global\pcol@scfnotetrue \global\pcol@mgfnotefalse
+  \globalcounter{footnote}\fncounteradjustment}
+\def\pcol@fnlayout@m{\pcol@fnlayout@p\global\pcol@mgfnotetrue}
+
+\let\multicolumnfootnotes\pcol@fnlayout@c
+\let\singlecolumnfootnotes\pcol@fnlayout@p
+\let\mergedfootnotes\pcol@fnlayout@m
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\@footnotetext}
+% \begin{macro}{\pcol@fntext}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for footnote encapsulation and deferring.}

+% \begin{macro}{\pcol@fntexttop}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for footnote encapsulation.}

+% \begin{macro}{\pcol@fntextother}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for footnote encapsulation and deferring.}

+% 

+% The macro \!\pcol@fntext!\marg{text} is our own version of \LaTeX's
+% \!\@footnotetext! used in \!\footnote! and \!\footnotetext! to \!\insert!
+% the footnote $\arg{text}$ through \!\footins!.  Since the original and our
+% own are made \!\let!-equal by \!\pcol@zparacol!, our own is active
+% throughout the environment.  The customization is done to examine if the
+% footnote should be deferred and to encapsulate the footnote in a \!\vbox!.
+% 
+% The deferred footnote insertion is in effect if the footnote typesetting
+% is \scfnote{} and \!\footnote! or \!\footnotetext!  appears in a page
+% $p<\ptop$.  If so, we put the footnote $\arg{text}$ encapsulated in a
+% \!\vbox! by \!\pcol@fntextbody! to the tail of $\df=\!\pcol@topfnotes!$
+% with \!\penalty!\!\interlinepenalty! preceding it for the split in
+% \!\pcol@deferredfootins!, using \!\pcol@fntextother!\marg{text} whose sole
+% user is this macro.  Note that the decision of deferring is done based on
+% $p=\!\pcol@page!$ which could be less than that of the page in which the
+% footnoted text appears because the paragraph having the text will have a
+% page break before the text.  Therefore, $p$ for the footnote can be
+% $\ptop$, but this misjudment will not cause problems because the footnote
+% will eventually be put in $\ptop$ through $\df$ when the page break
+% occurs.
+% 
+% Otherwise the footnote $\arg{text}$ is processed by
+% \!\pcol@fntexttop!\marg{text}, also used solely in this macro, to
+% \!\insert! it through \!\footins! as usual but after the encapsulation by
+% \!\pcol@fntextbody! and with \!\penalty!\!\interlinepenalty! following it
+% to allow \TeX's page builder to split footnotes.
+% 
+% Note that \!\pcol@fntexttop! and \!\pcol@fntextother! have \!\long!
+% property because $\arg{text}$ may have two or more paragraphs.
+% 

+%    \begin{macrocode}
+\def\pcol@fntext{%
+  \let\reserved@a\pcol@fntexttop
+  \ifpcol@scfnote \ifnum\pcol@page<\pcol@toppage
+    \let\reserved@a\pcol@fntextother
+  \fi\fi
+  \reserved@a}
+\long\def\pcol@fntexttop#1{%
+  \pcol@Logfn{\pcol@fntexttop{\@thefnmark}}%
+  \insert\footins{\pcol@fntextbody{#1}\penalty\interlinepenalty}}
+\long\def\pcol@fntextother#1{%
+  \global\setbox\pcol@topfnotes\vbox{\unvbox\pcol@topfnotes
+    \penalty\interlinepenalty\pcol@fntextbody{#1}}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@fntextbody}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for footnote encapsulation and height capping.}

+% 

+% The macro \!\pcol@fntextbody!\marg{text}, invoked from \!\pcol@fntexttop!
+% and \!\pcol@fntext~other!, encapsulates the footnote $\arg{text}$ in a
+% \!\vbox! whose height is $h_{\max}=\!\textheight!-\!\skip!\~\!\footins!$ at
+% tallest.  The encapsulation is to inhibit page breaks in a footnote
+% because the split by the break will make some skips and other items
+% eliminated causing a weird result when split portions are {\em joined}.
+% The height capping is thus required to find a page in which the footnote
+% resides.
+% 
+% The macro at first does operations done in \LaTeX's 
+% \!\@footnotetext! to put $\arg{text}$ in \!\@tempboxa! but with one
+% exception that $\!\hsize!=\!\textwidth!$ rather than \!\columnwidth! when
+% \Scfnote{} typesetting is in effect.  Note that this part is blindly copied
+% from the original though it should be meaningless to set
+% \!\interlinepenalty!, \!\splittopskip!, \!\splitmaxdepth! and
+% \!\floatingpenalty! because $\arg{text}$ is encapsulated.
+% 
+% Then the height-plus-depth of the box is compared with $h_{\max}$ and, if
+% it exceeds the limit, the height of the box is set $h_{\max}$, the
+% footnote is made followed by a \!\vss! to avoid overfull, and a warning
+% message of too tall is put by \!\PackageWarning!.  Finally, the box is put
+% into \!\footins! or $\df$ by the invoker of this macro.
+% 

+%    \begin{macrocode}
+\long\def\pcol@fntextbody#1{\setbox\@tempboxa\vbox{%
+    \reset@font\footnotesize
+    \interlinepenalty\interfootnotelinepenalty
+    \splittopskip\footnotesep
+    \splitmaxdepth\dp\strutbox \floatingpenalty\@MM
+    \hsize \ifpcol@scfnote \textwidth \else \columnwidth \fi
+    \@parboxrestore
+    \protected@edef\@currentlabel{\p@footnote\@thefnmark}%
+    \color@begingroup
+    \@makefntext{%
+      \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}%
+    \color@endgroup}%
+  \@tempdima\ht\@tempboxa \advance\@tempdima\dp\@tempboxa
+  \@tempdimb\textheight \advance\@tempdimb-\skip\footins
+  \ifdim\@tempdima>\@tempdimb
+    \setbox\@tempboxa\vbox to\@tempdimb{\unvbox\@tempboxa\vss}%
+    \PackageWarning{paracol}{Too tall footnote}%
+  \fi
+  \box\@tempboxa}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\fncounteradjustment}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to make \string\texttt{footnote} counter is consistent
+%	 with its origin at the beginning of \string\texttt{paracol} and the
+%	 number of footnotes given in the environment at its end.}

+% \begin{macro}{\nofncounteradjustment}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to disable the footnote counter adjustment.}

+% 

+% The API macros \!\fncounteradjustment! and \!\nofncounteradjustment! turns
+% |\ifpcol@|\~|fncounteradjustment|

+% 

+% \SpecialIndex{\ifpcol@fncounteradjustment} 
+% 

+% $\true$ or $\false$, to enable or disable the \counter{footnote} counter
+% adjustment letting $\!\c@footnote!=\bf+\nf$ in \Endparacol, respectively.
+% After the definition we disable the adjustment to give the default setting.
+% 

+%    \begin{macrocode}
+\def\fncounteradjustment{\global\pcol@fncounteradjustmenttrue}
+\def\nofncounteradjustment{\global\pcol@fncounteradjustmentfalse}
+\nofncounteradjustment
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\pcol@footnoterule}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to keep the original definition of \cs{footnoterule}.}

+% \begin{macro}{\pcol@@footnote}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to keep the original definition of \cs{footnote}.}

+% \begin{macro}{\pcol@@footnotemark}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to keep the original definition of \cs{footnotemark}.}

+% \begin{macro}{\pcol@@footnotetext}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced to keep the original definition of \cs{footnotetext}.}

+% 

+% The macros \!\pcol@footnoterule!, \!\pcol@@footnote!,
+% \!\pcol@@footnotemark! and \!\pcol@@footnotetext! are to keep the original
+% defitions of \!\footnoterule!, \!\footnote!, \!\footnotemark! and
+% \!\footnotetext! in them, respectively, so that we define our own versions
+% with references to the originals.
+% 

+%    \begin{macrocode}
+\let\pcol@footnoterule\footnoterule
+\let\pcol@@footnote\footnote
+\let\pcol@@footnotemark\footnotemark
+\let\pcol@@footnotetext\footnotetext
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \KeepSpace{4}
+% \begin{macro}{\footnote}
+% \begin{macro}{\pcol@footnote}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnote*} and footnote counter adjustment.}

+% \begin{macro}{\pcol@ifootnote}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnote*} and footnote counter adjustment.}

+% \begin{macro}{\footnotemark}
+% \begin{macro}{\pcol@footnotemark}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnotemark*} and footnote counter adjustment.}

+% \begin{macro}{\pcol@ifootnotemark}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnotemark*} and footnote counter adjustment.}

+% 

+% The macros \!\pcol@footnote! and \!\pcol@footnotemark! are the
+% implementations of our own versions of \!\footnote! and \!\footnotemark!
+% which are made \!\let!-equal to them by \!\pcol@zparacol!, respectively.
+% The reasons why we need to have our own are two-fold; to have starred
+% version of them; and to maintain $\nf=\!\pcol@nfootnotes!$ for the
+% \counter{footnote} counter adjustment.
+% 
+% The implementations of the starred versions
+% \!\footnote!|*|\oarg{num}\marg{text} and 
+% \!\footnotemark!|*|\~\oarg{num} have common structure in which we invoke
+% \!\pcol@adjustfnctr!$\arg{macro}$\oarg{num} if `|*|' is given, to let
+% \!\c@footnote! have the number relative to $\bf=\!\pcol@footnotebase!$ or
+% to itself.  Then the macros \!\pcol@ifootnote! or \!\pcol@ifootnotemark!
+% are invoked from \!\pcol@adjustfnctr! or the else-part of \!\@ifstar! to
+% perform the operations common to both cases with and without `|*|', i.e.,
+% invoking the original version \!\pcol@@footnote! or \!\pcol@@footnotemark!
+% after incrementing $\nf$.  One caution is that
+% $\arg{macro}=\!\pcol@ifootnote!$ for \!\footnote!, but
+% $\arg{macro}=|{|\!\pcol@ifootnotemark!\!\relax!|}|$ for \!\footnotemark!
+% so that \!\@ifnextchar! in \!\pcol@@footnotemark!  invoked from
+% \!\pcol@ifootnotemark! eats \!\relax! to terminate space skipping and thus
+% spaces following \oarg{num} are kept.
+% 

+%    \begin{macrocode}
+\def\pcol@footnote{\@ifstar{\pcol@adjustfnctr\pcol@ifootnote}\pcol@ifootnote}
+\def\pcol@ifootnote{\global\advance\pcol@nfootnotes\@ne \pcol@@footnote}
+\def\pcol@footnotemark{\@ifstar
+  {\pcol@adjustfnctr{\pcol@ifootnotemark\relax}}%
+  \pcol@ifootnotemark}
+\def\pcol@ifootnotemark{\global\advance\pcol@nfootnotes\@ne
+  \pcol@@footnotemark}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \KeepSpace{1}
+% \begin{macro}{\pcol@adjustfnctr}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnote*} and \cs{footnotemark*}.}

+% \begin{macro}{\pcol@iadjustfnctr}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnote*} and \cs{footnotemark*}.}

+% \begin{macro}{\pcol@calcfnctr}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnote*}, \cs{footnotemark*} and
+%	 \cs{footnotetext*}.}

+% 

+% The macro \!\pcol@adjustfnctr!$\arg{macro}$\oarg{num}, invoked from the
+% then-part of \!\@ifstar! in \!\pcol@footnote! and \!\pcol@footnotemark!,
+% calculates the number to be set into \!\c@footnote! by
+% \!\pcol@calcfnctr!$\arg{num}$\!\@nil! after processing the optional
+% argument $\arg{num}$ by \!\pcol@iadjustfnctr! with default `|+1|', and
+% then invoke $\arg{macro}$ being \!\pcol@ifootnote! or
+% \!\pcol@ifootnotemark!\!\relax!.  Since \!\pcol@calcfnctr! returns the
+% number \!\c@footnote! should have and the counter is incremented by
+% \!\stepcounter! in \!\pcol@@footnote! or \!\pcol@@footnotemark!, we
+% decrement the counter prior to invoke $\arg{macro}$.
+% 
+% The macro \!\pcol@calcfnctr!$\arg{num}$\!\@nil!, also invoked from
+% \!\pcol@iifootnotetext!, calculate $m$ specified by $\arg{num}$ as follows,
+% where $f=\!\c@footnote!$, to return it through \!\@tempcnta!.
+% $$
+% m=\cases{f+k&$\arg{num}=|+|k$\cr
+%           f-k&$\arg{num}=|-|k$\cr
+%           \bf+k&$\arg{num}=k$}
+% $$
+% 

+%    \begin{macrocode}
+\def\pcol@adjustfnctr#1{\@ifnextchar[%]
+  {\pcol@iadjustfnctr{#1}}{\pcol@iadjustfnctr{#1}[+1]}}
+\def\pcol@iadjustfnctr#1[#2]{\pcol@calcfnctr#2\@nil
+  \global\c@footnote\@tempcnta \global\advance\c@footnote\m@ne#1}
+\def\pcol@calcfnctr#1#2\@nil{\@tempcnta\c@footnote
+  \def\reserved@a{#1}\def\reserved@b{+}%
+  \ifx\reserved@a\reserved@b \advance\@tempcnta#2\relax
+  \else \def\reserved@b{-}%
+  \ifx\reserved@a\reserved@b \advance\@tempcnta-#2\relax
+  \else \@tempcnta\pcol@footnotebase \advance\@tempcnta#1#2\relax
+  \fi\fi}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 

+% \KeepSpace{2}
+% \begin{macro}{\footnotetext}
+% \begin{macro}{\pcol@footnotetext}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnotetext*}.}

+% \begin{macro}{\pcol@ifootnotetext}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnotetext*}.}

+% \begin{macro}{\pcol@iifootnotetext}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Introduced for \cs{footnotetext*}.}

+% 

+% The macros \!\pcol@footnotetext! is the implementation of our own versions
+% of \!\footnotetext!  which is made \!\let!-equal to it by
+% \!\pcol@zparacol!.  The reasons why we need to have our own is to have the
+% starred version.  That is, if `|*|' is not given, we simply invoke the
+% original version \!\pcol@@footnotetext!.  Otherwise we invoke
+% \!\pcol@ifootnotetext! which then examines if the optional argument
+% \oarg{num} is presented.  If so, we invoke \!\pcol@iifootnotetext! in
+% which \!\pcol@calcfnctr!$\arg{num}$\!\@nil! is invoked to have the value
+% $m$ being the footnote ordinal with which we invoke
+% \!\pcol@@footnotetext!\oarg{\mbox{$m$}} with two \!\expandafter!s to
+% extract $m$ from \!\@tempcnta!.  Otherwise, i.e., \oarg{num} is not given,
+% we increment \!\c@footnote! by \!\stepcounter! before invoking
+% \!\pcol@@footnotetext!.
+% 

+%    \begin{macrocode}
+\def\pcol@footnotetext{\@ifstar\pcol@ifootnotetext\pcol@@footnotetext}
+\def\pcol@ifootnotetext{\@ifnextchar[%]
+  \pcol@iifootnotetext{\stepcounter{footnote}\pcol@@footnotetext}}
+\def\pcol@iifootnotetext[#1]{\pcol@calcfnctr#1\@nil
+  \expandafter\pcol@@footnotetext\expandafter[\number\@tempcnta]}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \KeepSpace{13}
+% \section{Commands for Marginal Notes}
+% \label{sec:imp-mpar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Add the section ``Commands for Marginal Notes'' to describe newly
+%	 introduced macros for the emulation of \cs{marginnote}.}
+% 
+% \begin{macro}{\marginpar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Locally modified in \cs{pcol@zparacol} for the emulation of
+%	 \cs{marginnote}.}
+% \begin{macro}{\pcol@marginpar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced as the in-\texttt{paracol} version of \cs{marginpar} for
+%	 the emulation of \cs{marginnote}.}
+% \begin{macro}{\pcol@@marginpar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced to keep the orginal version of \cs{marginpar} for
+%	 the emulation of \cs{marginnote}.}
+% \begin{macro}{\@mn@@marginnote}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Locally modified in \cs{pcol@zparacol} for the emulation of
+%	 \cs{marginnote}.}
+% \begin{macro}{\pcol@marginnote}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced as the in-\texttt{paracol} version of
+%	 \cs{@mn@@marginnote} for the emulation of \cs{marginnote}.}
+% \begin{macro}{\pcol@mn@warning}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced to put a warning message to show \cs{marginnote} is
+%	 emulated.}
+% \begin{macro}{\@xympar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Locally modified in \cs{pcol@zparacol} for the emulation of
+%	 \cs{marginnote}.}
+% \begin{macro}{\pcol@xympar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced as the in-\texttt{paracol} version of
+%	 \cs{@xympar} for the emulation of \cs{marginnote}.}
+% \begin{macro}{\pcol@@xympar}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced to keep the orginal version of \cs{@xympar} for the
+%	 emulation of \cs{marginnote}.} 
+% \begin{macro}{\pcol@mparoffset}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Introduced to have the vertical offset for the emulation of
+%	 \cs{marginnote}.}
+% The API macro \!\marginnote!\oarg{left}\marg{right}\oarg{voffset} given by
+% the package \textsf{marginnote} is emulated using
+% \!\marginpar!\oarg{left}\marg{right} and \!\pcol@addmarginpar! in
+% \!\output! routine.  The basic mechanism is to pass the vertical offset
+% $\arg{voffset}$ to \!\pcol@addmarginpar! through $|\dimen|\arg{b}$ where
+% $b$ is the \!\insert! to carry $\arg{left}$.  The offset passing is
+% implemented as follows.
+% 

+% \begin{itemize}
+% \item
+% \!\marginpar! is made \!\let!-equal to our own version \!\pcol@marginpar!
+% in \!\pcol@zparacol! so that it \!\let! the macro \!\pcol@mparoffset! be
+% \!\z@! and then invoke \LaTeX's origincal version kept in
+% \!\pcol@@marginpar!, because the marginal note given by \!\marginpar! will
+% not be shifted.
+% 
+% \item
+% The internal macro
+% \!\@mn@@marginnote!\oarg{left}\marg{right}\oarg{voffset} defined in
+% \textsf{marginnote} is made \!\let!-equal to our own version
+% \!\pcol@marginnote! in \!\pcol@zparacol! so that it |\def|ines
+% \!\pcol@mparoffset! to have $\arg{voffset}$ and then invoke
+% \!\pcol@@marginpar!\oarg{left}\~\marg{right} for the emulation.  In the
+% invokation, \textsf{marginnote}'s typesetting macros \!\margin~font!,
+% \!\raggedleftmarginnote! and \!\raggedrightmarginnote! are attached to
+% $\arg{left}$ and $\arg{right}$.
+% 
+% \item
+% \LaTeX's internal macro \!\@xympar! for the last operations of
+% \!\marginpar! is made \!\let!-equal to our own version in
+% \!\pcol@zparacol! so that it assigns the offset in \!\pcol@mparoffset! to
+% |\dimen|\!\@marbox! for $\arg{left}$, if $\!\@floatpenalty!<0$ to mean
+% other macros for \!\marginpar! have not detected any errors.
+% \end{itemize}
+% 

+% In addition, we raise a warning that \!\marginnote! is emulated by
+% \!\pcol@mn@warning!, which is made \!\let!-equal to \!\relax! in the caller
+% \!\pcol@marginnote! after the invokation so that the warning message is
+% put just once.
+% 

+%    \begin{macrocode}
+%% Commands for Marginal Notes
+
+\def\pcol@marginpar{\let\pcol@mparoffset\z@ \pcol@@marginpar}
+\long\def\pcol@marginnote[#1]#2[#3]{\endgroup
+  \pcol@mn@warning \global\let\pcol@mn@warning\relax
+  \def\pcol@mparoffset{#3}%
+  \pcol@@marginpar[\marginfont\raggedleftmarginnote#1]%
+                  {\marginfont\raggedrightmarginnote#2}}
+\def\pcol@mn@warning{%
+  \PackageWarning{paracol}{\string\margninnote\space is emulated by
+    \string\marginpar.}}
+\def\pcol@xympar{%
+  \ifnum\@floatpenalty<\z@ \global\dimen\@marbox\pcol@mparoffset\relax \fi
+  \pcol@@xympar}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% 
+% \KeepSpace{9}
+% \section{Two-Sided Typesetting}
+% \label{sec:imp-swap}
+% \changes{v1.2-4}{2013/05/11}
+%	{Add the section ``Column-Swapping'' to describe newly
+%	 introduced macros for column-swapping.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Rename the section title from ``Column-Swapping'' to ``Two-Sided
+%	 Typesetting''.}
+% 
+% \begin{macro}{\twosided}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced as an easier API for various two-sided typesetting.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Add two-sided background painting.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add two-sided marginal note placement.}

+% \begin{macro}{\pcol@twosided}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to implement \cs{twosided}.}

+% \changes{v1.31}{2013/10/10}
+%	{Fix spelling ``twosiding'' replacing it with ``two-siding'' in the
+%	 error message.}

+% \begin{macro}{\pcol@twosided@p}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to implement \cs{twosided} with \string\texttt{[p]}.}

+% \begin{macro}{\pcol@twosided@c}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to implement \cs{twosided} with \string\texttt{[c]}.}

+% \begin{macro}{\pcol@twosided@m}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to implement \cs{twosided} with \string\texttt{[m]}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced for two-sided marginal note placement.}

+% \begin{macro}{\pcol@twosided@b}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduced to implement \cs{twosided} with \string\texttt{[b]}.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced for two-sided background painting.}

+% \begin{macro}{\swapcolumninevenpages}
+% \changes{v1.2-4}{2013/05/11}
+%	{Introduced to enable column-swapping.}

+% \begin{macro}{\noswapcolumninevenpages}
+% \changes{v1.2-4}{2013/05/11}
+%	{Introduced to disable column-swapping.}

+% 

+% \def\inornot{\mathrel{{\in}/{\notin}}}
+% 

+% The API macro $\!\twosided!|[|T|]|$ where $T=t_1t_2\cdots$ is to
+% enable\slash disable two-sided paging with
+% $\CSIndex{if@twoside}=\true/\false$ ($|p|\inornot T$), two-sided \cswap{}
+% with $\CSIndex{ifpcol@swapcolumn}\~={\true/\false}$ ($|c|\inornot T$),
+% two-sided % marginal note placement with
+% $\CSIndex{ifpcol@swapmarginpar}={\true/\false}$ ($|m|\inornot T$), and/or
+% two-sided \bgpaint{} with $\CSIndex{ifpcol@bg@swap}={\true/\false}$
+% ($|b|\inornot{}T$) individually, or to enable all of them as a whole
+% when the optional argument is not given.
+% 
+% The macro invokes \!\pcol@twosided! with the optional argument $T$ if
+% provided, or with $T=|pcmb|$ otherwise to enable all features.  Then
+% \!\pcol@twosided! at first turns all the switches $\false$ an then scans
+% all non-space tokens $t\in T$ invoking $|\pcol@twosided@|{\cdot}t$ if it
+% is defined and thus $t\in\{|p|,|c|,|m|,|b|\}$ to turn the corresponding
+% switch $\true$, or complains that the feature $t$ is unknown.
+% 
+% Note that backward-compatible API macros 
+% \!\swapcolumninevenpages! and \!\noswapcolumn~inevenpages! are still
+% availabel to turn $\CSIndex{ifpcol@swapcolumn}$ $\true$ an $\false$
+% respectivey.
+% 

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

+% \begin{macro}{\pcol@swapcolumn}
+% \changes{v1.2-4}{2013/05/11}
+%	{Introduced to convert column ordinal and its position.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add two arguments $C^0$ and $C^1$ as the third and fourth ones to
+%	 modifiy the calculation of $c_2$ with them for column-swapping with
+%	 parallel-paging.}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add the assignment of \cs{pcol@colsepid} to let it have $c_2-1$ if
+%	 swapped or $c_2$ otherwise.}
+% \changes{v1.3-4}{2013/09/17}
+%	{Add a user \cs{pcol@addmarginpar} and remove \cs{paracol},
+%	 \cs{pcol@sptxt} and \cs{pcol@switchcol}.} 
+% \begin{macro}{\pcol@colsepid}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to be let have $c_2-1$ if swapped or $c_2$ otherwise by
+%	 \cs{pcol@swapcolumn}.}
+% 

+% The macro \!\pcol@swapcolumn!$\<c_1\>\<c_2\>\<\Cfrom\>\<\Cto\>$ converts
+% the column ordinal $c$ or position $c'$ in the \!\count!
+% register\footnote{

+% 

+% Or the \!\dimen! register \!\z@!.}
+% 

+% $c_1$ to the position or ordinal to set it in the \!\count! register
+% $c_2$, for a \parapag{}e having columns $c\In\Cfrom\Cto$.  That is, we let
+% $c_2=(\Cto-1)-(c_1-\Cfrom)$ if $\CSIndex{ifpcol@swapcolumn}=\true$ to mean
+% the \cswap{} is in effect and \!\c@page! is even, while $c_2=c_1$
+% otherwise.  We also let $c^g=\!\pcol@colsepid!=c_2-1$ if swapped, or
+% $c^g=c_2$ otherwise, so that it has the ordinal of the \csepgap{}
+% {\em physically} following the column $c_2$.
+% 
+% The macro is used in \!\pcol@ioutputelt!, \!\pcol@addmarginpar!,
+% \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! with
+% $(c_1,c_2)=(c',c)$, and in \!\pcol@addmarginpar! (another use) with
+% $(c_1,c_2)=(c,c')$.  Note that in the uses in the macros above except for
+% \!\pcol@addmarginpar!, \!\c@page!  definitely has the page number for the
+% page to be shipped out.  As for \!\pcol@addmarginpar! on the other hand,
+% \!\c@page! can be different from the ship-out page number to produce a
+% weird result if their parities are different, due to page jump.  However
+% this problem is not so severe because it just affects the position of
+% marginal notes which \LaTeX{} itself may misplace.
+% 

+%    \begin{macrocode}
+\def\pcol@swapcolumn#1#2#3#4{%
+  \edef\pcol@colsepid{\number#1}%
+  \ifpcol@swapcolumn
+    \ifodd\c@page\relax #2#1\relax
+    \else
+      #2#4\relax \advance#2-#1\relax \advance#2#3\relax \advance#2-\tw@
+      \edef\pcol@colsepid{\number#2}%
+      \advance#2\@ne
+    \fi
+  \else #2#1\relax
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \KeepSpace{2}
+% \begin{macro}{\marginparthreshold}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to spacify the smallest ordinal of columns whose marginal
+%	 notes go to the right margin if not swapped.}
+% \begin{macro}{\pcol@marginparthreshold}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to implement \cs{marginparthreshold}.}
+% \begin{macro}{\pcol@mpthreshold@l}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to keep the value specified by \cs{marginparthreshold}
+%	 for columns in left parallel-pages.}
+% \begin{macro}{\pcol@mpthreshold@r}
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduced to keep the value specified by \cs{marginparthreshold}
+%	 for columns in right parallel-pages.}
+% 

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

+%    \begin{macrocode}
+\def\marginparthreshold#1{\@tempcnta#1\relax
+  \xdef\pcol@mpthreshold@l{\number\@tempcnta}%
+  \@ifnextchar[%]
+    \pcol@marginparthreshold{\xdef\pcol@mpthreshold@r{\number\@tempcnta}}}
+\def\pcol@marginparthreshold[#1]{\@tempcnta#1\relax
+  \xdef\pcol@mpthreshold@r{\number\@tempcnta}}
+\marginparthreshold{1}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% 
+% \KeepSpace{5}
+% \section{Commands for Text Coloring}
+% \label{sec:imp-commcolor}
+% \changes{v1.3-6}{2013/09/17}
+%	{Add the section ``Commands for Text Coloring'' to distinguish
+%	 macros inside and outside \cs{output} routine and describe latters
+%	 in this section.}
+% 
+% \begin{macro}{\columncolor}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to define the default color of a column.}

+% \changes{v1.22}{2013/06/30}
+%	{Add the definition of \cs{pcol@colorcommand} for warning in
+% 	 \cs{pcol@icolumncolor}.}

+% \begin{macro}{\pcol@xcolumncolor}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to implement \cs{columncolor}.}

+% \begin{macro}{\pcol@ycolumncolor}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to implement \cs{columncolor}.}

+% \begin{macro}{\pcol@columncolor}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to implement \cs{columncolor}.}

+% 

+% The API macro \!\columncolor!\oarg{mode}\marg{color}\oarg{c} defines the
+% default color specified by $\arg{color}$ optionally with color
+% $\arg{mode}$ of the column $c$ being the current column or that specified
+% by the optional argument.  After \!\def!ining \Midx{\!\pcol@colorcommand!}
+% being the \!\string! of this macro itself, and processing two optional
+% arguments $\arg{mode}$ and $c$ through macros \!\pcol@xcolumncolor!,
+% \!\pcol@ycolumncolor! and \!\pcol@columncolor!, the macro
+% \!\pcol@icolumncolor!\marg{cmd}\oarg{c} is invoked to perform real
+% operations with the coloring command
+% $\arg{cmd}=\!\color!$\oarg{mode}\marg{color}.
+% 

+%    \begin{macrocode}
+%% Commands for Text Coloring
+
+\def\columncolor{\def\pcol@colorcommand{\string\columncolor}%
+  \@ifnextchar[%]
+    \pcol@xcolumncolor\pcol@ycolumncolor}
+\def\pcol@xcolumncolor[#1]#2{\pcol@columncolor{\color[#1]{#2}}}
+\def\pcol@ycolumncolor#1{\pcol@columncolor{\color{#1}}}
+\def\pcol@columncolor#1{\@ifnextchar[%]
+  {\pcol@icolumncolor{#1}}{\pcol@icolumncolor{#1}[\number\pcol@currcol]}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\normalcolumncolor}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to define the default color of a column is
+%	 \cs{normalcolor}.}
 
+% \changes{v1.22}{2013/06/30}
+%	{Add the definition of \cs{pcol@colorcommand} for warning in
+% 	 \cs{pcol@icolumncolor}.}

+% 

+% The API macro \!\normalcolumncolor!\oarg{c} defines the default color of
+% the column $c$, being the current column or that specified by the optional
+% argument, is \!\normalcolor!.  That is, after \!\def!ining
+% \Midx{\!\pcol@colorcommand!}  being the \!\string! of this macro itself,
+% this macro simply invokes \!\pcol@icolumncolor!\marg{cmd}\oarg{c} to
+% perform real operations with the coloring command
+% $\arg{cmd}=\!\normalcolor!$.
+% 

+%    \begin{macrocode}
+\def\normalcolumncolor{\def\pcol@colorcommand{\string\normalcolumncolor}%
+  \@ifnextchar[%]
+    {\pcol@icolumncolor\normalcolor}%
+    {\pcol@icolumncolor\normalcolor[\number\pcol@currcol]}}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \KeepSpace{1}
+% \changes{v1.22}{2013/06/30}
+%	{\cs{pcol@getshadowcc} was introduced for setting $\hat\gamma_0^c$
+%	 into $\gamma_0^c$ locally, but removed in v1.34.}
 
+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@getshadowcc} is removed according to the change of text
+%	 coloring from \cs{output} to \cs{insert}.}

+% \begin{macro}{\pcol@icolumncolor}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to implement \cs{columncolor} and
+%	 \cs{normalcolumncolor}.}
 
+% \changes{v1.22}{2013/06/30}
+%	{Add warning of ineffective uses of \cs{columncolor} and
+%	 \cs{normalcolumncolor}, and modify the mechanism to update
+%	 $\gamma_0^c$ and to rewind\slash reestablish color stack.}

+% \changes{v1.23}{2013/07/08}
+%	{Add an argument of \cs{relax} to \cs{pcol@color@invokeoutput}
+%	 because any insertion after \cs{vadjust} is not required or
+%	 justified.}

+% \changes{v1.24}{2013/07/27}
+%	{Add math mode to the cases of ineffective use.}
+% \changes{v1.34}{2018/05/07}
+%	{Remove the invocations of \cs{pcol@iicolumncolor} for
+%	 $\cs{pcol@columncolor@shadow}\cdot c$ because it no longer exists,
+%	 completly change the opearations in the case the target column $c$
+%	 is the current one according to the new method with \cs{insert},
+%	 and add immediate setting of $\gamma_0^c$ in the case $c$ is not
+%	 current.}

+% \begin{macro}{\pcol@iicolumncolor}
+% \changes{v1.22}{2013/06/30}
+%	{Introduced for setting $\gamma_0^c$ and $\hat\gamma_0^c$, and
+%	 pushing $\chi$.}

+% \changes{v1.34}{2018/05/07}
+%	{Remove the third argument, change the second argument from a
+%	 control sequence name to the target column, add a grouping to
+%	 surround the entire body of the macro, and change the body of
+%	 $\gamma_0^c$ so that it only has the color information.}

+% \begin{macro}{\pcol@scancst@shadow}
+% \changes{v1.34}{2018/05/07}
+%	{Introduced to rewind or establish the color stack $\hat\Gamma^c$.}
+% 

+% The macro \!\pcol@icolumncolor!\marg{cmd}\oarg{c}, invoked from
+% \!\pcol@columncolor! and \!\normal~columncolor!, performs the operations to
+% define the default color of the column $c$ with the coloring command
+% $\arg{cmd}\in\{\!\color!\hbox{\oarg{mode}}\ARg{color},\,\!\normalcolor!\}$
+% as follows.  First we examine if \!\set@color! is not \!\relax! and we are
+% in non-internal vertical or non-restricted horizontal mode and, if not, we
+% complain the command whose name is in \!\pcol@colorcommand! is ineffective
+% by \!\PackageWarning! and do nothing.
+% 
+% Otherwise and if we are not in a \env{paracol} environment, i.e.,
+% \!\paracol! is not \!\let!-equal to \!\pcol@paracol!, we simply invoke
+% \!\pcol@iicolumncolor! to let $\Celtshadow^c=|\pcol@columncolor|\cdot c$
+% have the color $\chi$ specified by $\arg{cmd}$ so that the next
+% \beginparacol{} will let $\Celt^c$ have the coloring \!\special!  for
+% $\chi$.  If we are in a \env{paracol} environment but in a column $c'\neq
+% c$, on the other hand, we also let $\Celtshadow=\chi$ but in addition let
+% $\Celt^c=|\pcol@columncolor@box|\cdot c$ have the coloring \!\special! for
+% $\chi$ immediately so that it is effective in the next \cswitch{} to $c$.
+% This immediate setting of $\Celt^c$ is done by invoking $\arg{cmd}$ with
+% the original \!\set@color!  saved in \!\pcol@set@color! and the
+% nullification of \!\aftergroup!, after acquiring an \!\insert! for it if
+% necessary,
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% \SpecialArrayIndex{c}{\pcol@columncolor@box}

+% 
+% Otherwise, i.e., if we are in a \env{paracol} environment and in the
+% column $c$, at first we invoke \!\pcol@scancst@shadow! to rewind
+% $\CSTshadow^c$ applying $\!\@elt!=\!\reset@color!$ to
+% $\celtshadow_i\in\CSTshadow^c$.  Then, after letting $\Celtshadow^c=\chi$,
+% we invoke \!\pcol@scancst@shadow! again to reestablish $\CSTshadow^c$ with
+% the new $\Celtshadow^c$ so that $\Celtshadow^c$ is at the bottom of the
+% \colorstack{} in |.tex|.  In this scan $\!\@elt!\arg{\celtshadow_i}$
+% \!\def!ines \!\current@color! to let it have $\celtshadow_i$ and then
+% invokes \!\pcol@set@color! to put the coloring \!\special! for
+% $\celtshadow_i$ nullifying \!\aftergroup!.  Then we \!\insert! a \!\vbox!,
+% whose height and depth are 1\,|pt| and width is 0, having the coloring
+% \!\special! for $\chi$ so that \!\output! will let $\Celt^c$ have the
+% \!\special! in a synchronous manner.  After that we put a
+% $\!\penalty!=10000$ if $\CSIndex{if@nobreak}=\true$ to keep the
+% \!\insert!ion from being followed by a page break.
+% 
+% The macro $\!\pcol@iicolumncolor!\arg{cmd}\arg{c}$ at first
+% invokes $\arg{cmd}$ to let \!\current@color! have the printer-specific color
+% information $\chi$ of $\arg{color}$ or what \!\normalcolor! specifies,
+% temporarily letting \!\set@color! be \!\relax! to let \!\color! or
+% \!\normalcolor! just do the \!\def!inition of \!\current@color! without
+% putting coloring \!\special!s nor preparing \colorstack{} popping.  Then
+% we \!\xdef!ine $\Celtshadow^c=|\pcol@columncolor|{\cdot}c$ to have $\chi$.
+% 

+% \SpecialArrayIndex{c}{\pcol@columncolor}

+% 
+% \begingroup\hfuzz3.1pt
+% The macro \!\pcol@scancst@shadow! applies \!\@elt! to $\Celtshadow^c$ to
+% put a coloring or uncoloring \!\special! for it if it is defined, and then
+% do the same for all
+% $\celtshadow_i\in\cstshadow=\!\pcol@colorstack@shadow!$.
+% \par\endgroup
+% 

+%    \begin{macrocode}
+\def\pcol@icolumncolor#1[#2]{%
+  \@tempswafalse
+  \ifpcol@inner \@tempswatrue \fi
+  \ifinner      \@tempswatrue \fi
+  \ifmmode      \@tempswatrue \fi
+  \ifx\set@color\relax
+    \PackageWarning{paracol}{\pcol@colorcommand\space is not effective
+      without some coloring package}%
+  \else\if@tempswa
+    \PackageWarning{paracol}{\pcol@colorcommand\space is not effective
+      when not in outer par mode}%
+  \else
+    \begingroup
+    \let\@elt\relax
+    \ifx\pcol@paracol\paracol
+      \pcol@iicolumncolor{#1}{#2}%
+    \else\ifnum#2=\pcol@currcol
+      \def\@elt##1{\reset@color}\pcol@scancst@shadow
+      \pcol@iicolumncolor{#1}{#2}%
+      \def\@elt##1{\def\current@color{##1}\let\aftergroup\@gobble
+        \pcol@set@color}%
+      \pcol@scancst@shadow
+      \setbox\@tempboxa\vbox{\let\set@color\pcol@set@color
+        \let\aftergroup\@gobble #1}%
+      \ht\@tempboxa1sp \dp\@tempboxa1sp \wd\@tempboxa\z@\relax
+      \insert\pcol@colorins{\box\@tempboxa}%
+      \ifvmode\if@nobreak \nobreak \fi\fi
+    \else
+      \pcol@iicolumncolor{#1}{#2}%
+      \pcol@currcol#2\relax
+      \ifvoid\pcol@ccuse{@box}%
+        \@next\@currbox\@freelist{}\pcol@ovf
+        \pcol@ccxdef{\@currbox}%
+      \fi
+      \global\setbox\pcol@ccuse{@box}\vbox{\let\set@color\pcol@set@color
+        \let\aftergroup\@gobble #1}%
+    \fi\fi
+    \endgroup
+  \fi\fi
+  \ignorespaces}
+\def\pcol@iicolumncolor#1#2{{\let\set@color\relax #1%
+  \expandafter\xdef\csname pcol@columncolor#2\endcsname{\current@color}}}
+\def\pcol@scancst@shadow{%
+  \pcol@ifccdefined{\@elt{\pcol@ccuse{}}}\relax
+  \pcol@colorstack@shadow}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{1}
+% \begin{macro}{\pcol@mcpushlimit}
+% \changes{v1.24}{2013/07/27}
+%	{Introduced for coloring specified in math mode.}

+% \changes{v1.34}{2018/05/07}
+%	{Move down to place it just before the \cs{def}inition of
+%	 \cs{pcol@set@color@push} being the sole referrer, and change its
+%	 body from 100 to 1000.}
+% \begin{macro}{\set@color}
+% \begin{macro}{\pcol@set@color}
+% \begin{macro}{\pcol@set@color@push}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to work as \cs{set@color}.}

+% \changes{v1.22}{2013/06/30}
+%	{Modified to push color stack by \cs{output} always.}

+% \changes{v1.23}{2013/07/08}
+%	{Add an argument of null \cs{hskip} to \cs{pcol@color@invokeoutput}
+%	 so that the first word of a colored text is hyphenated.}

+% \changes{v1.24}{2013/07/27}
+%	{Add the mechanism special for math mode.}

+% \changes{v1.3-6}{2013/09/17}
+%	{Change the second argument of \cs{pcol@color@invokeoutput} from
+%	 \cs{hskip}\cs{z@} to \cs{pcol@fcwhyphenate} to make null skip
+%	 insertion conditional.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% 

+% The macro \!\pcol@set@color@push! is invoked whenever \LaTeX's
+% counterpart \!\set@color!  appears in a \env{paracol} environment through
+% coloring commands such as \!\color!, because \!\pcol@zparacol! replaces
+% \LaTeX's macro with it saving the original version in \!\pcol@set@color!,
+% if the original \!\set@color! is not \!\relax! to mean some coloring
+% package is in use.  This original version is used through
+% \!\pcol@set@color! by \!\pcol@bg@paintregion@i!, \!\pcol@output@start! and
+% \!\pcol@icolumncolor!  besides this macro \!\pcol@set@color@push!,
+% while \!\output! lets $\!\set@color!=\!\pcol@set@color!$ for the references
+% outside of our control.
+% 
+% The macro at first invokes its original version being \!\pcol@set@color!
+% to put an appropriate coloring \!\special! to |.dvi| and reserve the
+% invocation of \!\reset@color! by \!\aftergroup!.  Then, it performs one of
+% two different operations depending on TeX's mode, i.e., math mode or not.
+% If we are in math mode and not in a \!\vbox!, at first we increment
+% $m=\!\pcol@mcid!$ and examine if $m>\!\pcol@mcpushlimit!=1000$, and if so
+% we stop the execution with \!\PackageError!\footnote{

+% 

+% And let $m=1$ to allow a user to continue the execution bravely.}
+% 

+% in order to avoid too many macros $|\pcol@reset@color@mpop@|\cdot m$ are
+% defined\footnote{

+% 

+% \SpecialArrayIndex{m}{\pcol@reset@color@mpop@}

+% 

+% We could make the number of math-mode coloring operations virtually
+% unlimited by putting all digits of the decimal representation of $m$
+% followed by a terminator by multiple
+% \cs{aftergroup}s so that \cs{pcol@reset@color@mpop} is put by
+% \cs{aftergroup} prior to them to capture them as its argument, but 
+% limiting with $2^{31}-1$ is still necessary and that with 1000 is
+% reasonable.}. 
+% 

+% Otherwise, i.e., if $m\leq\!\pcol@mcpushlimit!$, we
+% reserve the invocation of the macro $|\pcol@reset@color@mpop@|{\cdot}i$
+% 

+% \SpecialArrayMainIndex{m}{\pcol@reset@color@mpop@}

+% 

+% for our own pop by \!\aftergroup! defining the macro as
+% $\!\pcol@reset@color@mpop!\Arg{m}$.  If we are not in math mode, on the
+% other hand, and neither in a \!\vbox!  nor in restricted horizontal mode,
+% we simply reserve the invocation of the macro $\pcol@reset@color@pop$.
+% 
+% Then, regardless that we are in math mode or not, we push the contents of
+% \!\current@color!, which \!\set@color! should refer to as the color
+% information to be set, into the shadow \colorstack{}
+% $\cstshadow=\!\pcol@colorstack@shadow!$ for the stack rewinding\slash
+% reestablishing in \!\columncolor! and \!\normalcolumncolor!.  Since this
+% push is done non-\!\global!ly with \!\edef!, we save\slash restore the
+% definition of \!\@elt! to\slash from \Midx{\!\pcol@elt@save!} before\slash
+% after the push, resepctively\footnote{

+% 

+% Just in case.}.
+% 

+% Then we \!\insert! a \!\vbox! through \!\pcol@colorins! for the push of
+% $\celt_i$ or $\mcelt_{i,m}$ to $\cstraw$ synchronous with a page break or
+% \cswitch{}.  The height of the \!\vbox! is 1\,|pt|, depth is 0 and
+% width is $m$\,|sp| if we are in math mode or 0 otherwise, and its
+% contents is the coloring \!\special! given by \!\pcol@set@color! so that
+% the \!\special! is what the macro put at the beginning of this macro but
+% without the reservation of \!\reset@color!.  After the insertion, we put
+% \!\pcol@fcwhyphenate!, being \!\hskip!\!\z@! when
+% \!\coloredwordhyphenated!  is effective, to split the coloring \!\special!
+% from the first colored word so that the word may be hyphenated if we are
+% in horizontal mode.  If we are in vertical mode, on the other hand, we do
+% \!\nobreak! if $\CSIndex{if@nobreak}=\true$ to keep the \!\insert!ion from
+% being followed by a page break.
+% 

+%    \begin{macrocode}
+\def\pcol@mcpushlimit{1000}
+\def\pcol@set@color@push{\pcol@set@color
+  \ifmmode\else\ifinner \pcol@innertrue \fi\fi
+  \ifpcol@inner\else
+    \ifmmode
+      \global\advance\pcol@mcid\@ne
+      \ifnum \pcol@mcid>\pcol@mcpushlimit\relax
+        \PackageError{paracol}{Too many coloring commands in math mode}\@ehb
+        \global\pcol@mdid\@ne
+      \fi
+      \@tempdima\pcol@mcid sp\relax
+      \expandafter\aftergroup
+        \csname pcol@reset@color@mpop@\number\pcol@mcid\endcsname
+      \expandafter\xdef
+        \csname pcol@reset@color@mpop@\number\pcol@mcid\endcsname
+          {\noexpand\pcol@reset@color@mpop{\number\pcol@mcid}}%
+    \else
+      \aftergroup\pcol@reset@color@pop \@tempdima\z@
+    \fi
+    \let\pcol@elt@save\@elt \let\@elt\relax
+    \edef\pcol@colorstack@shadow{\pcol@colorstack@shadow\@elt{\current@color}}%
+    \let\@elt\pcol@elt@save
+    \setbox\@tempboxa\vbox{\let\aftergroup\@gobble \pcol@set@color}%
+    \ht\@tempboxa1sp \dp\@tempboxa\z@ \wd\@tempboxa\@tempdima
+    \insert\pcol@colorins{\box\@tempboxa}\ifhmode \pcol@fcwhyphenate \fi
+    \ifvmode\if@nobreak \nobreak \fi\fi
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@reset@color@pop}
+% \changes{v1.2-1}{2013/05/11}
+% 	{Introduced to work as \cs{reset@color}.}

+% \changes{v1.22}{2013/06/30}
+%	{Modified to pop color stack by \cs{output} and to examine if
+%	 $\cs{ifpcol@output}\EQ\mathit{true}$.}

+% \changes{v1.23}{2013/07/08}
+%	{Add an argument of \cs{relax} to \cs{pcol@color@invokeoutput}
+%	 so that the last word of a colored text is not followed by a line
+%	 break candidate.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% \begin{macro}{\pcol@reset@color@mpop}
+% \changes{v1.24}{2013/07/27}
+%	{Introduced for coloring specified in math mode.}

+% \changes{v1.34}{2018/05/07}
+%	{Completely change its definition according to the new text coloring
+%	 with \cs{insert}.}

+% 

+% The macro \!\pcol@reset@color@pop! and its math-mode relative
+% $\!\pcol@reset@color@mpop!\~\Arg{m}$ are invoked by
+% \!\aftergroup! mechanism in \!\pcol@set@color@push!, directly for the
+% former and through the macro $|\pcol@reset@color@mpop@|{\cdot}m$
+% 

+% \SpecialArrayIndex{m}{\pcol@reset@color@mpop@}

+% 

+% for the latter.  They \!\insert! a \!\vbox! for $\celtpop_i$ or
+% $\mceltpop_{i,m}$ to add it to $\cstraw$ synchronously with a page break
+% or \cswitch{}.  Therefore, the height and depth of the \!\vbox! are 0 and
+% width is 0 for $\celtpop_i$ or $m$\,|sp| for $\mceltpop_{i,m}$.  The
+% contents of the \!\vbox! is an uncoloring \!\special! given by
+% \!\reset@color! but this is done just for debugging to show what
+% \!\pcol@colorins! has by, for example, \!\pcol@ShowBox!.  Then if we are
+% in vertical mode and $\CSIndex{if@nobreak}=\true$, we do \!\nobreak! to
+% keep the \!\insert!ion from being followed by a page break even in
+% \!\pcol@reset@color@mpop! because its corresponding
+% \!\pcol@set@color@push! may have been in a displayed math construct after
+% which we are in vertical mode.
+% 
+% One caution is that \!\pcol@reset@color@pop! can be invoked outside the
+% \env{paracol} environment in which the corresponding
+% \!\pcol@set@color@push! appears.  In this case with
+% $\CSIndex{ifpcol@output}=\false$, we don't need to do the pop operation
+% and cannot make the \!\insert!ion for it because \!\output! is not for
+% \env{paracol}.
+% 

+%    \begin{macrocode}
+\def\pcol@reset@color@pop{%
+  \ifpcol@output
+    \setbox\@tempboxa\vbox{\reset@color}%
+    \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa\z@
+    \insert\pcol@colorins{\box\@tempboxa}%
+    \ifvmode\if@nobreak \nobreak \fi\fi
+  \fi}
+\def\pcol@reset@color@mpop#1{%
+  \setbox\@tempboxa\vbox{\reset@color}%
+  \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa#1sp\relax
+  \insert\pcol@colorins{\box\@tempboxa}%
+  \ifvmode\if@nobreak \nobreak \fi\fi
+}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@color@invokeoutput} was introduced for \cs{output}
+%	 request for coloring but removed in v1.34.}

+% \changes{v1.23}{2013/07/08}
+%	{\cs{pcol@color@invokeoutput} was modified to add second argument
+%	 $s$ to insert a null skip after \cs{vadjust} only when the macro is
+%	 invoked from \cs{pcol@set@color@push} in horizontal mode.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@color@invokeoutput} is removed according to the change of
+%	 text coloring from \cs{output} to \cs{insert}.}

+% \changes{v1.22}{2013/06/30}
+% 	{\cs{pcol@color@invokeoutput@v} was introduced for \cs{output}
+%	 request for coloring but removed in v1.34.}

+% \changes{v1.34}{2018/05/07}
+%	{\cs{pcol@color@invokeoutput@v} is removed according to the change of
+%	 text coloring from \cs{output} to \cs{insert}.}

+% 
+% \KeepSpace{1}
+% \begin{macro}{\coloredwordhyphenated}
+% \changes{v1.3-6}{2013/09/17}
+%	{Introduced to enable null skip insertion before the first word
+%	 after a coloring command not always but conditionally.}

+% \begin{macro}{\nocoloredwordhyphenated}
+% \changes{v1.3-6}{2013/09/17}
+%	{Introduced to disable null skip insertion before the first word
+%	 after a coloring command.}

+% \begin{macro}{\pcol@fcwhyphenate}
+% \changes{v1.3-6}{2013/09/17}
+%	{Introduced to enable null skip insertion before the first word
+%	 after a coloring command not always but conditionally.}

+% 

+% The API macro \!\coloredwordhyphenated! \!\def!ines the macro
+% \!\pcol@fcwhyphenate! being \!\hskip!\!\z@! so that the null space is
+% inserted after the coloring \!\special! and \!\insert! put by
+% \!\pcol@set@color@push! if we are in horizontal mode, so that the word
+% following them can be hyphenated.  The other API macro
+% \!\nocoloredwordhyphenated! makes $\!\pcol@fcwhyphenate!=\!\relax!$ to
+% inhibit the insertion.  Since the null skip is a line break candidate, the
+% skip might cause an unexpected and undesirable line break.  However, this
+% demerit is less important than the merit of making it possible to
+% hyphenate the first word in multi-column documents with narrow lines, and
+% thus we make \!\coloredwordhyphenated! effective in default while giving
+% users a means to disable the insertion (occasionally) by
+% \!\nocoloredwordhyphenated!.
+% 

+%    \begin{macrocode}
+\def\coloredwordhyphenated{\def\pcol@fcwhyphenate{\hskip\z@}}
+\def\nocoloredwordhyphenated{\let\pcol@fcwhyphenate\relax}
+\coloredwordhyphenated
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 
+% 
+% 
+% \KeepSpace{8}
+% \section{Commands for Column-Separating Rule Color and Background Painting}
+% \label{sec:imp-commbg}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add the subsection ``Commands for Column-Separating Rule Color and
+%	 Background Painting'' to describe newly
+%	 introduced API macros to specify colors of column-separating rules
+%	 and background painting.}

+% 
+% \begin{macro}{\colseprulecolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to spcify the colors of column-separating rules.}

+% \begin{macro}{\pcol@defcseprulecolor@x}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{colseprulecolor}.}
+% \begin{macro}{\pcol@defcseprulecolor@y}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{colseprulecolor}.}
+% \begin{macro}{\pcol@defcseprulecolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{colseprulecolor}.}
+% \begin{macro}{\normalcolseprulecolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to spcify that color of column-separating rules is normal.}
+% \begin{macro}{\pcol@defcseprulecolor@i}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{colseprulecolor} and
+%	 \cs{normalcolseprulecolor}.}
+% \begin{macro}{\pcol@colseprulecolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to keep the color for all column-separating rules.}
+% 

+% The macro \!\colseprulecolor!\oarg{mode}\marg{color}$|[|c|]|$ \!\def!ines
+% \!\pcol@colseprulecolor! to have the $\arg{color}$ optionally with
+% coloring $\arg{mode}$ of all \cseprule{}s if the optional argument $c$ is
+% not provided, or $|\pcol@colseprulecolor|{\cdot}c$
+% 

+% \SpecialArrayMainIndex{c}{\pcol@colseprulecolor}

+% 

+% that of the rule drawn between a particular column pair $c$ and $c+1$.
+% After \!\def!ining \Midx{\!\pcol@colorcommand!} to be \!\colseprulecolor!
+% in case we have to give a warning, the macro invokes
+% \!\pcol@defcseprulecolor@x!\oarg{mode}\marg{color} or
+% \!\pcol@defcseprulecolor@y!\marg{color} according to the provision of the
+% optional argument $\arg{mode}$ to invoke \!\pcol@defcseprulecolor!  with
+% argument \marg{cmd}${}={}$\!\color!\oarg{mode}\marg{color} so that this
+% macro invokes $\!\pcol@defcseprulecolor@i!\ARg{cmd}|[|c|]|$ where
+% $c=\emptyset$ if the optional arguemnt $c$ is not provided.
+% 
+% The macro $\!\normalcolseprulecolor!|[|c|]|$, on the other hand, defines
+% $|\pcol@colseprule|\~|color|[{\cdot}c]$
+% 

+% \SpecialArrayIndex{c}{\pcol@colseprulecolor}

+% \SpecialIndex{\pcol@colseprulecolor}

+% 

+% with whatever \!\normalcolor! gives, and thus it invokes
+% \!\pcol@defcseprulecolor@i! letting $\arg{cmd}=\!\normalcolor!$, after
+% \!\def!ining \!\pcol@colorcommand! to be \!\normalcolsep~rule~color!.
+% 
+% The macro $\!\pcol@defcseprulecolor@i!\ARg{cmd}|[|c|]|$ examines if
+% $\!\set@color!=\!\relax!$ to mean no coloring packages have been loaded
+% and, if so, do nothing giving a warning the command in
+% \!\pcol@colorcommand! is not effective.  Otherwise, we examine if
+% $\arg{cmd}$ has proper arguments by invoking it but temporally nullifying
+% \!\set@color! and then \!\def!ine $|\pcol@colseprulecolor|[{\cdot}c]$
+% 

+% \SpecialArrayIndex{c}{\pcol@colseprulecolor}

+% \SpecialIndex{\pcol@colseprulecolor}

+% 

+% to be $\arg{cmd}$.
+% 
+% Note that at the top level we \!\def!ine \!\pcol@colseprulecolor! to be
+% \!\normalcolor! to give the default for all \cseprule{}s.  Also note that
+% macros $|\pcol@colseprulecolor|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@colseprulecolor}

+% 

+% are referred to solely in \!\pcol@hfil!
+% which also uses \!\pcol@colseprulecolor! for columns for which
+% $|\pcol@colseprulecolor|{\cdot}c$
+% 

+% \SpecialArrayIndex{c}{\pcol@colseprulecolor}

+% 

+% is not defined.
+% 

+%    \begin{macrocode}
+%% Commands for Column-Separating Rule Color and Background Painting
+
+\def\colseprulecolor{\def\pcol@colorcommand{\string\colseprulecolor}%
+  \@ifnextchar[%]
+    \pcol@defcseprulecolor@x\pcol@defcseprulecolor@y}
+\def\pcol@defcseprulecolor@x[#1]#2{\pcol@defcseprulecolor{\color[#1]{#2}}}
+\def\pcol@defcseprulecolor@y#1{\pcol@defcseprulecolor{\color{#1}}}
+\def\pcol@defcseprulecolor#1{\@ifnextchar[%]
+  {\pcol@defcseprulecolor@i{#1}}{\pcol@defcseprulecolor@i{#1}[]}}
+\def\normalcolseprulecolor{%
+  \def\pcol@colorcommand{\string\normalcolseprulecolor}%
+  \@ifnextchar[%]
+    {\pcol@defcseprulecolor@i\normalcolor}%
+    {\pcol@defcseprulecolor@i\normalcolor[]}}
+\def\pcol@defcseprulecolor@i#1[#2]{%
+  \ifx\set@color\relax
+    \PackageWarning{paracol}{\pcol@colorcommand\space is not effective
+      without some coloring package}%
+  \else
+    {\let\set@color\relax #1}%
+    \global\@namedef{pcol@colseprulecolor#2}{#1}%
+  \fi}
+\gdef\pcol@colseprulecolor{\normalcolor}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{8}
+% \begin{macro}{\backgroundcolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to define colors for background painting.}

+% \begin{macro}{\nobackgroundcolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to undefine colors for background painting.}

+% \begin{macro}{\pcol@backgroundcolor@e}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \changes{v1.31}{2013/10/10}
+%	{Fix the mispell ``colorling'' in the error message.}

+% \begin{macro}{\pcol@backgroundcolor@i}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@bg@region}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@ii}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@iii}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@iv}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@v}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% 

+% {\nosv\gdef\|{\;|\;}}

+% \def\fdef{f_{\mathit{def}}}

+% 

+% The macro
+% \!\backgroundcolor!\marg{region}\oarg{mode}\marg{color}
+% defines the $\arg{color}$ optionally with $\arg{mode}$ of the
+% $\arg{region}$ whose syntax is specified as follows.
+% 

+% % \begin{eqnarray*}
+% \arg{region}&{:}{:}{=}&\arg{regionid}\arg{extension}\\
+% \arg{regionid}&{:}{:}{=}&\<a\>\|\arg{corg}|[|c|]|\\
+% \arg{a}&{:}{:}{=}&\arg{corg}\||s|\||S|\||t|\||T|\||l|\||L|\||r|\||R|\|
+%                               |f|\||F|\||n|\||N|\||p|\||P|\\
+% \arg{corg}&{:}{:}{=}&|c|\||C|\||g|\||G|\\
+% \arg{extension}&{:}{:}{=}&\emptyset\||(|x_0|,|y_0|)|\|
+%                                      |(|x_0|,|y_0|)(|x_1|,|y_1|)|
+% \end{eqnarray*}
+% % 

+% On the other hand, the counteraprt macro
+% \!\nobackgroundcolor!\marg{region} undefines the color of $\arg{region}$.
+% Both macros invoke \!\pcol@backgroundcolor! giving all arguments to it to
+% parse the argument $\arg{region}$, after letting
+% $\fdef=\CSIndex{if@tempswa}=\true$ and
+% $\!\pcol@backgroundcolor@e!=\!\pcol@backgroundcolor@w!$ in
+% \!\backgroundcolor!, or $\fdef=\CSIndex{if@tempswa}=\true$ and
+% $\!\pcol@backgroundcolor@e!=\!\pcol@backgroundcolor@z!$ in
+% \!\nobackgroundcolor!.  Note that the \!\let!-assignment to
+% \!\pcol@backgroundcolor@e! is effective when we found an error in the
+% parse of the argument $\arg{region}$ to throw away what remains in the
+% argument unprocessed and, for \!\backgroundcolor!, the other arguments
+% \oarg{mode}\marg{color}.
+% 
+% Then the macro \!\pcol@backgroundcolor! examines if $|\pcol@bg@@|{\cdot}a$
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@@}
+% 

+% is defined, and if not, raises an error that $a$ is invalid and then, in case
+% the user dare to continue the execution, invokes
+% \!\pcol@backgroundcolor@e! to throw all arguments away after letting
+% $a'=\!\pcol@bg@region!=|xx|$ so that the undefining
+% $|\pcol@bg@color|{\cdot}a'$ does not cause any troubles.
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% 

+% Otherwise, i.e., if $|\pcol@bg@@|{\cdot}a$ is defined, it 
+% invokes $\!\pcol@backgroundcolor@i!|[|c|]|$ or \!\pcol@backgroundcolor@ii!
+% according to the provision of the optional argument $|[|c|]|$, after
+% \!\def!ining $a'=\Midx{\!\pcol@bg@region!}$ to be $a$.  Then
+% \!\pcol@backgroundcolor@i! examines if $|\pcol@bg@|\~|mayhavecol@|{\cdot}a$
+% 

+% \SpecialIndex{\pcol@bg@mayhavecol@c}\SpecialIndex{\pcol@bg@mayhavecol@C}

+% \SpecialIndex{\pcol@bg@mayhavecol@g}\SpecialIndex{\pcol@bg@mayhavecol@G}

+% 

+% is defined, and if not, raises an error again in a similar way, or
+% otherwise invokes \!\pcol@backgroundcolor@ii! after re\!\def!ining
+% $a'=a{\cdot}|@|{\cdot}c$.
+% 
+% Then if $\fdef=\true$, the macro \!\pcol@backgroundcolor@ii! examines if
+% $\!\set@color!=\!\relax!$, and if so it complains that any coloring
+% packages have not been loaded and invokes \!\pcol@backgroundcolor@w! just
+% for throwing away optional arguments for \bgext{} and
+% \oarg{mode}\marg{color}.  Otherwise, i.e., if $\!\set@color!\neq\!\relax!$,
+% it invokes \!\pcol@backgroundcolor@iii!  after adding $a'$ to the tail of
+% \!\pcol@bg@defined!.  On the other hand if $\fdef=\false$, it invokes
+% \!\pcol@backgroundcolor@z! without checking the availability of coloring
+% macros.
+% 
+% The macro \!\pcol@backgroundcolor@iii! at first invokes
+% $\!\pcol@bg@defext!\Arg{d}\Arg{e}$ with $e=0$ for all
+% $d\in\{|l|,|r|,|t|,|b|\}$ to have default (no) \bgext{}s.  Then if
+% $|(|x_0|,|y_0|)|$ is provided, \!\pcol@bg@defext! is invoked again by
+% \!\pcol@backgroundcolor@iv! for all
+% $d\in\{|l|,|r|,|t|,|b|\}$ but with $e=x_0$ for
+% $d\in\{|l|,|r|\}$ and with $e=y_0$ for $d\in\{|t|,|b|\}$.
+% Further, if % $|(|x_1|,|y_1|)|$ is also provided, \!\pcol@bg@defext! is
+% invoked once again by \!\pcol@backgroundcolor@v! for all
+% $(d,e)\in\{(|r|,x_1),(|b|,y_1)\}$.  Finally \!\pcol@backgroundcolor@v!
+% invokes \!\pcol@backgroundcolor@x!, which is also invoked from
+% \!\pcol@backgroundcolor@iii! and \!\pcol@backgroundcolor@iv! if they find no
+% (further) \bgext{}s.
+% 

+%    \begin{macrocode}
+\def\backgroundcolor#1{\@tempswatrue
+  \let\pcol@backgroundcolor@e\pcol@backgroundcolor@w
+  \pcol@backgroundcolor#1\@nil}
+\def\nobackgroundcolor#1{\@tempswafalse
+  \let\pcol@backgroundcolor@e\pcol@backgroundcolor@z
+  \pcol@backgroundcolor#1\@nil}
+\def\pcol@backgroundcolor#1{%
+  \@ifundefined{pcol@bg@@#1}%
+    {\PackageError{paracol}%
+       {Invalid background coloring region identifier #1}%
+     \def\pcol@bg@region{xx}\pcol@backgroundcolor@e}%
+    {\def\pcol@bg@region{#1}%
+     \@ifnextchar[%]
+       \pcol@backgroundcolor@i \pcol@backgroundcolor@ii}}
+\def\pcol@backgroundcolor@i[#1]{%
+  \@ifundefined{pcol@bg@mayhavecol@\pcol@bg@region}%
+    {\PackageError{paracol}%
+       {Column number \number#1 is not effective for background coloring region
+        \pcol@bg@region}%
+     \def\pcol@bg@region{xx}\pcol@backgroundcolor@e}%
+    {\edef\pcol@bg@region{\pcol@bg@region @#1}%
+     \pcol@backgroundcolor@ii}}
+\def\pcol@backgroundcolor@ii{%
+  \if@tempswa
+    \ifx\set@color\relax
+      \PackageWarning{paracol}{\string\backgroundcolor\space is not effective
+        without some coloring package}%
+      \let\reserved@b\pcol@backgroundcolor@w
+    \else
+      \let\reserved@b\pcol@backgroundcolor@iii
+      \@cons\pcol@bg@defined{{\pcol@bg@region}}%
+    \fi
+  \else
+    \let\reserved@b\pcol@backgroundcolor@z
+  \fi
+  \reserved@b}
+\def\pcol@backgroundcolor@iii{%
+  \pcol@bg@defext{l}\z@ \pcol@bg@defext{r}\z@
+  \pcol@bg@defext{t}\z@ \pcol@bg@defext{b}\z@
+  \@ifnextchar(%)
+    \pcol@backgroundcolor@iv \pcol@backgroundcolor@x}
+\def\pcol@backgroundcolor@iv(#1,#2){%
+  \pcol@bg@defext{l}{#1}\pcol@bg@defext{r}{#1}%
+  \pcol@bg@defext{t}{#2}\pcol@bg@defext{b}{#2}%
+  \@ifnextchar(%)
+    \pcol@backgroundcolor@v \pcol@backgroundcolor@x}
+\def\pcol@backgroundcolor@v(#1,#2){%
+  \pcol@bg@defext{r}{#1}\pcol@bg@defext{b}{#2}%
+  \pcol@backgroundcolor@x}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@backgroundcolor@x}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@y}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% 

+% The macro \!\pcol@backgroundcolor@x! is used in
+% \!\pcol@backgroundcolor@iii!, \!\pcol@backgroundcolor@iv! and
+% \!\pcol@backgroundcolor@v! to define the color for \bgpaint{} of the
+% region $a'=\!\pcol@bg@region!$.  Since the macro is followed by the
+% arguments \oarg{mode}\marg{color} of \!\backgroundcolor!, the macro
+% invokes \!\color! to let it \!\def!ine \!\current@color! but without real
+% coloring operations by letting
+% \!\set@color!${}={}$\!\pcol@backgroundcolor@y!.  Therefore
+% \!\pcol@backgroundcolor@y! is invoked in \!\color! and it \!\xdef!ines
+% $|\pcol@bg@colpr|{\cdot}a'$ to let it have whatever \!\current@color! has.
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% 

+%    \begin{macrocode}
+\def\pcol@backgroundcolor@x#1\@nil{\begingroup
+  \let\set@color\pcol@backgroundcolor@y \color}
+\def\pcol@backgroundcolor@y{%
+  \expandafter\xdef\csname pcol@bg@color@\pcol@bg@region\endcsname
+   {\current@color}%
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\pcol@backgroundcolor@z}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@w}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% \begin{macro}{\pcol@backgroundcolor@wi}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@bg@color@xx}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% 

+% The macro \!\pcol@backgroundcolor@z! is invoked from
+% \!\pcol@backgroundcolor@ii! directly to work for \!\nobackgroundcolor! to
+% disable the \bgpaint{} for a region $a'=\!\pcol@bg@region!$, or from
+% \!\pcol@backgroundcolor! and \!\pcol@backgroundcolor@i! through
+% \!\pcol@backgroundcolor@e! when they find an error in the argument
+% $\arg{region}$ of \!\nobackground~color!.  Similarly the macro
+% \!\pcol@backgroundcolor@w! is invoked from \!\pcol@background~color@ii!
+% directly when it finds no coloring packages have not been loaded, or
+% \!\pcol@backgroundcolor! and \!\pcol@backgroundcolor@i! through
+% \!\pcol@backgroundcolor@e! on error too but in the argument of
+% \!\backgroundcolor!.  Both macros throw away whatever remains in
+% $\arg{region}$ unprocessed and then invoke \!\pcol@backgroundcolor@wi!,
+% but \!\pcol@backgroundcolor@z! gives it a dummy argument pair, while
+% \!\pcol@backgroundcolor@w! passes \oarg{mode}\marg{color} to it.
+% 
+% Then \!\pcol@backgroundcolor@wi! throw all arguments away and lets
+% $|\pcol@bg@color@|{\cdot}a'\~=\!\relax!$ so that the region $a'$ is
+% untouched in \bgpaint{} macros.  Note that since
+% $a'=|xx|$ being an absolutely non-exsistent region when this macro is used
+% for error recovery, undefining \pcol@bg@color@xx is not harmful.
+% 

+%    \begin{macrocode}
+\def\pcol@backgroundcolor@z#1\@nil{\pcol@backgroundcolor@wi[]{}}
+\def\pcol@backgroundcolor@w#1\@nil{\@ifnextchar[%]
+  \pcol@backgroundcolor@wi{\pcol@backgroundcolor@wi[]}}
+\def\pcol@backgroundcolor@wi[#1]#2{%
+  \expandafter\global\expandafter\let
+    \csname pcol@bg@color@\pcol@bg@region\endcsname\relax}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \KeepSpace{2}
+% \begin{macro}{\pcol@bg@mayhavecol@c}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@bg@mayhavecol@C}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@bg@mayhavecol@g}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% \begin{macro}{\pcol@bg@mayhavecol@G}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor} and
+%	 \cs{nobackgroundcolor}.}

+% 

+% The macros $|\pcol@bg@mayhavecol@|{\cdot}a$ where $a\in\{|c|,|C|,|g|,|G|\}$
+% are used in \!\pcol@background~color@i! when the region specifier $a$ in
+% $\arg{region}$ argument of \!\backgroundcolor! or \!\noback~groundcolor! is
+% followed by optional $|[|c|]|$, so that the invoker macro examines if $a$
+% can have the optional column oridinal.
+% 

+% \SpecialArrayMainIndex{a}{\pcol@bg@mayhavecol@}

+% 

+% Therefore, the macros just need not to be \!\relax! and thus commonly have
+% empty bodies.
+% 

+%    \begin{macrocode}
+\def\pcol@bg@mayhavecol@c{}
+\def\pcol@bg@mayhavecol@C{}
+\def\pcol@bg@mayhavecol@g{}
+\def\pcol@bg@mayhavecol@G{}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@bg@defext}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{backgroundcolor}.}

+% The macro $\!\pcol@bg@defext!\Arg{d}\Arg{e}$ is used by
+% \!\pcol@backgroundcolor@iii!,
+% \!\pcol@back~groundcolor@iv! and \!\pcol@backgroundcolor@v! to \!\def!ine 
+% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'$ be $e=0$ for all
+% $d\in\{|l|,|r|,|t|,|b|\}$ in the first, be $e=x_0$ for $d\in\{|l|,|r|\}$
+% and $e=y_0$ for $d\in\{|t|,|b|\}$ in the second, and be $e=x_0$, $x_1$,
+% $y_0$ and $y_1$ for $d$ being |l|, |r|, |t|, |b| respectively in the last.
+% 

+% \SpecialArrayMainIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% \SpecialArrayMainIndex
+%   {d{\cdot}\string\texttt{@}{\cdot}a{\cdot}\string\texttt{@}{\cdot}c}

+%   {\pcol@bg@ext@}

+% 

+% The macro at first lets \!\@tempdima! have $e$ to confirm $e$ is a proper
+% dimension and then \!\xdef!ines
+% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'$ to let it have the integer
+% representaion of $e$ followed by |sp|.
+% 

+% \SpecialArrayMainIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}

+% \SpecialArrayMainIndex
+%   {d{\cdot}\string\texttt{@}{\cdot}a{\cdot}\string\texttt{@}{\cdot}c}

+%   {\pcol@bg@ext@}

+% 

+% 

+%    \begin{macrocode}
+\def\pcol@bg@defext#1#2{%
+  \@tempdima#2\relax
+  \expandafter\xdef\csname pcol@bg@ext@#1@\pcol@bg@region\endcsname{%
+    \number\@tempdima sp}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\resetbackgroundcolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to disable background-paiting for all regions.}

+% \begingroup \let\SMALL\small \let\small\footnotesize
+% \begin{macro}{\pcol@resetbackgroundcolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{resetbackgroundcolor}.}

+% \let\small\SMALL
+% \begin{macro}{\pcol@bg@defined}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduced to implement \cs{resetbackgroundcolor}.}

+% 

+% The API macro \!\resetbackgroundcolor! disables \bgpaint{} of all regions
+% whose colors have been specified by \!\backgroundcolor!.  Since the region
+% specifiers $a'_1$, $a'_2$, \ldots, $a'_n$ for which \bgpaint{} is specified
+% are recorded in $\!\pcol@bg@defined!=
+% \!\@elt!\Arg{a'_1}\!\@elt!\Arg{a'_2}\cdots\!\@elt!\Arg{a'_n}$ by
+% \!\pcol@backgroundcolor!, the macro invokes \!\pcol@bg@defined!
+% temporarily letting $\!\@elt!=\!\pcol@resetbackgroundcolor!$ to let
+% $|\pcol@bg@|\~|color@|{\cdot}a'_i$ be \!\relax! for all $i\in[1,n]$, and
+% clears \!\pcol@bg@defined!, whose initial state is also empty.
+% 

+% \SpecialArrayIndex{a}{\pcol@bg@color@}

+% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}

+% 

+%    \begin{macrocode}
+\def\resetbackgroundcolor{{%
+  \let\@elt\pcol@resetbackgroundcolor \pcol@bg@defined
+  \gdef\pcol@bgdefined{}}}
+\def\pcol@resetbackgroundcolor#1{%
+  \expandafter\global\expandafter\let\csname pcol@bg@color@#1\endcsname\relax}
+\gdef\pcol@bg@defined{}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\endgroup\end{macro}
+% 
+% 
+% 
+% \section{Closing Environment}
+% \label{sec:imp-end}
+% 
+% \begin{macro}{\endparacol}
+% \changes{v1.0}{2011/10/10}
+%	{Replace \cs{par} with \cs{pcol@par}.}

+% \changes{v1.2-2}{2013/05/11}
+%	{Add pre-flushing column height check and footnote counter
+%	 adjustment.}

+% \changes{v1.2-5}{2013/05/11}
+%	{Remove \cs{global} assignment of \cs{hsize} and \cs{linewidth}
+%	 because assigments of them in \string\texttt{paracol} are now
+%	 perfectly local.}
+% \changes{v1.31}{2013/10/10}
+%	{Add saving $c$ into \cs{pcol@lastcol} to let \cs{pcol@output@end}
+%	 know the column visited last.}

+% \begin{macro}{\pcol@lastcol}
+% \changes{v1.31}{2013/10/10}
+%	{Introduced to keep the column visited last to pass its typesetting
+%	 parameters to post-environment.}

+% 

+% The macro \!\endparacol! is invoked from \Endparacol{} to close
+% \env{paracol} environment.  After making it sure to be in vertical mode by
+% \!\pcol@par!, we switch to the column 0 by \!\pcol@switchcol! to let
+% \lcounter{} have the values for the column 0 so that they are referred to
+% outside the environment, after saving the current column $c$ in
+% \!\pcol@lastcol! to be referred to in \!\pcol@output@end! so that
+% $\cc_c(\sw)$ and $\cc_c(\ep)$ are passed to \postenv.
+% 
+% \begin{Sloppy}{1800}
+% Then we invoke \!\pcol@flushclear! for \pfcheck{}, turning
+% $\CSIndex{ifpcol@lastpage}=\true$ to tell \!\pcol@output@switch! for the
+% check that it works on the \lpage, and giving $\bot$ to \!\pcol@flushclear! 
+% as its argument, unless footnote typesetting is \scfnote{} but not
+% \mgfnote{} for which we give $\df$ to ensure all deferred footnotes are
+% put in the checking process.  Note that the argument for \Mcfnote{}
+% typesetting is $\df$ but it is definitely $\bot$ in this mode.  After that
+% we make an \!\output! request by \!\pcol@invokeoutput! with
+% $\!\penalty!=\!\pcol@op@end!$ and still with
+% $\CSIndex{ifpcol@lastpage}=\true$ to build the \lpage.
+% \end{Sloppy}
+% 
+% Next, we let $\!\columnwidth!=\!\textwidth!$ and
+% $\CSIndex{if@twocolumn}=\false$ for single-column typesetting, and also
+% let $\!\topskip!=\!\pcol@topskip!$ to make it sure that the parameter has
+% the value used outside in \env{paracol} environment.  Finally, if the
+% \counter{footnote} counter adjustment is required by
+% $\CSIndex{ifpcol@fncounteradjustment}=\true$, we let
+% $\!\c@footnote!=\bf+\nf$.
+% 

+%    \begin{macrocode}
+%% Closing Environment
+
+\def\endparacol{\pcol@par
+  \edef\pcol@lastcol{\number\pcol@currcol}%
+  \pcol@nextcol\z@ \pcol@switchcol
+  \pcol@lastpagetrue
+  \ifpcol@mgfnote \pcol@flushclear\voidb@x
+  \else \pcol@flushclear\pcol@topfnotes
+  \fi
+  \pcol@invokeoutput\pcol@op@end
+  \global\columnwidth\textwidth
+  \global\@twocolumnfalse
+  \global\topskip\pcol@topskip
+  \ifpcol@fncounteradjustment
+    \global\c@footnote\pcol@footnotebase
+    \global\advance\c@footnote\pcol@nfootnotes
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@restoreeveryvbox}
+% \changes{v1.22}{2013/06/30}
+% 	{Introduced to reflect \cs{global} updates on \cs{everyvbox} in
+%	 \string\texttt{paracol} environments.}
+% 

+% The macro \!\pcol@restoreeveryvbox! is invoked just after \Endparacol{} by
+% \!\aftergroup! mechanism activated by \!\pcol@zparacol!.  It examines if
+% \!\pcol@everyvbox! has tokens different from \!\pcol@dummytoken! which
+% \!\pcol@zparacol! \!\global!ly assigned to the register.  Since the dummy
+% token cannot be assigned to \!\everyvbox!\footnote{

+% 

+% Unless a very surprising coincidence happens or a user intentionally
+% violates the coherence of the implementation.},
+% 

+% the difference means the \!\everyvbox! has been \!\global!ly updated with
+% the value that \!\pcol@everyvbox! has now.  Therefore if so, we
+% globally update \!\everyvbox! with \!\pcol@everyvbox! to refrect the
+% global update in the environment.
+% 

+%    \begin{macrocode}
+\def\pcol@restoreeveryvbox{%
+  \expandafter\def\expandafter\reserved@a\expandafter{\the\pcol@everyvbox}%
+  \def\reserved@b{\pcol@dummytoken}%
+  \ifx\reserved@a\reserved@b\else \global\everyvbox\pcol@everyvbox \fi}
+%    \end{macrocode}
+% \end{macro}
+%\iffalse
+%</paracol>
+%\fi
+\endinput
diff --git a/macros/latex/contrib/paracol/man.dtx b/macros/latex/contrib/paracol/man.dtx
new file mode 100644
index 0000000000..f604ba24fa
--- /dev/null
+++ b/macros/latex/contrib/paracol/man.dtx
@@ -0,0 +1,863 @@
+% \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 arbitrarily 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{fn:first}}.
+% 
+% \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 ordinal of the column you are leaving from 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 single-column {\em\Uidx\mctext} whose bottom is the
+% vertical alignment point of columns.  For example, \!\section!
+% commands in this manual are given as optional arguments
+% of \!\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}]
+% \Uidx{\Index{column-switching environment}}

+% \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-structuralization 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[Environments \texttt{leftcolumn} and \texttt{rightcolumn}]

+%     {Environments \texttt{leftcolumn} and\\\texttt{rightcolumn}}
+% The environments \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}| to switch
+% to the left(most) column and
+% \!\begin!|{|\env{nthcolumn}|}{1}| to the right (but may not be rightmost)
+% one.
+% 

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

+% 
+% \begin{figure*}\nosv
+% \def\arraystretch{0.8}
+% \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
+% \def\arraystretch{0.8}
+% \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{%
+%  Environments \texttt{leftcolumn} and\\
+%  \texttt{rightcolumn}}
+%The environments |leftcolumn| and
+%|rightcolumn| (and their starred versions
+%with an optional argument) are available as
+%more convenient means than saying
+%|\begin{nthcolumn}{0}| to switch to the
+%left(most) column and ...
+%\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
+% \def\arraystretch{0.8}
+% \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}]
+% \changes{v1.2-7}{2013/05/11}
+% 	{Remove \cs{nosv} from verbatim example of Table~1 shown in the right
+%	 column.}
+% \changes{v1.32-3}{2015/10/10}
+% 	{Add footnote to mention the page-wise float problem.}
+% \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\footnote{

+% 

+% See Section~\ref{sec:problem} for the appearance order issue of
+% double-column floats.}.
+% 

+% A single-column figure\slash table will be placed in the column in which
+% you put \env{figure} and \env{table}.  For example, the body of a
+% \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 be 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 this page into the \env{leftcolumn*} and \env{rightcolumn}
+% environment for the previous section.
+% 
+% \subsection{Footnotes and Marginal Notes}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Add a footnote mentioning page-wise footnotes.}

+%
+% Footnotes are also put at the bottom of the column in which \!\footnote!
+% commands and their references reside (like this\footnote{

+% 

+% Unless you specify to make footnotes {\em page-wise} as explained in
+% Section \ref{sec:ref-scfnote} and \ref{sec:fnnp}.}),
+% 

+% as shown in page~\pageref{fn:first} 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 in the right margin in default setting.  The
+% \textsf{paracol} package solves the placement problem of marginal notes
+% from two or more columns sharing a side margin by moving some of them down
+% if they conflict over the space with each other.}.
+% 
+% \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, subsection 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 values
+% of the \lcounter{}s are the values they have at
+% \!\begin!|{|\env{paracol}|}|.  After you close the \env{paracol}
+% environment, the values of the leftmost 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{fn:right3} and \pageref{fn:right4}.
+% 
+% This broadcasting of a \lcounter{} value can be done explicitly in
+% \env{paracol} environments 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!} performs 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 document is
+% \counter{section}.  As explained in Section~\ref{sec:sync}, an optional
+% \mctext{} of \cswitch{} is considered as in the leftmost column.  Since
+% \!\section! commands in this document are always given in \mctext{}s, so
+% far, it seems unnecessary to make \counter{section} global because it is
+% incremented correctly in the leftmost column.  However, the stepping
+% \counter{section} has a side effect to reset its descendent counter
+% \counter{subsection} and referred to from \!\thesubsection! command.  Thus
+% if \counter{section} were local, the right-column subsections 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 subsections of this section would be ``0.4'', ``0.5'' and
+% ``0.6'' because stepping \counter{section} local to the left column would
+% not reset \counter{subsection} local to the right column.
+% 
+% 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]
+%\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{fn:right3}}. ...}
+% 
+% \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 reside (like
+%this\footnote{...}), 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 note in this
+%\end{Verbatim}
+% |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*}
+%\begin{rightcolumn}
+%\end{Verbatim}
+% \textit{source}.\\
+% |\end{rightcolumn}|
+%
+% \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 the \env{paracol} environment above is closed.  As you are seeing, a
+% \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\label{fn:flush}.
+% 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{paracol}{2}
+%\begin{leftcolumn}
+%The environment may also be restarted
+%anywhere you like as shown here. ...
+%\end{leftcolumn}
+%\begin{rightcolumn}
+%\end{Verbatim}
+% \textit{source}\\
+% |\end{rightcolumn}|\\
+% |\end{paracol}|\\
+% |Now the aurthor will do ...|
+% \end{rightcolumn}
+% \end{paracol}
+% 
+% \changes{v1.1}{2012/05/11}
+% 	{Add \cs{columnratio}\texttt{\char`\{0.6\char`\}} and a phrase
+%	 for it.}
+% Now the author will do |\flushpage| shortly to start a real binlingual
+% example from the next page, after showing another example of closing 
+% \env{paracol} environments in this sentence and of restarting in the next
+% one, in which {\em unbalanced column width} is demonstrated using
+% \Uidx{\!\columnratio!} command shown in Section~\ref{sec:ref-colwidth}.
+% 
+% \columnratio{0.6}
+% \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}
+%\columnratio{0.6}
+%\begin{paracol}{2}
+%\begin{leftcolumn}
+%O.K., ...
+%\end{leftcolumn}
+%\end{Verbatim}
+% |\begin{rightcolumn}| \textit{source}\\
+% |\end{rightcolumn}|
+% \flushpage
+% \end{rightcolumn}
+% 
+% 
+% 
+% \changes{v1.2-7}{2013/05/11}
+% 	{Correct a few words in German and English libretti.}
+% \newenvironment{Gverse}{\ensurevspace{2\baselineskip}\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}\label{page:bfreude}\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, I could find
+% the German translation of the right column footnote \ref{fn:right4} is
+% ``Dieser Teil wurde van Beethoven hinzugef\"ugt'' by myself without
+% the kind help from a user.}.
+% \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{fn:right4}}.
+% \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 brothers\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, alle 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}
+% \label{page:efreude}
+% \endgroup
+\endinput
diff --git a/macros/latex/contrib/paracol/paracol-man.pdf b/macros/latex/contrib/paracol/paracol-man.pdf
new file mode 100644
index 0000000000..514fdec6dd
--- /dev/null
+++ b/macros/latex/contrib/paracol/paracol-man.pdf
diff --git a/macros/latex/contrib/paracol/paracol.dtx b/macros/latex/contrib/paracol/paracol.dtx
new file mode 100644
index 0000000000..98de092916
--- /dev/null
+++ b/macros/latex/contrib/paracol/paracol.dtx
@@ -0,0 +1,825 @@
+%\iffalse
+%<paracol>%% Style file `paracol'.
+%<man>%% LaTeX file 'paracol-man'.
+%<*paracol|man>
+%% Copyright (C) 2005-2018
+%%   Hiroshi Nakashima <h.nakashima@DOMAIN;  DOMAIN=media.kyoto-u.ac.jp>
+%%   (Kyoto University)
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License distributed from CTAN
+%% archives in directory macros/latex/base/lppl.txt; either
+%% version 1 of the License, or any later version.
+
+%</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}
+[2018/12/31 v1.35 ]
+% \iffalse
+%<*man>
+\documentclass{ltxdoc}\normalmarginpar
+\usepackage{color}
+\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|}
+% \gdef\Bar{|}
+% \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
+% 
+% \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
+% \edef\RAFCIfPrefix{\expandafter\string\csname if\endcsname}
+% \edef\RAFCIfPrefix{\expandafter\RAFCgobble\RAFCIfPrefix}
+% \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\RAFCIfPrefix
+%	\else\ifx\RAFCtempb\CommonCSPrefix
+%	\else\ifx\RAFCtempb\CommonIfPrefix
+%	\else \def\RAFCtempa{}\def\next{\xRemoveAtFromCS#2@#3\NIL}

+% 	\fi\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}

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

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

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

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

+%	\texttt{\@tempb}

+% 	\expandafter\SpecialIndex\@tempa}
+% \def\CSINDEX#1{\expandafter\def\expandafter\@tempa\expandafter{\csname
+% 	#1\endcsname}

+% 	\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\Oarg#1{\texttt{[\textit{#1}]}}
+% \def\Sub#1{{\hbox to0pt{\hss$\scriptstyle #1$\hss}}}
+% \def\PT{\,{\rm pt}}
+% 
+% \def\Sloppy#1{\tolerance#1\hbadness#1\relax}
+% \let\endSloppy\par
+% \def\Hfuzz#1{\hfuzz#1\relax}
+% \let\endHfuzz\par
+% \def\KeepSpace#1{\par \vskip-\lastskip \vskip#1\baselineskip \allowbreak
+%   \vskip-#1\baselineskip\nobreak}
+% 
+% 
+% 
+% \edef\CommonCSPrefix{\expandafter\RAFCgobble\string\pcol}
+% \edef\CommonIfPrefix{\expandafter\RAFCgobble\string\ifpcol}
+% 
+% \def\beginenv#1{\CSIndex{begin}\allowbreak
+% 	\texttt{\char`{#1\char`}}\EnvIndex{#1}}
+% \def\beginparacol{\beginenv{paracol}}
+% 
+% \def\bgext{extension\Index{extension of background painting region}}
+% \def\bginfext{infinite extension

+%     \Index{infinite extension of background painting region}}
+% \def\bgpaint{background painting\Index{background painting}}
+% \def\bground{background\Index{background painting}}
+% \def\bpage{base page\Index{base page}}
+% \def\colorctext{color context\Index{color context}}
+% \def\colorstack{color stack\Index{color stack}}
+% \def\cctext{column-context\Index{column-context}}
+% \def\colpage{column-page\Index{column-page}}
+% \def\colpream{column preamble\Index{column preamble}}
+% \def\Colpream{preamble\Index{column preamble}}
+% \def\cscan{column-scan\Index{column-scan}}
+% \def\csepgap{column-separating gap\Index{column-separating rule}}
+% \def\cseprule{column-separating rule\Index{column-separating rule}}
+% \def\cswap{column-swapping\Index{column-swapping}}
+% \def\cswitch{column-switching\Index{column-switching}}
+% \def\csenv{column-switching environment\Index{column-switching environment}}
+% \def\cwise{column-wise\Index{column-wise stuff}}
+% \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\Mcfnote{column-wise footnote\Index{column-wise footnote}}
+% \def\mcfnote{column-wise\Index{column-wise footnote}}
+% \def\Mgfnote{merged footnote\Index{merged footnote}}
+% \def\mgfnote{merged\Index{merged footnote}}
+% \def\mctext{spanning text\Index{spanning text}}
+% \def\mirror{mirror\Index{mirrored background painting}}
+% \def\mvlfloat{MVL-float\Index{MVL-float}}
+% \def\npaired{non-paired\Index{non-paired parallel-paging}}
+% \def\paired{paired\Index{paired parallel-paging}}
+% \def\parapag{parallel-pag\Index{parallel-paging}}
+% \def\pctext{page context\Index{page context}}
+% \def\pfcheck{pre-flushing column height check

+%	\Index{pre-flushing column height check}}
+% \def\Postenv{post-environment\Index{post-environment stuff}}
+% \def\postenv{post-environment stuff\Index{post-environment stuff}}
+% \def\Preenv{pre-environment\Index{pre-environment stuff}}
+% \def\preenv{pre-environment stuff\Index{pre-environment stuff}}
+% \def\prespan{pre-spanning-text stuff\Index{pre-spanning-text stuff}}
+% \def\prim{page rim\Index{page rim}}
+% \def\pwise{page-wise\Index{page-wise stuff}}
+% \def\pwstuff{page-wise stuff\Index{page-wise stuff}}
+% \def\Scfnote{page-wise footnote\Index{page-wise footnote}}
+% \def\scfnote{page-wise\Index{page-wise footnote}}
+% \def\spanning{spanning stuff\Index{spanning stuff}}
+% \def\sptext{spanning text\Index{spanning text}}
+% \def\spage{starting page\Index{starting page}}
+% \def\sync{synchroniz\Index{synchronize}}
+% \def\tpage{top page\Index{top page}}
+% 
+% \def\vb{\Index[$\kappa_c(\beta)$]{-k_c(-b)}\beta}
+% \def\pd{\Index[$\kappa_c(\delta)$]{-k_c(-d)}\delta}
+% \def\Celt{\Index[$\gamma_0^c$]{-c^c_0}\gamma_0}
+% \def\Celtshadow{\Index[$\hat\gamma_0^c$]{-c^xc_0}\hat\gamma_0}
+% \def\celt{\Index[$\gamma_i$]{-c^a_i}\gamma}
+% \def\celtpop{\Index[$\gamma_i^-$]{-c^m_i}\gamma^-}
+% \def\celtshadow{\Index[$\hat\gamma_i$]{-c^x_i}\hat\gamma}
+% \def\mcelt{\Index[$\gamma_{i,m}$]{-c^a_i,m}\gamma}
+% \def\mceltpop{\Index[$\gamma_{i,m}^-$]{-c^m_i,m}\gamma^-}
+% \def\cst{\Index[$\string\mathit{\Gamma}$]{-C^a}\mathit{\Gamma}}
+% \def\CST{\Index[$\string\mathit{\Gamma}^c$]{-C^c}\mathit{\Gamma}}
+% \def\CSTraw{\Index[$\string\mathit{\Gamma}^c_r$]{-C^c_r}\mathit{\Gamma}_r}
+% \def\cstraw{\Index[$\string\mathit{\Gamma}_r$]{-C^a_r}\mathit{\Gamma}_r}
+% \def\csts{\Index[$\string\mathit{\Gamma}_s$]{-C_s}\mathit{\Gamma}_s}
+% \def\CSTshadow{\Index[$\hat\string\mathit{\Gamma}^c$]{-C^xc}

+%   \hat\mathit{\Gamma}}
+% \def\cstshadow{\Index[$\hat\string\mathit{\Gamma}$]{-C^x}\hat\mathit{\Gamma}}
+% \def\ep{\Index[$\kappa_c(\varepsilon)$]{-k_c(-e)}\varepsilon}
+% \def\clist{\Index[$\zeta(\theta)$]{-f(-j)}\zeta}
+% \def\fh{\Index[$\kappa_c(\eta)$]{-k_c(-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\CTL{\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[$\kappa_c(\lambda_b)$]{-k_c(-l_b)}\lambda_b}
+% \def\dl{\Index[$\kappa_c(\lambda_d)$]{-k_c(-l_d)}\lambda_d}
+% \def\ml{\Index[$\kappa_c(\lambda_m)$]{-k_c(-l_m)}\lambda_m}
+% \def\tl{\Index[$\kappa_c(\lambda_t)$]{-k_c(-l_t)}\lambda_t}
+% \def\lrm{\Index[$\mu$]{-m}\mu}
+% \def\bn{\Index[$\kappa_c(\nu_b)$]{-k_c(-n_b)}\nu_b}
+% \def\cn{\Index[$\kappa_c(\nu_c)$]{-k_c(-n_c)}\nu_c}
+% \def\tn{\Index[$\kappa_c(\nu_t)$]{-k_c(-n_t)}\nu_t}
+% \def\tf{\Index[$\kappa_c(\xi)$]{-k_c(-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[$\kappa_c(\rho_b)$]{-k_c(-r_b)}\rho_b}
+% \def\tr{\Index[$\kappa_c(\rho_t)$]{-k_c(-r_t)}\rho_t}
+% \def\sw{\Index[$\kappa_c(\sigma)$]{-k_c(-s)}\sigma}
+% \def\ft{\Index[$\kappa_c(\tau)$]{-k_c(-t)}\tau}
+% \def\df{\Index[$\string\mathit{\Phi}$]{-U}\mathit{\Phi}}
+% 
+% \def\bf{\Index[$b_f$]{b_f}b_f}
+% \def\bgc{\Index[$B_a$]{B_a}B}
+% \def\bge{\Index[$e_a(d^\pm)$]{e_a(d^+)}e}
+% \def\bgr{\Index[$R_a$]{R_a}R}
+% \def\C{\Index[$C$]{C}C}
+% \def\Cfrom{\Index[$C^0$]{C0^0}{C^0}}
+% \def\CBfrom{\Index[$C_b^0$]{C0_b^0}{C_b^0}}
+% \def\CBto{\Index[$C_b^1$]{C0_b^1}{C_b^1}}
+% \def\CL{\Index[$C_L$]{C0_L}C_L}
+% \def\Cto{\Index[$C^1$]{C0^1}{C^1}}
+% \def\cmax{\Index[$c_{\max}$]{c0_max}c_{\max}}
+% \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[$F_c(X)$]{F0_c}F_c}
+% \def\fc{\Index[$f_c(x)$]{f0_c}f_c}
+% \def\gap{\Index[$g_c$]{g_c}g}
+% \def\HB{\Index[$H_B$]{H_B}H_B}
+% \def\HM{\Index[$H_M$]{H_M}H_M}
+% \def\HN{\Index[$H_N$]{H_N}H_N}
+% \def\HP{\Index[$H_P$]{H_P}H_P}
+% \def\HR{\Index[$H_R$]{H_R}H_R}
+% \def\HS{\Index[$H_S$]{H_S}H_S}
+% \def\HT{\Index[$H_T$]{H_T}H_T}
+% \def\mplist{\Index[$I$]{I}I}
+% \def\nf{\Index[$n_f$]{n_f}n_f}
+% \def\npop{\Index[$n_{\rm pop}$]{n_pop}n_{\rm pop}}
+% \def\mpar{\Index[$\mathit{mpar}(t_i,b_i)$]{mpar(t_i,b_i)}\mathit{mpar}}
+% \def\mpb{\Index[$M_{\{L,R\}}^{\{l,r\}}$]{M0_{L,R}^{l,r}}M}
+% \def\mpbout{\Index[${\string\cal{M}}$]{M1}{\cal M}}
+% \def\mpboutz{\Index[${\string\cal{M}}_0$]{M1_0}{\cal M}_0}
+% \def\pbase{\Index[$p_b$]{p0_b}p_b}
+% \def\ptop{\Index[$p_t$]{p0_t}p_t}
+% \def\page{\Index[$\string\mathit{page}(p)$]{page(p)}\mathit{page}}
+% \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\spt{\Index[$\mathit{span}(H_i,h_i)$]{span(H_i,h_i)}\mathit{span}}
+% \def\T{\Index[$T$]{T}T}
+% \def\true{\Index[$\string\mathit{true}$]{true}\mathit{true}}
+% \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[$v_c(x)$]{v1_c}v_c}
+% \def\VB{\Index[$V_B$]{V0_B}V_B}
+% \def\VE{\Index[$V_E$]{V0_E}V_E}
+% \def\VP{\Index[$V_P$]{V0_P}V_P}
+% \def\VPP{\Index[$V'_P$]{V0_Px}V'_P}
+% \def\VT{\Index[$V_T$]{V0_T}V_T}
+% \def\w{\Index[$w_c$]{w1_c}w}
+% \def\W{\Index[$W_c$]{W0_c}W}
+% \def\WM{\Index[$W_M$]{W0_M}W_M}
+% \def\WP{\Index[$W_P$]{W0_P}W_P}
+% \def\WR{\Index[$W_R$]{W0_R}W_R}
+% \def\WT{\Index[$W_T$]{W0_T}W_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}
+%
+% \def\Dotfill{\leavevmode\cleaders\hbox to.44em{\hss.\hss}\hfill\kern0pt}
+% \def\Marginpar#1{\marginpar{\raggedright#1}}
+% \def\Emph#1{{\bfseries#1}}
+% \def\Hrule{\hbox to\linewidth{\hrulefill}}
+% \def\\{\hfil\break\null\ignorespaces}
+% 
+% \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. (2005/01/28)}
+% \changes{v0.91}{2011/09/16}
+%	{The style is included in CTAN with a very small
+%	 modification. (2011/09/16) }
+% \changes{v1.0}{2011/10/10}
+%	{Add this document and fix the following problems on the author's
+%	 30th wedding anniversary. (2011/10/10)}
+% \changes{v1.1}{2012/05/11}
+% 	{Add \cs{columnratio} and variable column width. (2012/05/11)}
+% \changes{v1.2-1}{2013/05/11}
+%	{Make \string\texttt{paracol} environment accept \cs{color} and add
+%	 \cs{columncolor}. (2013/05/11)}
+% \changes{v1.2-2}{2013/05/11}
+%	{Add page-wise and merged footnote functions. (2013/05/11)}
+% \changes{v1.2-3}{2013/05/11}
+%	{Fix a problem in synchronization. (2013/05/11)}
+% \changes{v1.2-4}{2013/05/11}
+%	{Add column-swapping functions. (2013/05/11)}
+% \changes{v1.2-5}{2013/05/11}
+%	{Allow a \string\texttt{paracol} envrionment is enclosed in list-like
+%	 environments. (2013/05/11)}
+% \changes{v1.2-6}{2013/05/11}
+%	{Add \cs{localcounter}. (2013/05/11)}
+% \changes{v1.2-7}{2013/05/11}
+%	{Bug fixes and minor revisions as follows. (2013/05/11)}
+% \changes{v1.21}{2013/06/06}
+%	{Fix the bug by which a column having empty column-pages followed by
+%	 a synchronization point is lost or placed in a wrong
+%	 page. (2013/06/06)} 
+% \changes{v1.22}{2013/06/30}
+%	{Fix the bug that \cs{color} and its relatives in a paragraph or
+%	 around page top causes inconsistency of color context. (2013/06/30)}
+% \changes{v1.23}{2013/07/08}
+%	{Fix the problem that a colored text has a line break candidate at
+%	 its end inappropriately. (2013/07/08)}
+% \changes{v1.24}{2013/07/27}
+%	{Fix the problem caused by the concealment of \cs{vadjust} in math
+%	 group. (2013/07/27)}
+% \changes{v1.3-1}{2013/09/17}
+%	{Fix the known problem of the placement of page-crossing spanning
+%	 texts. (2013/09/17)}
+% \changes{v1.3-2}{2013/09/17}
+%	{Introduce parallel-paging. (2013/09/17)}
+% \changes{v1.3-3}{2013/09/17}
+%	{Introduce column-separating rule drawing and background
+%	 painting. (2013/09/17) }
+% \changes{v1.3-4}{2013/09/17}
+%	{Introduce API for column/gap width and marginal note position
+%	 specification. (2013/09/17)}
+% \changes{v1.3-5}{2013/09/17}
+%	{Introduce \cs{thecolumn} and \cs{ensurevspace},
+%	 \cs{footnotelayout}, \cs{twosided} and
+%	 \cs{cleardoublepage}. (2013/09/17)}
+% \changes{v1.3-6}{2013/09/17}
+%	{Fix a few problems mainly related to synchronization and ordinary
+%	 footnotes. (2013/09/17)} 
+% \changes{v1.31}{2013/10/10}
+%	{Add passing paramenters related sectioning commmands beyond
+%	 \cs{end}\texttt{\char`\{paracol\char`\}} and fix misspells in
+%	 error messages. (2013/10/10)}
+% \changes{v1.32-1}{2015/10/10}
+% 	{Add \cs{globalcounter*} to make all counters global. (2015/10/10)}
+% \changes{v1.32-2}{2015/10/10}
+% 	{Fix a memory leak in \cs{pcol@startcolumn}. (2015/10/10)}
+% \changes{v1.32-3}{2015/10/10}
+% 	{Fix a page-wise float problem. (2015/10/10)}
+% \changes{v1.33-1}{2016/11/19}
+% 	{Fix a marginal note problem. (2016/11/19)}
+% \changes{v1.33-2}{2016/11/19}
+% 	{Non-logical modifications to obey the coding convention, for
+%	 clarification, etc.. (2016/11/19)}
+% \changes{v1.34}{2018/05/07}
+% 	{Fix a text coloring problem in non-breakable sequences of vertical
+%	 items. (2018/05/07)}
+% \changes{v1.35-1}{2018/12/31}
+% 	{Fix a page break problem with a tall item in the very first line of
+%	 the first column. (2018/12/31)}
+% \changes{v1.35-2}{2018/12/31}
+% 	{Fix a vertical space problem with \texttt{trivlist} immediately
+%	 surrounding \texttt{paracol}. (2018/12/31)}
+% \changes{v1.35-3}{2018/12/31}
+% 	{Fix a bug in \cs{pcol@addmarginpar} and add emulation of
+%	 \cs{marginnnote}. (2018/12/31)}
+% \changes{v1.35-4}{2018/12/31}
+% 	{Add \cs{belowfootnoteskip} for the additional space below the
+%	 non-merged pre-environment footnotes. (2018/12/31)}
+% \changes{v1.35-5}{2018/12/31}
+% 	{Add \cs{definecolumnpreamble}. (2018/12/31)}
+% \changes{v1.35-6}{2018/12/31}
+% 	{Add error check if \texttt{paracol} environment is not in outer par
+%	 mode and is with ordinary two-column typesetting. (2018/12/31)}
+%
+% 
+% 
+% \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 \ifodd\c@page\else \hbox{}\newpage \fi
+% 
\vbox to\unitlength{\unvbox0\vfil}
+% \part{User's Manual}\label{part:man}
+% \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|.
+% \ifx\ONLYDESCRIPTION\undefined\else
+% See p.\Tie\pageref{page:toc} for the table of contents of this manual.
+% \fi
+% \end{abstract}
+% 
+% 
\tracingpages1 \tracingoutput1 \showboxdepth10000 \showboxbreadth10000
+% \input{man.dtx}
+% 
\tracingpages0 \tracingoutput0
+% \newpage
+% \input{ref.dtx}
+% \newpage
+% \input{pwfnote.dtx}
+% \newpage
+% \twosided
+% \edef\OddSideMargin{\number\oddsidemargin}
+% \advance\oddsidemargin1in
+% \evensidemargin1.25\oddsidemargin \advance\evensidemargin-1in
+% \oddsidemargin.75\oddsidemargin \advance\oddsidemargin-1in
+% \input{ppts.dtx}
+% \newpage
+% \input{bgpaint.dtx}
+% \newpage
+% \twosided[]\oddsidemargin\OddSideMargin sp
+% \resetbackgroundcolor \columnratio{}
+% \input{probs.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}
+% \addcontentsline{toc}{part}{\protect\numberline{}{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 the following people;
+% 

+% Robin Fairbairns who kindly invited the style to CTAN after the author's
+% lazy six years failing to upload the style;
+% 

+% Joseph
+% G.\ Rosenstein and Dieter K\"ohler who suggested the author adding the
+% function of unbalanced column width incorporated in version 1.1;
+% 

+% Joaqu\'in Blas who motivated the author to challenge page-wise footnotes;
+% 

+% Olivier Vogel who pointed out the compatibility problem with coloring
+% packages;
+% 

+% Heiner Richter who asked for the possibility of swapping unbalanced
+% columns, revealed two bugs in version 1.22 related to coloring and
+% float pages, showed the necessity of \!\coloredwordhyphenated!, and finally
+% found the necessity of \!\globalcounter!|*|;
+% 

+% an anonymous user who reported a very rare-case but severe bug in the
+% version~1.1 by which a page can be lost (whoops!);
+% 

+% Olivier Gerard who found another terrible bug fixed in version 1.21 but
+% hidden in \textsf{paracol} for two years by which a column disappears or
+% moves to a wrong page (another whoops!\@), suggested to implement
+% \!\setcolumnwidth!, \!\marginparthreshold! and \!\thecolumn!  introduced
+% in version 1.3, and kindly proofread this manual;
+% 

+% George Kamel who let the author know the coloring function newborn in
+% version 1.2 had a bug fixed in version 1.22 to which he also made a great
+% contribution testing many tentative versions with his own colored
+% documents;
+% 

+% another anonymous user who pointed out version 1.22 had yet another
+% coloring bug fixed in version 1.24;
+% 

+% Jean Druel who motivated the author to implement an advanced functionality
+% parallel-paging;
+% 

+% Tilo Arens and other patient users who had wished \Paracol{} would have the
+% capability of rule drawing in the gaps separating columns and painting
+% backgrounds of columns and so on;
+% 

+% Michael Bolin who gave the author motivated examples showing the
+% necessity of \!\ensurevspace!.
+% 

+% Tigran Aivazian who reported a memory leak problem fixed in version 1.32;
+% 

+% Marcus Zelezny and Touhami Mamouni who found an incompatibility with
+% \LaTeX{} itself (2015/01/10 or later) and enlighten the author on the cause
+% of the problem;
+% 

+% Manuel Kuehner who reported a bug in text coloring which had hidden
+% for five years until the version 1.34 was released;
+% 

+% ZongXian Wang who found that the paracol misbehaves when an environment
+% starts with an unusually tall item;
+% 

+% and Frank Mittelbach who pointed out bugs in \cs{marginpar} implementation
+% and vertical spacing with \cs{trivlist}-like environments, and suggested
+% new functionality with \cs{marginnote}, \cs{belowfootnoteskip} and
+% \cs{definecolumnpreamble}.
+% 
+% For the implementation of the style file, the author referred to the base
+% implementations of \cs{output} and othe many macros of \LaTeXe{} written
+% by Leslie Lamport, Johannes Braams and other authors.  The author also
+% referred to \textsf{color} written by David Carlisle and
+% \textsf{marginnote} written by Markus Kohm to make the package working
+% well with them.
+%
+% \ifx\ONLYDESCRIPTION\undefined\else
+% \newpage\label{page:toc} \tableofcontents
+% \fi
+% 
+% \PrintIndex}
+% 
+% \newpage
+% \addtocounter{page}{2}
+% \let\Midx\MidxSave
+% \advance\oddsidemargin1in\evensidemargin\oddsidemargin
+% \advance\textwidth-1in\columnwidth\textwidth
+% \hsize\textwidth \linewidth\textwidth
+% \part{Implementation}\label{part:impl}
+% \input{impl.dtx}
+% 
+% \IndexPrologue{\newpage\section*{Index}
+% \addcontentsline{toc}{part}{\protect\numberline{}{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{if@}, \cs{pcol@} and 
+% \cs{ifpcol@} from its name if it has one of them.}
+% \Finale
+% \GlossaryPrologue{\newpage\section*{Revision History}
+% \addcontentsline{toc}{part}{\protect\numberline{}{Revision History}}}
+% \def\EQ{=} \def\GT{>} \def\BAR{|} \def\NEQ{\neq} \def\S{\Sec}
+% \PrintChanges
+\endinput
diff --git a/macros/latex/contrib/paracol/paracol.ins b/macros/latex/contrib/paracol/paracol.ins
new file mode 100644
index 0000000000..28955d06e4
--- /dev/null
+++ b/macros/latex/contrib/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/macros/latex/contrib/paracol/paracol.pdf b/macros/latex/contrib/paracol/paracol.pdf
new file mode 100644
index 0000000000..d7610852ea
--- /dev/null
+++ b/macros/latex/contrib/paracol/paracol.pdf
diff --git a/macros/latex/contrib/paracol/ppts.dtx b/macros/latex/contrib/paracol/ppts.dtx
new file mode 100644
index 0000000000..cc7847db7c
--- /dev/null
+++ b/macros/latex/contrib/paracol/ppts.dtx
@@ -0,0 +1,472 @@
+% \def\oddeven#1#2{\ifodd\value{page}#1\else#2\fi}
+% \marginparpush5pt \@mparswitchtrue
+% \section{Two-Sided Typesetting and Parallel-Paging}
+% \label{sec:ppts}
+% \changes{v1.3-2}{2013/09/17}
+%	{Add the section ``Two-Sided Typesetting and Parallel-Paging''.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add the section ``Two-Sided Typesetting and Parallel-Paging''.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Add the section ``Two-Sided Typesetting and Parallel-Paging''.}

+% 
+% This and the next section are typeset with \Uidx{\!\twosided!} enabling
+% features |p|, |c| and |m| and also |b| for a part of the next section.
+% The effect of |p| feature can be seen by the \oddeven{left}{right}, or in
+% other word inside, margin of this \oddeven{odd}{even}-numbered page is
+% narrower than that of the previous pages because the author reduced the
+% effective \oddeven{left}{right} side margin being calculated from
+% \oddeven{\cs{oddsidemargin}}{\cs{evesidemargin}}
+% 

+% \SpecialIndex{\oddsidemargin}

+% \SpecialIndex{\evensidemargin}

+% 

+% by 75\,\%\footnote{

+% 

+% This document itself does not have |twoside| option in its
+% \!\documentclass! but the inconsistency between the option and
+% \!\twosided! is not visible because \!\pagestyle! is |plain|.}.
+% 

+% This setting makes the \oddeven{right}{left} side or outside margin of
+% this page enlarged by 125\,\%, as well as the \oddeven{left}{right} side
+% and outside margin of the next \oddeven{even}{odd}-numbered page specified
+% by \oddeven{\cs{evensidemargin}}{\cs{oddsidemargin}}.
+% 
+% Next, we see the effects of |c| and |m| features by the \env{paracol}
+% environment below for which \Uidx{\!\columnratio!}|{0.6}| and
+% \Uidx{\!\marginparthreshold!}|{0}| are declared to make the \emph{inside}
+% columns (\oddeven{left}{right} ones in \oddeven{odd}{even}-numbered pages)
+% are wider than the \emph{outside} ones and all marginal notes go to
+% outside (\oddeven{right}{left} in \oddeven{odd}{even}-numbered pages)
+% margins.
+% 

+% \columnratio{0.6}\marginparthreshold{0}
+% 

+% \par\Hrule
+% \begin{paracol}{2}
+% \switchcolumn
+% \footnotetext*{Since the author is temporarily disabling the warning from
+% marginal note placement mechanism of \LaTeX, pushing down the second
+% marginal note from column-1 is silently performed when you process this
+% document.}
+% \switchcolumn
+% This line\Marginpar{First marginal note from column-0.} of the first
+% paragraph of the inside column-0 has a marginal note.  Now the author puts
+% a few dummy lines to keep a space below the marginal note.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\par
+% 
+% This line\Marginpar{Second marginal note from column-0.} of the second
+% paragraph of the inside column-0 also has a marginal note.  Now the author
+% puts a few dummy lines again but this time to go down to the bottom of the
+% page.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\par
+% 
+% This is the third paragraph of the inside column-0 having a page break in
+% it.  Since shortly we will be in an \oddeven{even}{odd}-numbered page
+% \pageref{page:ppts2} (now), this wider column\Marginpar{Third marginal
+% note from column-0} is now \oddeven{right}{left} one keeping it
+% inside, while the marginal note given in the first line of this page goes
+% to \oddeven{left}{right} and outside.  Now we will have a \!\switchcolumn!
+% below this paragraph to go to the column-1 and back to the previous page
+% \pageref{sec:ppts}.\label{page:ppts2}
+% \switchcolumn
+% \it
+% This is the first paragraph in the narrower, italicized and outside
+% column-1.  In this paragraph, we shortly have a marginal note, italicized
+% too, which goes to the outside margin shared by all marginal notes from
+% both columns.\Marginpar{\it First marginal note from column-1.}  The
+% marginal note given here is placed its natural position and its first line
+% is aligned to the first line of the second sentence of this paragraph by
+% exploitation of the space between two marginal notes from the column-0,
+% though we already have had three notes from the column.
+% 
+% Now\Marginpar{\it Second marginal note from column-1.} the author puts
+% another marginal note whose first line would be aligned to that of this
+% paragraph, but it is pushed down below the second marginal note from the
+% column-0 because two notes conflict with each other over the
+% space\footnotemark*[+0].  Note that since the note from this column is given
+% \emph{after} that from the column-0 was given, the conflict is solved
+% pushing the note from this column down rather than that from the
+% column-0.  Now the author puts a few dummy lines to go to the second last
+% line of this page.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\par
+% 
+% This is the third paragraph of the outside column-1, which becomes
+% \oddeven{left}{right} shortly by the page break.\Marginpar{\it Third
+% marginal note from column-1.}  The third marginal note is given in the
+% first line of this page, but it is pushed down again due to the conflict
+% with the note from the column-0.
+% \end{paracol}
+% \Hrule
+% 
+% Note that the position of the last marginal note in the \env{paracol}
+% \Marginpar{Marginal note given after \env{paracol} environment is closed.}
+% environment which we just have closed affects the marginal note placement
+% in \postenv.  For example, the marginal note given in the first line of
+% this paragraph is pushed down.
+% 
+% \ifodd\value{page}
+% We will see a few examples of \parapag{}ing shortly, but before that we
+% will have an intentional black page to make the first page of the example
+% odd-numbered to avoid you have an impression that its layout is
+% incorrect\footnote{

+% 

+% At least the author himself had such impression without the blank page.}
+% 

+% because if it were in an even page you would see the {\em outside\/} third
+% and fourth supplementary {\em columns\/} at first.
+% 

+% \newpage\vspace*{\fill}\centerline{(intentionally blanked page)}\vfill
+% 

+% \else
+% From the next page, we will see a few examples of \parapag{}ing.
+% \fi
+% 
+% 
+% 
+% \newpage
+% \subsection{Example of Paired Parallel-Paging}
+% \label{sec:ppts-paired}
+% 
+% Shortly we will start a \env{paracol} environment by \beginparacol|[2]{4}|
+% having four columns but two for each of left and right \paired{}
+% \parapag{}es.  Since the author declares \!\columnratio!|{0.6}[0.5]|, the
+% columns in left pages are made unbalanced while those in right pages are
+% balanced.
+% 

+% \columnratio{0.6}[0.5]
+% \par\Hrule
+% \begin{paracol}[2]{4}
+% This is the first paragraph of the leftmost column-0,
+% \Marginpar{Marginal note from column-0.}
+% whose first line has a marginal note placed in the right margin because
+% the setting of \!\marginparthreshold! being 0 is still effective and we
+% are in the odd-numbered page \pageref{sec:ppts-paired}.  Now we
+% have a \!\switchcolumn! to the next column-1.
+% 
+% \switchcolumn
+% \begin{Hfuzz}{1.1pt}\it
+% This is the first paragraph of the second and right column-1 in the left
+% \parapag{}e.  We shortly give an italicized mar\-gin\-al note carefully, so
+% that it does not conflict with the marginal note from the column-0.
+% \Marginpar{\it Marginal note from column-1.}
+% That is, now the author puts the note.  Now we
+% have a \!\switchcolumn! to the next column-2.
+% \end{Hfuzz}
+% \footnotetext*{This footnote is put in the left \parapag{}e together with
+% another footnote below given in the column-2 in the right \parapag{}e.
+% \label{fn:ppts-paired1}}
+% 
+% \switchcolumn
+% \begingroup\sf
+% This is the first paragraph of the column-2 being the left column of the
+% right \parapag{}e.  Though we are in a page different from that column-0
+% and 1 reside in, this page is still numbered \pageref{sec:ppts-paired}
+% because the left and right page is \paired.  Therefore, the left margin of
+% this page is narrower than the right margin because the page number is
+% odd.
+% 

+% \footnotetext*{This footnote is \emph{not} put in the right \parapag{}e
+% though it is given in the column-2 in the right \parapag{}e and thus its
+% reference is in the column, of course.\label{fn:ppts-paired2}}
+% 
+% You have to notice
+% \Marginpar{\sf Marginal note from column-2.}
+% the first paragraph does not start from the page top
+% but above it we have some space of exactly same size as the \preenv{}
+% shown in the left \parapag{}e.  Therefore, the top of the first paragraphs
+% in all columns are aligned.  The marginal note given in the first line of
+% this paragraph goes to the right margin of this page because of the
+% \!\marginparthreshold! setting and the parity of this page.  Now we have a
+% \!\switchcolumn! to the next column-3.
+% \par\endgroup
+% \begin{figure*}\nosv
+% \def\arraystretch{0.8}
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     \sf page-wise figure given in column-2\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Page-Wise Figure}
+% \end{figure*}
+% 
+% \switchcolumn
+% \begingroup\sl
+% This is the first paragraph
+% \Marginpar{\sl Marginal note from column-3.}
+% in the last rightmost column-3 whose width is equal to that of the column-2.
+% The marginal note given in the first line goes to right and does not
+% conflict with that from the column-2.  We are now going back to the
+% column-0 by a {\rm\!\switchcolumn!|*|} with a \mctext.
+% \endgroup
+% 
+% \switchcolumn*[\subsection*{A Spanning Text: though this is wider than the
+% page width, this text does not span the boundary between the left and
+% right parallel-pages.}]
+% 
+% We have come back to this column-0.  The space above the \mctext{} is due
+% to the \sync{}ation because two paragraphs in the column-2 are
+% significantly taller in total than the paragraphs in other columns.  As
+% the spanning text itself says, it cannot extend to the right \parapag{}e.
+% The author puts dummy lines to go to the page bottom.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\par
+% 
+% Now we will have a page break shortly.  You could be surprised by seeing
+% this column is not in the left \parapag{}e after the break but in the
+% right one.  This is because the feature |c| is enabled to swap not only
+% columns in a page but also the left and right \paired{} \parapag{}es when
+% they are even-numbered.  The other feature |p| makes the left outside
+% margins of this right and the previous left pages wider than the right
+% inside margins.\label{page:ppts-paired2}
+% 
+% \switchcolumn
+% \begingroup\it
+% We have restarted this column-1.  This paragraph has a
+% footnote\footnotemark*[-1] as shown below.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\par
+% 
+% After the page break below, this column also goes to the right page
+% together with the column-0
+% \Marginpar{\it Another marginal note from column-1.}
+% and is placed outside (left) in the page, as well as the marginal note
+% in this right page but in the outside margin.
+% \par\endgroup
+% 
+% \switchcolumn
+% \begingroup\sf
+% We have a few other materials not shown in right \parapag{}es.  The space
+% above this paragraph is for the \mctext{} placed in the left \parapag{}e.
+% The \Scfnote{} given here\footnotemark{} is also not in this page but in
+% the left.  Finally, the author has put a page-wise figure spanning columns
+% just before \!\switchcolumn! by which we left this column, but it will be
+% in the right page \pageref{page:ppts-paired2} together with column-0 and
+% 1.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\par
+% 
+% Though the footnote numbered \ref{fn:ppts-paired2} goes to the left page,
+% its space and that of \ref{fn:ppts-paired1} make this and the next columns
+% shorter in the previous page.  Similarly, we have a space above for the
+% page-wise figure shown in the right page.
+% \par\endgroup
+% 
+% \switchcolumn
+% \begingroup\sl
+% As expected, this line is aligned to the first line of the paragraph in
+% the column-2 as well as those in column-0 and 1.  It is also consistent
+% the first lines including that of this paragraph are not indented because
+% the \mctext{} is given by {\rm\!\subsection!|*|} which makes first
+% paragraphs unindented.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\par
+%
+% After the page break we will have shortly, this column becomes the
+% leftmost in the left \parapag{}e, as you are seeing now,
+% \Marginpar{\sl Another marginal note from column-3.}
+% but still outermost as well as the marginal note in the outside left
+% margin.
+% \endgroup
+% \end{paracol}
+% \Hrule
+% 
+% Now you are seeing yet another material placed only in the page in which
+% the column-0 resides and thus being the right page now, i.e., this
+% paragraph and the next one in the \postenv.  You might be disappointed by
+% the fact the \emph{outside} pages, i.e., left in this page
+% \pageref{page:ppts-paired2} and right in the previous page
+% \pageref{sec:ppts-paired}, cannot have \pwstuff{} but it is what the
+% author can do now for the version 1.3 and thus you have to wait some
+% future versions in which the author could devise a mechanism to exploit
+% the corresponding space in the pages\footnote{

+% 

+% You might complain the immaturity of \parapag{}ing and might claim that it
+% should be included in \Paracol{} after the author implements the
+% mechanism.  In fact the author himself is frustrated current features of
+% \parapag{}ing but he dared to release the version 1.3 knowing that there
+% are people who happily typeset their \parapag{}ed documents with the
+% current limited features.}.
+% 

+% In addition, you might think it is weird that the |c| feature of
+% \!\twosided! swaps columns \emph{and} paired pages.  However this swapping
+% is a natural consequence of the combination of \cswap{} and \paired{}
+% \parapag{}ing.  Therefore, you can simply disable the |c| feature (maybe
+% together with other features) to have more intuitive results.
+% 
+% In the next Section~\ref{sec:ppts-npaired}, you will see another kind of
+% \parapag{}ing namely \npaired{} one.  Before that, we need a blank page to
+% let the \npaired{} \parapag{}ing start from an even-numbered page so that
+% a left and right page pair comprises a double spread.  A short remark on
+% the blank next page is that it does not have a right counterpart
+% \parapag{}e because the page is outside \env{paracol} environments and does
+% not have any portion from the environments\footnote{

+% 

+% To illustrate this fact, the author dares to put a real blank page rather
+% than stepping the \counter{page} counter.}.
+% 

+% \newpage\vspace*{\fill}\centerline{(intentionally blanked page)}\vfill
+% 
+% 
+% 
+% \newpage
+% \subsection{Example of Non-Paired Parallel-Paging}
+% \label{sec:ppts-npaired}
+% 
+% This and following three pages are to show an example of \npaired{}
+% \parapag{}ing, in which the author keeps the setting of \!\twosided!,
+% \!\columnratio! and \!\marginparthreshold! unchanged.
+% The arguments of \beginparacol{} for column population are also unchanged
+% to have $2+2$ configuration, but the first argument is followed by |*| for
+% \npaired{} typesetting.  That is, the environment below starts by
+% \beginparacol|[2]*{4}|.  The contents of the environment is also almost
+% same as the previous Section~\ref{sec:ppts-paired}, while
+% \Emph{bold-faced} words show the difference from the \paired{}
+% typesetting.
+% 

+% \columnratio{0.6}[0.5]
+% \par\Hrule
+% \begin{paracol}[2]*{4}
+% This is the first paragraph of the leftmost column-0,
+% \Marginpar{Marginal note from column-0.}
+% whose first line has a marginal note placed in the \Emph{left} margin
+% because the setting of \!\marginparthreshold! being 0 is still effective
+% and we are in the \Emph{even}-numbered page
+% \Emph{\pageref{sec:ppts-npaired}}.  Now we have a \!\switchcolumn! to the
+% next column-1.
+% 
+% \switchcolumn
+% \begingroup\it
+% This is the first paragraph of the second and right column-1 in the left
+% \parapag{}e.  We shortly give an italicized mar\-gin\-al note carefully, so
+% that it does not conflict with the marginal note from the column-0.
+% \Marginpar{\it Marginal note from column-1.}
+% That is, now the author puts the note.  Now we
+% have a \!\switchcolumn! to the next column-2.
+% \par\endgroup
+% \footnotetext*{This footnote is put in the left \parapag{}e together with
+% another footnote below given in the column-2 in the right \parapag{}e.
+% \label{fn:ppts-npaired1}}
+% 
+% \switchcolumn
+% \begingroup\sf\label{page:ppts-npaired1r}
+% This is the first paragraph of the column-2 being the left column of the
+% right \parapag{}e.  \Emph{Since we are in the page next to} that column-0
+% and 1 reside in, this page is numbered \Emph{\pageref{page:ppts-npaired1r}}
+% because the left and right page is \Emph{\npaired}.  Therefore, the left
+% margin of this page is narrower than the right margin because the page
+% number is odd.
+% 

+% \footnotetext*{This footnote is \emph{not} put in the right \parapag{}e
+% though it is given in the column-2 in the right \parapag{}e and thus its
+% reference is in the column, of course.\label{fn:ppts-npaired2}}
+% 
+% You have to notice
+% \Marginpar{\sf Marginal note from column-2.}
+% the first paragraph does not start from the page top
+% but above it we have some space of exactly same size as the \preenv{}
+% shown in the left \parapag{}e.  Therefore, the top of the first paragraphs
+% in all columns are aligned.  The marginal note given in the first line of
+% this paragraph goes to the right margin of this page because of the
+% \!\marginparthreshold! setting and the parity of this page.  Now we have a
+% \!\switchcolumn! to the next column-3.
+% \par\endgroup
+% \begin{figure*}\nosv
+% \def\arraystretch{0.8}
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     \sf page-wise figure given in column-2\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Page-Wise Figure}
+% \end{figure*}
+% 
+% \switchcolumn
+% \begingroup\sl
+% This is the first paragraph
+% \Marginpar{\sl Marginal note from column-3.}
+% in the last rightmost column-3 whose width is equal to that of the column-2.
+% The marginal note given in the first line goes to right and does not
+% conflict with that from the column-2.  We are now going back to the
+% column-0 by a {\rm\!\switchcolumn!|*|} with a \mctext.
+% \endgroup
+% 
+% \switchcolumn*[\subsection*{A Spanning Text: though this is wider than the
+% page width, this text does not span the boundary between the left and
+% right parallel-pages.}]
+% 
+% We have come back to this column-0.  The space above the \mctext{} is due
+% to the \sync{}ation because two paragraphs in the column-2 are
+% significantly taller in total than the paragraphs in other columns.  As
+% the spanning text itself says, it cannot extend to the right \parapag{}e.
+% The author puts dummy lines to go to the page bottom.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\par
+% 
+% Now we will have a page break shortly.  You \Emph{will not} be surprised
+% by seeing this column \Emph{is still in the left \parapag{}e after the
+% break.}  This is because the feature |c| is \Emph{not effective in
+% \npaired{} \parapag{}ing.}  The other feature |p| \Emph{consistently makes
+% the left outside margins of this and the previous page in which this
+% column resides} wider than the right inside margins.
+% \label{page:ppts-npaired2}
+% 
+% \switchcolumn
+% \begingroup\it
+% We have restarted this column-1.  This paragraph has a
+% footnote\footnotemark*[-1] as shown below.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\par
+% 
+% After the page break below, this column also \Emph{stays in the left page}
+% together with the column-0
+% \Marginpar{\it Another marginal note from column-1.}
+% and is placed \Emph{inside (right)} in the page, as well as the marginal
+% note in this \Emph{left} page \Emph{still} in the outside margin.
+% \par\endgroup
+% 
+% \switchcolumn
+% \begingroup\sf
+% We have a few other materials not shown in right \parapag{}es.  The space
+% above this paragraph is for the \mctext{} placed in the left \parapag{}e.
+% The \Scfnote{} given here\footnotemark{} is also not in this page but in
+% the left.  Finally, the author has put a page-wise figure spanning columns
+% just before \!\switchcolumn! by which we left this column, but it will be
+% in the \Emph{left} page \Emph{\pageref{page:ppts-npaired2}} together with
+% column-0 and 1.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\par
+% 
+% Though the footnote numbered \Emph{\ref{fn:ppts-npaired2}} goes to the
+% left page, its space and that of \Emph{\ref{fn:ppts-npaired1}} make this
+% and the next columns shorter in the previous page.  Similarly, we have a
+% space above for the page-wise figure shown in the \Emph{left} page.
+% \par\endgroup
+% 
+% \switchcolumn
+% \begingroup\sl
+% As expected, this line is aligned to the first line of the paragraph in
+% the column-2 as well as those in column-0 and 1.  It is also consistent
+% the first lines including that of this paragraph are not indented because
+% the \mctext{} is given by {\rm\!\subsection!|*|} which makes first
+% paragraphs unindented.\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\par
+%
+% After the page break we will have shortly, this column \Emph{is kept being
+% the rightmost in the right \parapag{}e}, as you are seeing now,
+% \Marginpar{\sl Another marginal note from column-3.}
+% \Emph{and} still outermost as well as the marginal note in the outside
+% \Emph{right} margin.
+% \endgroup
+% \end{paracol}
+% \Hrule
+% 
+% As the \postenv{} in Section~\ref{sec:ppts-paired} is, this paragraph
+% being the \postenv{} of the \npaired{} \parapag{}es appears only in the
+% \parapag{}e in which the column-0 belongs to, and thus in the left
+% \parapag{}e in this case.
+% \endinput
diff --git a/macros/latex/contrib/paracol/probs.dtx b/macros/latex/contrib/paracol/probs.dtx
new file mode 100644
index 0000000000..4d6ee18c7c
--- /dev/null
+++ b/macros/latex/contrib/paracol/probs.dtx
@@ -0,0 +1,262 @@
+% \section{Known and Unknown Problems}
+% \label{sec:problem}
+% \changes{v1.2-7}{2013/05/11}
+% 	{Add the section ``Known and Unknown Problems'' to summarize a few
+% 	 typesetting issues and warn users of the possiblity of bugs.}

+% \changes{v1.3-1}{2013/09/17}
+%	{Remove the problem description of the placement of page-crossing
+%	 spanning texts because it has been solved.}

+% \changes{v1.3-3}{2013/09/17}
+%	{Remove the problem description of the lack of column-separating rule
+%	 drawing because it has been implmented.}

+% 
+% Here a few problems you could face in the use of \textsf{paracol} are
+% summarized.
+% 

+% \begin{itemize}
+% \item
+% If your (e.g.,) left column goes ahead too much farther than the right
+% column, \LaTeX{} could stop with the following error message.
+% 

+% \begin{quote}
+% |! Package paracol Error: Too many unprocessed columns/floats.|
+% \end{quote}
+% 

+% This usually means that the internal space to keep materials in the left
+% column is exhausted.  More specifically, suppose at some point in your
+% |.tex| the left column is in the page $p$ while the right is in $q<p$.
+% We need $(p-q)$ \emph{boxes} to keep the left column contents in the pages
+% $q$, $q+1$, \ldots, $p-1$ because these pages cannot be \emph{printed} yet
+% until the right column fills them.  In addition, we also need two boxes
+% for the left column in $p$ and the right column in $q$ so that you make
+% \cswitch{} between them keeping unprinted contents in them.  Therefore, at
+% least we need to have $(p-q)+2$ boxes, while the number of them provided
+% by \LaTeX{} is only 18\footnote{

+% 

+% Readers who are acquainted with \LaTeX{} implementation will understand
+% that 18 is the cardinality of the set $\{\cs{bx@A},\ldots,\cs{bx@R}\}$ for
+% floats acquired by \cs{newinsert}.  Those who are more familiar with that
+% might know that most \LaTeX{}, based on e-\TeX{} or others having similar
+% extensions, now have 52 \cs{insert}s
+% $\{\cs{bx@A},\ldots,\cs{bx@Z},\cs{bx@AA},\ldots,\cs{bx@ZZ}\}$ for floats
+% and materials of \Paracol, since 2015}.
+% 

+% Therefore, \textsf{paracol} cannot continue its work if $(p-q)$ reaches
+% 17.  Furthermore, other stuff also consumes the boxes as follows.
+% 

+% \begin{itemize}
+% \item
+% If there are $n$ pages in $q$, $q+1$, \ldots, $p$ having \preenv{} or
+% page-wise floats, $n$ boxes are consumed by them.  Similarly, if $m$ pages
+% in them have \Scfnote{}s, $m$ boxes are given to them.
+% 
+% \item
+% If the left (resp.\ right) column has \Mcfnote{}s in $p$ (resp.\ $q$), a box
+% is used for them.
+% 
+% \item
+% If the left (resp.\ right) column has $k$ floats to be placed in $p$
+% (resp.\ $q$) or to be deferred to $p+1$ (resp.\ $q+1$) or a succeeding page,
+% $k$ boxes are reserved for them.
+% \end{itemize}
+% 

+% Therefore, it should be safe to keep $(p-q)$ from exceeding 10 or so
+% placing \!\switchcolumn! in both columns fairly frequently.
+% 
+% \item
+% As discussed in Section~\ref{sec:ref-switchcolumn}, setting a \sync{}ation
+% point in a page brings the following side effects.
+% 

+% \begin{itemize}
+% \item
+% Stretch and shrink factors of all vertical skips in the page are
+% nullified.  The nullification of stretch factors could make a sparse
+% column in the page have a vertical space at its bottom as if
+% \!\raggedbottom! setting is in effect even with \!\flushbottom! one,
+% rather than distributing the amount of the space to the skips so that the
+% bottom line is aligned at the page bottom.  As for the nullification of
+% shrink factors, it makes the page have lines a little bit less than that
+% it would have without \sync{}ation because lines above the (last)
+% \sync{}ation point cannot be compressed.  The other effect is a little bit
+% subtle because the shrink factors below the last \sync{}ation point are
+% taken care of by \TeX{}'s page builder when it examine the appropriateness
+% of each breakable point, but they are nullified when the page is printed.
+% That is, if \TeX{} finds a good break point which needs that the stuff
+% between the \sync{}ation and break points is compressed a little bit, the
+% stuff is printed without compression making its bottom edge a little
+% bit below the page bottom.
+% 
+% \item
+% After a \sync{}ation point is set, columns in the page cannot have top
+% floats any more even if a column has space above the \sync{}ation point
+% and large enough to place the float.  Therefore, if you like to exploit
+% the space, you have to place the \env{figure} or \env{table} environment
+% in question prior to the \cswitch{} command or environment for the
+% \sync{}ation.
+% \end{itemize}
+% 
+% \item
+% \changes{v1.3-6}{2013/09/17}
+%	{Add comments about usage of \cs{paragraph} etc.\ in spanning texts.}

+% \begingroup\parskip\z@
+% As the author did for Section\Tie1 to \ref{sec:float}, sometimes you will
+% make a section header spanning all columns by giving a sectioning command
+% such as \!\section!, \!\subsection! and \!\subsubsection! to the optional
+% argument of \!\switchcolumn!|*| or \!\begin! of a \sync{}ing \csenv.
+% These three commands work well and you will have what you intend to have,
+% but you have to be careful with lower-level commands \!\paragraph! and
+% \!\subparagraph!.  Unlike higher-level relatives, these lower-level
+% commands does \emph{not} put the header \emph{immediately} but keep it
+% somewhere\footnote{

+% 

+% For people familiar to \TeX's \emph{dangerous bends}, the header is kept in
+% \!\everypar!.}
+% 

+% so that when the paragraph following the command starts it is put as the
+% leading part of the paragraph.  Therefore if the \mctext{} has (e.g.)
+% \!\paragraph! only, the header is not put as a \mctext{} but at the head of
+% the first paragraph of the column to which you switch, leaving an
+% empty \mctext{} with some large space as follows.
+% 

+% \par\leavevmode\Hrule
+% \columnsep\z@
+% \begin{paracol}{2}
+% This left-column paragraph precedes a \sync{}ed \cswitch.
+% \switchcolumn
+% This right-column paragraph precedes a \sync{}ed \cswitch.
+% \switchcolumn*[\paragraph{A Spanning Text Given by \cs{paragraph}}]
+% This left-column paragraph follows the \sync{}ation but is led by
+% \!\paragraph! given to the optional argument of \!\switchcolumn!|*| for
+% \mctext.
+% \switchcolumn
+% This right-column paragraph follows the \sync{}ation with an empty \mctext.
+% \end{paracol}
+% \par\leavevmode\Hrule\par
+% 

+% Therefore, unless this is what you intend to do, you have to give some
+% paragraph together with \!\paragraph! to the optional argument for
+% \mctext.  For example, \!\mbox!|{}| is a good candidate as the paragraph
+% following \!\paragraph! because it produces (almost) nothing.  By using
+% this technique the example above becomes the followings.
+% 

+% \par\leavevmode\Hrule
+% \begin{paracol}{2}
+% This left-column paragraph precedes a \sync{}ed \cswitch.
+% \switchcolumn
+% This right-column paragraph precedes a \sync{}ed \cswitch.
+% \switchcolumn*[\paragraph{A Spanning Text Given by \cs{paragraph} Followed
+% by \cs{mbox}\texttt{\char`\{\char`\}}}\mbox{}]
+% This left-column paragraph follows the \mctext{} above.
+% \switchcolumn
+% This right-column paragraph follows the \mctext{} above.
+% \end{paracol}
+% \par\leavevmode\Hrule
+% \endgroup
+% 
+% \item
+% As shown in Section~\ref{sec:fnnp}, it is not easy to have good numbering
+% and stacking order of \Scfnote{}s even with the supports from
+% \!\footnote!|*| and its relatives.  In addition, a footnote in a
+% \env{paracol} environment cannot be broken into two (or more) pages.
+% 
+% \item
+% \changes{v1.3-2}{2013/09/17}
+%	{Add comments about the limitaion of parallel-paging.}

+% 

+% As the author confessed in Section\Tie\ref{sec:ppts-paired}, right
+% \parapag{}es cannot have \pwstuff{} but have blank spaces in the
+% corresponding region for them.  The author will try to remove this
+% limitation from a future version of \Paracol, in the version 1.4 hopefully.
+%
+% \item
+% \changes{v1.3-3}{2013/09/17}
+%	{Add comments about the imperfectnss of extention of backgrond
+%	 painting regions.}

+% \begin{Hfuzz}{1.5pt}
+% As discussed in Section\Tie\ref{sec:bgpaint-me}, it is desirable that
+% \bgpaint{} region definition in \!\backgroundcolor! has position dependent
+% extensions.  The author is fairly optimistic about the incorporation of
+% this advanced feature in the version 1.4.
+% \end{Hfuzz}
+% 
+% \item
+% \changes{v1.32-3}{2015/10/10}
+%	{Add comments about the out-of-order appearance of page-wise floats
+%	 even with \protect\LaTeX-2015/01/10 or later.}
+% In the release dated 2015/01/10, \LaTeX{} changed its mechanism of the
+% placement of double-column floats (or in our terminology, \pwise{}
+% floats) to avoid {\em out-of-order\/} appearance of them.  That is, until
+% the release on 2014/05/01 a double-column float (e.g., \env{figure*}) can
+% be overtaken by a single-column float of the same category (e.g.,
+% \env{figure}) when they cannot be put into the page in which texts around
+% them are put.  In order to cope with the problem, the new version merged
+% two lists to keep {\em deferred\/} double- and single-column floats into
+% one so that the appearance order of them is determined by their order in
+% the single list.  Though this change should have made people happy when
+% they typeset {\em ordinary\/} two-column (or multiple-column) documents,
+% the new feature might not be welcomed by \Paracol{} users because your
+% parallel-columns have their own {\em streams\/} of floats to be put in the
+% corresponding columns.  Therefore, and for the sake of simplicity of
+% \Paracol's implementation, the author decided to nullify this new feature
+% in \env{paracol} environments.  That is, even with new releases of
+% \LaTeX{}, your \pwise{} floats given in a \env{paracol} environment can be
+% overtaken by \cwise{} floats.
+% \end{itemize}
+% 
+% In addition to the problems above known to the author, there may be (or
+% should be, honestly speaking) other unknown problems in \textsf{paracol}
+% because it cannot be perfect though the author has made his best effort
+% for testing and debugging it.  Particularly, sometimes it is very tough,
+% if not impossible, to make \textsf{paracol} compatible with other
+% packages, especially with those having dark magic as \textsf{paracol} has
+% in it\footnote{

+% 

+% For example, the author knows it is almost impossible to make
+% \textsf{paracol} compatible with one of the author's own package available
+% in CTAN.}.
+% 

+% Therefore, though reporting incompatibleness with a package you use is
+% very welcome\footnote{

+% 

+% For example, \textsf{paracol} is now compatible with \textsf{color}
+% package thanks to a report from a user.},
+% 

+% you should kindly understand the toughness of the compatibility issue.
+% 
+% Furthermore, even without such problematic packages, \textsf{paracol}
+% might produce weird results due to its bug.  If your document has
+% something to make unknown bugs visible, you might have one (or more) of
+% the followings which the author encountered in his debugging work.
+% 

+% \begin{itemize}
+% \item
+% A page, a column, a footnote and/or a float disappears\footnote{

+% 

+% In fact, a bug fixed in version 1.2 caused page losing though it happens
+% very very rarely but an unlucky user encountered it.}.
+% 
+% \item
+% A page, a column, a footnote and/or a float is duplicated.
+% 
+% \item
+% A message like ``{\tt Overfull |\vbox| (1.23456pt too high) has occurred
+% while |\ouptut| is active}'' is shown.
+% 
+% \item
+% A message ``{\tt Underfull |\vbox| (badness 10000) has occurred while
+% |\ouptut| is active}'' is shown.  This message, however, does not always
+% mean a bug but may just be a complaint that a column or a page is too
+% sparse to meet your request to align the bottom of all columns and pages
+% by \!\flushbottom! setting.  Therefore, if you have this message and you
+% cannot be sure whether it means a bug or not, try \!\raggedbottom! setting
+% to see if you still have the message, before sending a bug report to the
+% author.
+% \end{itemize}
+% 

+% If you encounter anything like them (or whatever you cannot solve by
+% yourself), don't hesitate to report it to the author with minimum source
+% file to produce the problem\footnote{

+% 

+% And with patience because your problem might not be solved quickly.}.
+% 
+% \endinput
diff --git a/macros/latex/contrib/paracol/pwfnote.dtx b/macros/latex/contrib/paracol/pwfnote.dtx
new file mode 100644
index 0000000000..8fcf377159
--- /dev/null
+++ b/macros/latex/contrib/paracol/pwfnote.dtx
@@ -0,0 +1,608 @@
+% \def\Dotquad{\leavevmode\cleaders\hbox to.44em{\hss.\hss}%
+%   \hskip\parindent\kern0pt}
+% \def\fnpar#1#2{#1 paragraph\Dotfill\\\Dotfill with a footnote#2\Dotfill
+%   in it.\par}
+% \def\Fnpar#1#2#3{#1 paragraph\Dotfill\\\Dotfill with a footnote#2\Dotfill
+%   in it.\\#3\par}
+% 
+% \section{Numbering and Placement of Page-Wise Footnotes}
+% \label{sec:fnnp}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Add the section ``Numbering and Placement of Single-Columned
+%	 Footnotes'' to describe page-wise footnotes in detail.}
+% \changes{v1.3-5}{2013/09/17}
+%	{Rename the section title from ``Numbering and Placement of
+%	 Single-Columned Footnotes''to ``Numbering and Placement of
+% 	``Page-Wise Footnotes'' following new naming.}

+% 
+% Here we have a simple example of \scfnote{} but not-merged
+% footnotes\footnote{
.
+% 

+% Because of the non-merged typesetting, this footnote is put above the
+% example.\par\Hrule\label{fn:preenv}}.
+%
+% \footnotelayout{p}
+% \begin{paracol}{2}
+% \fnpar{First left-column}{\footnote{First left-column footnote.}}
+% \fnpar{Second left-column}{\footnote{Second left-column footnote.}}
+% \switchcolumn
+% \fnpar{First right-column}{\footnote{First right-column footnote.}}
+% \fnpar{Second right-column}{\footnote{Second right-column footnote.
+% This and all other footnotes above are \scfnote{} and, since footnote
+% typesetting is non-merged, they are put above the \postenv.}}
+% \end{paracol}
+% \Hrule
+% 
+% As shown above, it is easy to have a reasonable result of footnote
+% numbering and placement as far as your \env{paracol} environment is
+% completely included in a page and you accept the numbering in
+% left-column-first manner constructing the environment as follows
+% exploiting the fact \counter{footnote} is made global, where $b$ is the
+% value of \counter{footnote} counter at \beginparacol, i.e., the number
+% given to the footnote just preceding the environment, and thus
+% $b=\ref{fn:preenv}$ in the example above.
+% 

+% \begin{quote}\vskip-1pt
+% |\begin{paracol}{2}|\\
+% \textit{left-column stuff having $n$ footnotes numbered $b+1$, $b+2$,
+% \ldots, $b+n$}\\
+% |\switchcolumn|\\
+% \textit{right-column stuff having $m$ footnotes numbered $b+n+1$, $b+n+2$,
+% \ldots, $b+n+m$}\\
+% |\end{paracol}|
+% \end{quote}\vskip-1pt
+% 

+% The real life is, however, tougher than that, because the assumptions above
+% are too optimistic as described in the following subsections.
+% \vskip-3pt\vskip0pt
+% 
+% 
+% \subsection{Multiple \cs{switchcolumn} in a Page}
+% \label{sec:fnnp-multsc}
+% 
+% Here we have an example with three \!\switchcolumn! commands in a page
+% having six footnotes.  Hereafter, footnotes are typeset with
+% \Uidx{\!\footnotelayout!}|{m}|\footnote{

+% 

+% And thus this footnote is merged with those in the \env{paracol}
+% environment.}.
+% 
+% \footnotelayout{m}
+% \Hrule
+% \begin{paracol}{2}
+% \fnpar{First left-column}{\footnote{First left-column
+% footnote.\label{fn:2L1}}}
+% \Fnpar{Second left-column}{\footnote{Second left-column
+% footnote.\label{fn:2L2}}}{

+% It is followed by a \cs{switchcolumn}.}
+% \switchcolumn
+% \Fnpar{First right-column}{\footnote{First right-column footnote but
+% following the second left-column one.\label{fn:2R1}}}{It is followed by a
+% \cs{switchcolumn*}.}
+% \switchcolumn*
+% \Fnpar{Third and synchronized left-column}{\footnote{Third left-column
+% footnote but following the first right-column one.\label{fn:2L3}}}{It is
+% followed by a \cs{switchcolumn}.}
+% \switchcolumn
+% \fnpar{Second and synchronized right-column}{\footnote{Second right-column
+% footnote but following the third left-column one.\label{fn:2R2}}}
+% \fnpar{Third right-column}{\footnote{Third right-column
+% footnote.\label{fn:2R3}}}
+% \end{paracol}
+% \newpage
+% 
+% The example in the previous page should look weird because the order of
+% the third footnote in the left column \ref{fn:2L3} and the first in the
+% right \ref{fn:2R1} are reversed in their numbers and in the stack at the
+% page bottom.  However, the result is \emph{natural} because they are
+% numbered and stacked in the order of occurrence in the source |.tex| as
+% always done in any documents without \textsf{paracol} and with it but
+% \mcfnote{} footnote typesetting.  Since the \textsf{paracol} cannot
+% maintain the order automatically\footnote{

+% 

+% So far, because the maintenance is extremely tough.  But since it is not
+% impossible, some day you could have an improved version of
+% \textsf{paracol} with the automatic ordering.},
+% 

+% you have to maintain it by yourself.
+% 
+% The problem is partly solved by using \!\footnote! with its optional
+% argument \oarg{num} to number the first right-column and the third
+% left-column footnotes explicitly, i.e., to give
+% $\mathit{num}=\ref{fn:2L3}$ to the former and $\mathit{num}=\ref{fn:2R1}$
+% to the latter.  One caution is that you have to remember that \!\footnote!
+% with the optional \meta{num} does not update \counter{footnote} counter
+% and thus you have to do
+% \!\setcounter!|{footnote}{|\texttt{\ref{fn:2L3}}|}| or
+% \!\addtocounter!|{footnote}{2}| after the third left-column footnote.
+% 
+% This remedy, however, cannot change the stacking order of these two
+% footnotes of course.  Therefore, you need another trick with
+% \!\footnotemark! and \!\footnotetext! to stack the third left-column
+% footnote above the first right-column one.  More specifically, you can
+% solve the problem inserting
+% 

+% \begin{quote}
+% \!\footnotetext!\texttt{[\ref{fn:2R1}]}

+%     |{|\textit{text for the third left footnote}|}|
+% \end{quote}
+% 

+% somewhere between \!\footnote! commands for the second left-column and the
+% first right-column ones, e.g., at the end of the second left-column
+% paragraph, and attaching its mark to the appropriate word for the footnote
+% by \!\footnotemark!\texttt{[\ref{fn:2R1}]}, to have the following.
+% 
+% \Hrule
+% \begin{paracol}{2}
+% \fnpar{First left-column}{\footnote{First left-column
+% footnote.\label{fn:3L1}}}
+% \Fnpar{Second left-column}{\footnote{Second left-column
+% footnote.\label{fn:3L2}}}{

+% It is followed by \cs{footnotetext}\texttt{[\ref{fn:3L3}]}\marg{text}
+% and a \cs{switchcolumn}.}
+% \addtocounter{footnote}{1}
+% \footnotetext[\arabic{footnote}]{Third left-column footnote given by
+% \cs{footnotetext}\texttt{[\ref{fn:3L3}]}\marg{text} placed at the end of
+% the second left-column paragraph.\label{fn:3L3}}
+% \switchcolumn
+% \addtocounter{footnote}{1}
+% \Fnpar{First right-column}{\footnote[\arabic{footnote}]{First right-column
+% footnote whose number \ref{fn:3R1} is explicitly given by
+% \cs{footnote}\texttt{[\ref{fn:3R1}]}\marg{text}.\label{fn:3R1}}}{It is
+% followed by a \cs{switchcolumn*}.}
+% \addtocounter{footnote}{-1}
+% \switchcolumn*
+% Third and synchroized left-column paragraph\Dotfill\\
+% \Dotfill with a footnote whose mark
+% here\footnotemark[\arabic{footnote}]\Dotfill\\
+% \Dotfill is given by \!\footnotemark!\texttt{[\ref{fn:3L3}]}\Dotfill in
+% it.\\
+% It is followed by \!\addtocounter!|{footnote}{2}| and a \!\switchcolumn!.
+% \addtocounter{footnote}{1}
+% \switchcolumn
+% \fnpar{Second and synchronized right-column}{\footnote{Second right-column
+% footnote correctly following the first right-column one.\label{fn:3R2}}}
+% \fnpar{Third right-column}{\footnote{Third right-column
+% footnote.\label{fn:3R3}}}
+% \end{paracol}
+% \Hrule
+% 
+% Though this solution gives a good result, however, it has the following
+% two problems.  First, you have to explicitly specify the footnote number
+% through the optional arguments \oarg{num} of \!\footnote!,
+% \!\footnotetext! and \!\footnotemark!.  This problem is quite severe
+% because, for example, if you add a footnote somewhere preceding the
+% \env{paracol} environment in question, you have to modify all
+% \oarg{num} arguments of footnote-related commands in the environment.
+% This means that when the footnote addition is done in the first page of a
+% 100-page document having \env{paracol} environments with explicitly numbered
+% footnotes in every page, you have to make the corrections for environments
+% in 99 pages.  The other a little bit less severe problem is that you have
+% to keep \counter{footnote} counter having correct value by
+% \!\setcounter!, \!\addtocounter! or \!\stepcounter! for footnotes following
+% those with explicit numbering so that their numbers are given by the
+% default action of \!\footnote!.
+% 
+% To cope with these two problems, \textsf{paracol} provides you with the
+% \emph{starred} versions of \!\footnote! and its relatives as introduced in
+% Section~\ref{sec:ref-scfnote} and detailedly explained in the next
+% Section~\ref{sec:fnnp-starred}.
+% 
+% 
+% 
+% \subsection{Commands \cs{footnote*} and Relatives}
+% \label{sec:fnnp-starred}
+% 
+% \begin{description}
+% \item[\Midx{\!\footnote!}\texttt{*}\oarg{|+|disp}\marg{text}]\mbox{}
+% \Item[\Midx{\!\footnote!}\texttt{*}\oarg{|-|disp}\marg{text}]\mbox{}
+% \Item[\Midx{\!\footnote!}\texttt{*}\oarg{disp}\marg{text}]\mbox{}\par
+% The command is similar to its non-starred counterpart but the explicit
+% numbering with the optional argument is done in \emph{self-relative} or
+% \emph{base-displacement} style.  That is, if the optional argument has a
+% leading `|+|' or `|-|',  the number given to the footnote is
+% $f+\meta{disp}$ or $f-\meta{disp}$ respectively where $f$ is the value of
+% \counter{footnote} counter, or in other words the number given to the last
+% footnote\footnote{

+% 

+% If it is put by the ordinary \cs{footnote}.}.
+% 

+% Otherwise, i.e., the optional argument is a number without |+|/|-| sign,
+% the number given to the footnote is $b+\meta{disp}$ where $b$ is the base
+% value of \counter{footnote} counter at \beginparacol{} for the environment
+% in which the command appears, or in other words the number given to the
+% last \Preenv{} footnote\footnote{

+% 

+% Or the last footnote in the previous \env{paracol} environment,
+% etc.\label{fn:4L0}}.
+% 
+% In addition, unlike the non-starred version, this command updates
+% \counter{footnote} counter with the number given to the footnote, i.e.,
+% $f\gets f+\meta{disp}$, $f\gets f-\meta{disp}$ or $f\gets b+\meta{disp}$
+% is performed, so that following \!\footnote! without explicit numbering
+% option have numbers $f+1$, $f+2$ and so on with new $f$.
+% 

+% \begin{itemize}
+% \item
+% If the optional argument is not provided, it is assumed that |[+1]| is
+% given and thus \!\footnote!|*|\marg{text} acts as \!\footnote!\marg{text}.
+% \end{itemize}
+% 
+% \item[\Midx{\!\footnotemark!}\rm|*[|{[|+-|]}\meta{disp}{|]|}]\mbox{}\par
+% This command is a mixture of its non-starred counterpart and
+% \!\footnote!|*|.  That is the number for the footnote mark is calculated
+% in the way of \!\footnote!|*| and \counter{footnote} counter is updated.
+% 
+% \item[\Midx{\!\footnotetext!}\rm|*[|{[|+-|]}\meta{disp}{|]|}\marg{text}]
+% \mbox{}\par
+% Without the optional argument |[|[|+-|]\meta{disp}|]|, this command does what
+% \!\footnotetext!\marg{text} does but in addition increments
+% \counter{footnote} counter before that.  With the optional argument, on
+% the other hand, the number given to the footnote \meta{text} is calculated
+% as done in \!\footnote!, but the \counter{footnote} counter is not
+% updated.
+% \end{description}
+% 
+% With these starred commands, you can produce the following using the
+% base-displacement mechanism without worrying about the absolute value of
+% \!\footnote! counter and its change.
+% 
+% \Hrule
+% \begin{paracol}{2}
+% \tolerance5000\hbadness5000
+% \fnpar{First left-column}{\footnote{First left-column
+% footnote.\label{fn:4L1}}}
+% \Fnpar{Second left-column}{\footnote{Second left-column
+% footnote.\label{fn:4L2}}}{

+% It is followed by \cs{footnotetext}|*[3]|\marg{text} and a
+% \cs{switchcolumn}.}
+% \footnotetext*[3]{Third left-column footnote given by
+% \cs{footnotetext}|*[3]|\marg{text} placed at the end of
+% the second left-column paragraph to have
+% $\ref{fn:4L3}=\ref{fn:4L0}+3$.\label{fn:4L3}}
+% \switchcolumn
+% \Fnpar{First right-column}{\footnote*[4]{First right-column
+% footnote whose number \ref{fn:4R1} is given by
+% \cs{footnote}|*[4]|\marg{text} because
+% $\ref{fn:4R1}=\ref{fn:4L0}+4$.\label{fn:4R1}}}{It is followed by a
+% \cs{switchcolumn*}.}
+% \switchcolumn*
+% Third and synchronized left-column paragraph\Dotfill\\
+% \Dotfill with a footnote whose mark
+% here\footnotemark*[3]\Dotfill\\
+% is given by \!\footnotemark!|*[3]| because $\ref{fn:4L3}=\ref{fn:4L0}+3$.
+% It is followed by a \!\switchcolumn!.
+% \switchcolumn
+% \fnpar{Second and synchronized right-column}{\footnote*[5]{Second right-column
+% footnote produced by \cs{footnote}|*[5]|\marg{text} because
+% $\ref{fn:4R2}=\ref{fn:4L0}+5$.\label{fn:4R2}}}
+% \fnpar{Third right-column}{\footnote{Third right-column
+% footnote produced by \cs{footnote}\marg{text} because
+% $\ref{fn:4R3}=\ref{fn:4R2}+1$.\label{fn:4R3}}}
+% \end{paracol}
+% \newpage
+% 
+% The other way to produce the same result except for the absolute footnote
+% numbers is to use the self-relative mechanism and to exploit the progress
+% of \counter{footnote} counter as follows.
+% 
+% \Hrule
+% \begin{paracol}{2}
+% \tolerance5000\hbadness5000
+% \fnpar{First left-column}{\footnote{First left-column
+% footnote.\label{fn:5L1}}}
+% \Fnpar{Second left-column}{\footnote{Second left-column
+% footnote.\label{fn:5L2}}}{

+% It is followed by \cs{footnotetext}|*|\marg{text} and a
+% \cs{switchcolumn}.}
+% \footnotetext*{Third left-column footnote given by
+% \cs{footnotetext}|*|\marg{text} placed at the end of
+% the second left-column paragraph because it follows the second footnote
+% \ref{fn:5L2}.\label{fn:5L3}}
+% \switchcolumn
+% \Fnpar{First right-column}{\footnote{First right-column
+% footnote whose number \ref{fn:5R1} is given by
+% \cs{footnote}\marg{text} because
+% $\ref{fn:5R1}=\ref{fn:5L3}+1$ and \cs{footnotetext*} for \ref{fn:5L3} lets
+% \counter{footnote} have the value.\label{fn:5R1}}}{It is followed by a
+% \cs{switchcolumn*}.}
+% \switchcolumn*
+% Third and synchronized left-column paragraph\Dotfill\\
+% \Dotfill with a footnote whose mark
+% here\footnotemark*[-1]\Dotfill\\
+% is given by \!\footnotemark!|*[-1]| because $\ref{fn:5L3}=\ref{fn:5R1}-1$.
+% It is followed by a \!\switchcolumn!.
+% \switchcolumn
+% \fnpar{Second and synchronized right-column}{\footnote*[+2]{Second
+% right-column footnote produced by \cs{footnote}|*[+2]|\marg{text} because
+% $\ref{fn:5R2}=\ref{fn:5L3}+2$.\label{fn:5R2}}}
+% \fnpar{Third right-column}{\footnote{Third right-column
+% footnote produced by \cs{footnote}\marg{text} because
+% $\ref{fn:5R3}=\ref{fn:5R2}+1$.\label{fn:5R3}}}
+% \end{paracol}
+% \Hrule
+% 
+% It depends on the structure of your document which of the
+% base-displacement and self-relative is better.  If your document has
+% frequent switching between single- and multi-column text typesetting and
+% thus the contents of a \env{paracol} environment is relatively small, the
+% base-displacement is a good choice because you may concentrate on one
+% base value of \counter{footnote} counter.  Otherwise, especially when your
+% document consists of one single and large \env{paracol} environment, the
+% base-displacement is almost equivalent to maintaining absolute values and
+% thus the self-relative should be preferred.
+% 
+% Note that if the last \!\footnote! or \!\footnotemark! in a \env{paracol}
+% environment is starred, the command lets \counter{footnote} counter have
+% some value smaller than that for the last stacked footnote.  For example, 
+% if the second and third right-column footnotes \ref{fn:5R2} and
+% \ref{fn:5R3} are omitted from the example above, the last footnote-related
+% command will be \!\footnotemark!|*[-1]| which makes the counter at
+% \Endparacol{} \ref{fn:5L3} rather than \ref{fn:5R1}.  You may not worry
+% about this problem, however, because \Endparacol{} automatically maintains
+% the counter letting it have $b+n$ where $n$ is the number of \!\footnote!
+% and \!\footnotemark! in the environment, if the maintenance is ordered by
+% the command \!\fncounteradjustment! which is automatically executed by
+% \!\footnotelayout! with the argument |p| or |m|.
+% 
+% 
+% 
+% \subsection{Page Break}
+% \label{sec:fnnp-pbreak}
+% 
+% When a \env{paracol} environment with footnotes lays across a page boundary,
+% you could have some weird result even if the environment have just one
+% \!\switchcolumn! as shown below.
+% 
+% \Hrule
+% \begin{paracol}{2}
+% First left-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{First left-column
+% footnote.\label{fn:6L1}}\Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill in it.
+% \par
+% Second left-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{Second left-column
+% footnote.\label{fn:6L2}}

+% \Dotfill in it.
+% \switchcolumn
+% First right-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{First right-column
+% footnote weirdly placed here while the footnoted main text is in the
+% previous page.\label{fn:6R1}}\Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill in it.
+% \par
+% Second right-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{Second right-column
+% footnote whose mark in the main text gives impression that footnote
+% numbering jumps from \ref{fn:6L2} to \ref{fn:6R2}.\label{fn:6R2}}

+% \Dotfill in it.
+% \end{paracol}
+% \Hrule
+% 
+% Since the part of the source |.tex| for this example above is
+% fundamentally same as that in p.~\pageref{sec:fnnp} at the beginning of
+% this Section~\ref{sec:fnnp}, footnotes are simply numbered in
+% left-column-first manner without any tricks.  However it results in
+% giving an impression that two paragraphs in each of both columns at the
+% bottom of the last page have footnote marks of inconsecutive numbers
+% \ref{fn:6L1} and \ref{fn:6R1} due to the second left-column paragraph and
+% the footnote \ref{fn:6L2} in it.  More weirdly, the first right-column
+% footnote \ref{fn:6R1} is not put in the last page where its mark is shown
+% but is stacked below \ref{fn:6L2} in this page.
+% 
+% The reason why this happens is that a footnote is not immediately put to
+% the bottom of the page where its mark resides but to the page constructing
+% at the time when the footnote is processed at the end of the paragraph in
+% which the corresponding \!\footnote! (or \!\footnotetext!)
+% occurs\footnote{

+% 

+% More accurately, the footnote is kept in a place in \TeX{} together with
+% other preceding but still unprocessed footnotes and then \TeX{} examines
+% them at the end of a paragraph in which a page break is found to decide
+% whether each of them is included in the page just being completed.}.
+% 

+% Therefore, it may happen even in an ordinary single-column document or a
+% \env{paracol}ed multi-column one with \Mcfnote{}s that a
+% footnote is thrown to the page $p+1$ next to the page $p$ in which its
+% mark is left, when the mark is placed around the bottom of the page
+% $p$.
+% 
+% This footnote placement mechanism becomes clearly visible in the example
+% above in which the footnote \ref{fn:6R1} is processed {\em after} the
+% second left-column paragraph is processed to complete the last page giving
+% no chance to the footnote placed in the page\footnote{%
+% 

+% In fact, even \cs{footnote} for the footnote is processed after the page
+% break in this case.}.
+% 

+% Therefore, the solution of this placement problem is to let the first
+% right-column footnote processed {\em before} the page is broken by the
+% progress of the left-column.  That is, in the solution shown below the
+% author inserted \!\switchcolumn! after the first left-column paragraph to
+% let the first right-column paragraph and its footnote are processed, and
+% then did \!\switchcolumn! again after the right-column paragraph to go
+% back to the left-column.
+% 
+% \Hrule
+% \begin{paracol}{2}
+% First left-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{First left-column
+% footnote.\label{fn:7L1}}\Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\
+% \Dotfill in it.\\
+% It is followed by a \!\switchcolumn!.
+% \par\switchcolumn
+% First right-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{First right-column
+% footnote which is now placed in this page where its mark \ref{fn:7R1}
+% resides.\label{fn:7R1}}\Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\ \Dotfill\\
+% \Dotfill in it.\\
+% It is followed by a \!\switchcolumn! to go back to the left column.
+% \par\newpage\switchcolumn
+% Second left-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{Second left-column
+% footnote whose number \ref{fn:7L2} follows the right-column footnote
+% \ref{fn:7R1} in the last page.\label{fn:7L2}}

+% \Dotfill in it.\\
+% It is also followed by a \!\switchcolumn!.
+% \switchcolumn
+% Second right-column paragraph \Dotfill\\
+% \Dotfill with a footnote\footnote{Second right-column
+% footnote whose number \ref{fn:7R2} follows the left-column footnote
+% \ref{fn:7L2}.\label{fn:7R2}}

+% \Dotfill in it.
+% \end{paracol}
+% \Hrule
+% 
+% Unfortunately, this tactics does not always solve the problem.  If a
+% left-column paragraph has a page break in it and a footnote before the
+% break, doing \!\switchcolumn! after the paragraph is too late to let
+% right-column footnotes reside in the page just having been broken, while
+% inserting \!\switchcolumn! before the paragraph should cause incorrect
+% stacking order.
+% 
+% The remedy for this problem is similar to that shown in
+% Section~\ref{sec:fnnp-multsc} to cope with multiple \!\switchcolumn! in a
+% \env{paracol} environment.  Here it is shown a little bit more formally.
+% Suppose we have a page in a \env{paracol} environment in which a page
+% break occurs in $p_l$-th and $p_r$-th paragraphs in the left and right
+% columns respectively.  Thus we have $p_l-1$ and $p_r-1$ completed
+% paragraphs in each of both columns.  Let $n_l$ (resp.\ $n_r$) be the
+% number of footnotes in the pre-break left-column (resp.\ right-column)
+% paragraphs, and $m_l$ (resp.\ $m_r$) be the number of pre-break footnotes
+% in the $p_l$-th (resp.\ $p_r$-th) paragraph.  Thus we have $n_l+m_l$
+% (resp.\ $n_r+m_r$) footnotes in the left (resp.\ right) column of the page
+% before the break.  The following construct assures that those footnotes
+% are properly numbered and stacked at the bottom of the page.
+% 

+% \begin{list}{}{\rightmargin\leftmargin \itemindent-.5\leftmargin
+% \listparindent\itemindent \leftmargin1.5\leftmargin \parsep0pt}\it\item
+% First to $(p_l-1)$-th paragraphs with $n_l$ footnotes in total given by
+% {\rm\!\footnote!\marg{text}}.\par
+% {\rm\!\footnotetext!|*{|{\it 1st footnote in $p_l$-th paragraph}|}|}\par
+% \mbox{\qquad}\ldots\par
+% {\rm\!\footnotetext!|*{|{\it$m_l$-th footnote in $p_l$-th paragraph}|}|}\par
+% \!\switchcolumn!\par
+% First to $(p_r-1)$-th paragraphs with $n_r$ footnotes in total given by
+% {\rm\!\footnote!\marg{text}}.\par
+% {\rm\!\footnotetext!|*{|{\it 1st footnote in $p_r$-th paragraph}|}|}\par
+% \mbox{\qquad}\ldots\par
+% {\rm\!\footnotetext!|*{|{\it$m_r$-th footnote in $p_r$-th paragraph}|}|}\par
+% \!\switchcolumn!\par
+% $p_l$-th paragraph whose first footnote mark is given by
+% {\rm\!\footnotemark!|*[-|$(m_l{+}n_r{+}m_r{-1})$|]|}, while second to
+% $m_l$-th ones are given by \!\footnotemark! without {\rm|*|} nor optional
+% {\rm\oarg{num}}.  The first subsequent footnotes beyond the page break, if
+% any, is given by {\rm\!\footnote!|*[+|$(n_r{+}m_r{+1})$|]|\marg{text}}
+% while further subsequent ones are given by
+% {\rm\!\footnote!\marg{text}}.\par
+% \!\switchcolumn!\par
+% $p_r$-th paragraph whose first footnote mark is given by
+% {\rm\!\footnotemark!|*[-|$(m_r{+}k_l{-1})$|]|} where $k_l$ is the number
+% of left-column footnotes beyond the break, while second to $m_r$-th ones
+% are given by \!\footnotemark!.  The first subsequent footnotes beyond the
+% page break, if any, is given by
+% {\rm\!\footnote!|*[+|$(k_l{+1})$|]|\marg{text}}, while further subsequent
+% ones are given by {\rm\!\footnote!\marg{text}}.
+% \end{list}
+% %
+% The example shown in the next two pages is for the case of
+% $p_l=p_r=n_l=n_r=m_l=m_r=k_l=2$.
+% 
+% \newpage
+% \Hrule
+% \begin{paracol}{2}
+% First left-column paragraph with two footnotes\break
+% \mbox{}\Dotquad here\footnote{First left-column footnote given by
+% \cs{footnote}\marg{text}.\label{fn;8L1}} by
+% \!\footnote!\marg{text}\Dotfill\\
+% \Dotquad and here\footnote{Second left-column footnote also given by
+% \cs{footnote}\marg{text}.\label{fn:8L2}} also by
+% \!\footnote!\marg{text}\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% followed by a series of \!\footnotetext!|*|\marg{text} and then a
+% \!\switchcolumn!.
+% \footnotetext*{Third left-column footnote given by
+% \cs{footnotetext*}\marg{text}.\label{fn:8L3}}
+% \footnotetext*{Fourth left-column footnote given by
+% \cs{footnotetext*}\marg{text}.\label{fn:8L4}}
+% 
+% \switchcolumn
+% First right-column paragraph with two footnotes\break
+% \mbox{}\Dotquad here\footnote{First right-column footnote given by
+% \cs{footnote}\marg{text}.\label{fn;8R1}} by
+% \!\footnote!\marg{text}\Dotfill\\
+% \Dotquad and here\footnote{Second right-column footnote also given by
+% \cs{footnote}\marg{text}.\label{fn:8R2}} also by
+% \!\footnote!\marg{text}\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% followed by a series of \!\footnotetext!|*|\marg{text} and then a
+% \!\switchcolumn!.
+% \footnotetext*{Third right-column footnote given by
+% \cs{footnotetext*}\marg{text}.\label{fn:8R3}}
+% \footnotetext*{Fourth right-column footnote given by
+% \cs{footnotetext*}\marg{text}.\label{fn:8R4}}
+% 
+% \switchcolumn
+% Second left-column paragraph across two pages\break
+% \mbox{}\Dotquad with two pre-break footnotes\Dotfill\\
+% \Dotquad here\footnotemark*[-5] by \!\footnotemark!|*[-5]|
+% because $m_l+n_r+m_r-1=2+2+2-1=5$ and thus
+% $\ref{fn:8L3}=\ref{fn:8R4}-5$\Dotfill\\
+% \Dotquad and here\footnotemark{} by \!\footnotemark!\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\
+% \Dotquad and two post-break footnotes\Dotfill\\
+% \Dotquad here\footnote*[+5]{Fifth left-column footnote given by
+% \cs{footnote}|*[+5]| because $n_r+m_r+1=2+2+1=5$ and thus
+% $\ref{fn:8L5}=\ref{fn:8L4}+5$.\label{fn:8L5}} by
+% \!\footnote!|*[+5]|\marg{text}\Dotfill\\
+% \Dotquad and here\footnote{Sixth left-column foootnote given by
+% \cs{footnote}\marg{text}.\label{fn:8L6}} by
+% \!\footnote!\marg{text}\Dotfill\\
+% followed by a \!\switchcolumn!.
+% 
+% \switchcolumn
+% Second right-column paragraph across two pages\break
+% \mbox{}\Dotquad with two pre-break footnotes\Dotfill\\
+% \Dotquad here\footnotemark*[-3] by \!\footnotemark!|*[-3]|
+% because $m_r+k_l-1=2+2-1=3$ and thus
+% $\ref{fn:8R3}=\ref{fn:8L6}-3$\Dotfill\\
+% \Dotquad and here\footnotemark{} by \!\footnotemark!\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\\Dotfill\\
+% \Dotfill\\\Dotfill\\
+% \Dotquad and two post-break footnotes\Dotfill\\
+% \Dotquad here\footnote*[+3]{Fifth right-column footnote given by
+% \cs{footnote}|*[+3]| because $k_l+1=3$ and thus
+% $\ref{fn:8R5}=\ref{fn:8R4}+3$.\label{fn:8R5}} by
+% \!\footnote!|*[+3]|\marg{text}\Dotfill\\
+% \Dotquad and here\footnote{Sixth right-column foootnote given by
+% \cs{footnote}\marg{text}.\label{fn:8R6}} by
+% \!\footnote!\marg{text}\Dotfill.
+% \end{paracol}
+% \Hrule
+% 
+% Note that though the remedy works well as shown above, it is not a good
+% idea to do that when you are writing draft versions of your document
+% because page break points go up and down by your modifications to the
+% document.  Therefore, it is recommended to put all footnotes by
+% non-starred \!\footnote! until your document becomes perfect except for
+% footnote numbering and placement and then to adjust them by the techique
+% described in this section.
+% 
+% \endinput
diff --git a/macros/latex/contrib/paracol/ref.dtx b/macros/latex/contrib/paracol/ref.dtx
new file mode 100644
index 0000000000..4025a65d08
--- /dev/null
+++ b/macros/latex/contrib/paracol/ref.dtx
@@ -0,0 +1,1535 @@
+% \footnotelayout{m}
+% \columnratio{}
+% \section{Reference Manual}
+% \label{sec:ref}
+% \subsection{Environment \texttt{paracol}}
+% \label{sec:ref-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
+% \changes{v1.2-2}{2013/05/11}
+% 	{Add a footnote mentioning page-wise footnotes merged with
+%	 pre-environment staff.}

+% \changes{v1.35-4}{2018/12/31}
+% 	{Add description of \cs{belowfootnoteskip}.}

+% 

+% 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
+% {\em\Uidx\preenv} 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\footnote{

+% 

+% With \Mgfnote{} layout shown in Section~\ref{sec:ref-scfnote}, the
+% footnotes in the single-column contents are merged with those in
+% \env{paracol} environment and are put at the bottom of the \spage{}
+% together as shown in this page.}
+% 

+% or bottom floats.  If these kinds of bottom stuff exist, they are
+% put above the multi-columned \meta{body}, or the spanning \meta{text}
+% 

+% \UsageIndex{spanning text}

+% 

+% if provided, with a vertical skip of \!\textfloatsep! separating them if
+% bottom floats exist, or of \!\belowfootnoteskip! described in
+% Section~\ref{sec:ref-scfnote} if only footnotes exist.  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
+% \pwise{} floats given in the environment.
+% 
+% \item
+% \changes{v1.2-5}{2013/05/11}
+% 	{Add an item to show that \string\texttt{paracol} can be enclosed in
+%	 a \string\texttt{list}-like environment.}

+% 

+% The environment can be enclosed in a \env{list}{\em-like environment} such
+% as \env{enumerate}, \env{itemize} and \env{description}.  If so, \!\item!s
+% in each column are typeset using the parameters of the surrounding
+% environment such as \!\leftmargin! and \!\rightmargin!.  For example, the
+% following short \env{paracol} environment is included in an \env{itemize}
+% for this and other \!\item!s in this page.
+% 

+% \begin{paracol}{2}
+% \item
+% This is the first \!\item! in the left column.
+% 
+% \item
+% This is the second \!\item! in the left column followed by a
+% \!\switchcolumn!\footnote{
.
+% 

+% This footnote is to show the footnotes in this page are merged.}.
+% \switchcolumn
+% 
+% \item
+% This is the first \!\item! in the right column.
+% 
+% \item
+% This is the second \!\item! in the right column.
+% 
+% \item
+% This is the third and last \!\item! in the right column.
+% \end{paracol}
+% You are now seeing the switching to/from multi-columned and \env{itemize}d
+% texts are naturally connected with the last and this single-columned
+% sentences.  You may feel the space between two columns above is too large
+% but it simply results from the large total \!\leftmargin!s of the outer
+% \env{description} and this \env{itemize}, which make the right column
+% shifted right.  A simple remedy for this large space is to make
+% \!\columnsep! narrower, for example 0\,pt as shown below.
+% 

+% \columnsep0pt
+% \begin{paracol}{2}
+% \item
+% This \!\item! is wider than the last \!\item! above because
+% \!\columnsep! is 0\,pt.
+% \switchcolumn
+% 
+% \item
+% Therefore, this \!\item! is shifted left a little bit to make
+% inter-column spece narrower.
+% \end{paracol}
+% 
+% \item
+% All \Uidx\lcounter{}s in all columns are initialized to have the values at
+% \beginparacol{} on its first occurrence.  On the second and succeeding
+% occurrences 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 columns
+% commonly have the value at \beginparacol.
+% 
+% \item
+% \changes{v1.2-2}{2013/05/11}
+% 	{Add a footnote mentioning page-wise footnotes merged with
+%	 post-environment staff.}

+% 

+% 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{} in the {\em\Uidx\lpage} of the environment may not
+% start from the top of a page.  If any columns don't have deferred
+% \cwise{} floats and the most advanced {\em\Uidx\lcolumn} at
+% \Endparacol{} has neither of footnotes\footnote{

+% 

+% With \Mgfnote{} layout shown in Section~\ref{sec:ref-scfnote}, the
+% footnotes in the closing \env{paracol} environment are merged with those
+% in \postenv{} and are put at the bottom of the page{} together as shown in
+% this page.}
+% 

+% 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 \cwise{} 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
+% \pwise{} floats given in the environment are considered as deferred
+% (single-) \cwise{} 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}
+% 
+% 
+% 
+% \item[\ENV{paracol}{\oarg{numleft}\marg{num}\oarg{text}}]\mbox{}
+% \Item[\ENV{paracol}{\oarg{numleft}\texttt{*}\marg{num}\oarg{text}}]

+%   \mbox{}\par
+% \changes{v1.3-2}{2013/09/17}
+%	{Add description of parallel-paging.}
+% 

+% If a \beginparacol{} has the optional \meta{numleft} argument to specify
+% the number of leading columns $n_l$ together with the total $n$ given by
+% \meta{num}, columns in the environment are laid out across two adjacent
+% pages.  In this {\em\Uidx\parapag{}e} typesetting, the first $n_l$ columns
+% are placed in the {\em left} page while remaining $n_r=n-n_l$ columns go to
+% the next {\em right} page.  The pair of left and right pages is
+% considered as comprising a virtual {\em\Uidx\paired} page and thus shares
+% a common page number, unless {\em\Uidx\npaired} typesetting is specified
+% by the optional `|*|' following the optional \meta{numleft} argument.  In
+% the \npaired{} \parapag{}ing, when the leading $n_l$ columns are put in a
+% page $p$, the trailing $n_r$ columns are in the page $p+1$.
+% 

+% \begin{itemize}
+% \item
+% All {\em\Uidx\pwstuff}, i.e., \Preenv{} and \postenv, \pwise{} floats,
+% \mctext{} and (\mgfnote{} or non-merged) \Scfnote{}s, are placed only in
+% left \parapag{}es leaving corresponding regions in right \parapag{}es
+% blank\footnote{

+% 

+% Someday the author could devise an advanced mechanism to exploit the space
+% in right \parapag{}es.}.
+% 
+% \item
+% A \npaired{} left \parapag{}e is not necessary to be even-numbered, though
+% the printing tradition requires so if you naturally want to have a
+% \parapag{}e pair in a double spread.  The page number given to the first
+% left \parapag{}e is simply the number of the page $p_1$ in which
+% \beginparacol{} reside, and that for the $k$-th left \parapag{}e is
+% $p_1+2(k-1)$\footnote{

+% 

+% Unless you make some change to \counter{page} counter.}.
+% 

+% Therefore, to make it sure $p_1$ is even, you might need to have an
+% ordinary page of blank, a title, etc., or to let \counter{page} counter have
+% an even number by \!\setcounter!, etc., before starting a \env{paracol}
+% environment.
+%
+% \item
+% Section~\ref{sec:ppts} shows examples of \parapag{}ing together with
+% related issues on two-sided typesetting.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Column-Switching Command and Environments}
+% \label{sec:ref-switchcolumn}
+% 
+% \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 spanning
+% \meta{text} is put.
+% 

+% \Index{spanning text}

+% 

+% \begin{itemize}
+% \item
+% Using \!\switchcolumn! in a \env{list}-like environment \emph{included} in
+% a \env{paracol} environment 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\footnote{

+% 

+% Or below top floats deferred to the page.}.
+% 
+% \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 ignored.  Therefore, even if you specify \!\flushbottom!,
+% the page is typeset as if \!\raggedbottom! were specified.
+% 
+% \item
+% After a \sync{}ation point is set, no top floats will be inserted in the page
+% having the point, thus they will be deferred to the next page or further one.
+% \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 spanning \meta{text} is put.
+% 

+% \Index{spanning 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 occurrences which don't switch to the column 1
+% (i.e., right column if two-columned) but stay in the leftmost column 0.
+% More precisely, \!\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
+% \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{} command\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 spanning \meta{text} is put.
+% 

+% \Index{spanning 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
+% \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{} command\slash environment is given.
+% \end{itemize}
+% 
+% 
+% 
+% \KeepSpace{4}
+% \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 spanning \meta{text} is put.
+% 

+% \Index{spanning 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}
+% 
+% 
+% 
+% \item[\Midx{\!\thecolumn!}]\mbox{}\par
+% \changes{v1.3-5}{2013/09/17}
+%	{Add description of \cs{thecolumn}.}

+% The command gives you the zero-origin ordinal of the column in which this
+% command appears.  Therefore, the following code snip;
+% 

+% \begin{itemize}\item[]
+% |\begin{paracol}{3}|\\
+% |Column-\thecolumn.\switchcolumn|
+% |Column-\thecolumn.\switchcolumn|
+% |Column-\thecolumn.|\\
+% |\end{paracol}|
+% \end{itemize}
+% 

+% gives us the followings.
+% 

+% \par\medskip
+% \begin{paracol}{3}
+% Column-\thecolumn.\switchcolumn
+% Column-\thecolumn.\switchcolumn
+% Column-\thecolumn.
+% \end{paracol}
+% 

+% \begin{itemize}
+% \item
+% The command is {\em neither} a \LaTeX's counter nor \!\count! register of
+% native \TeX{}, and thus the value it keeps cannot be modified.  However,
+% it can be used wherever an integer number is required or appropriate.
+% Therefore for example, \!\setcounter!|{mycounter}{|\!\thecolumn!|}| works
+% well to give the column ordinal to the counter |mycounter|.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\definecolumnpreamble!}\marg{col}\marg{pream}]\mbox{}\par
+% \changes{v1.35-5}{2018/12/31}
+% 	{Add description of \cs{definecolumnpreamble}.}

+% The command is to define the {\Uidx\colpream} \meta{pream} for the column
+% \meta{col}, which is inserted at every \cswitch{} to the column.  More
+% specifically, the command let \!\switchcolumn! to \meta{col} act as if you
+% sepcify;
+% 

+% \begin{itemize}\item[]
+% \!\switchcolumn! $\arg{pream\ for\ col}$
+% \end{itemize}
+% 

+% and \csenv{}s such as \env{nthcolumn} act as if you specify;
+% 

+% \begin{itemize}\item[]
+% |\begin{nthcolumn}{|\meta{col}|}| $\arg{pream\ for\ col}$
+% 

+% \end{itemize}
+% 

+% \begin{itemize}
+% \item
+% \begingroup\hfuzz1.5pt
+% The optional \sptext{} of \!\switchcolumn!, \csenv{}s and \beginparacol{}
+% is considered to be in a virtual column $-1$, and thus if you need a
+% \Colpream{} for \sptext{}s do \!\definecolumnpreamble!|{-1}|\marg{pream}.
+% \par\endgroup
+% 
+% \item
+% The command may appear in a \env{paracol} environment and, if so,
+% \meta{pream} is effective from the succeeding \cswitch{} to \meta{col}.
+% 
+% \item
+% The definition of \meta{pream} is made globally.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\ensurevspace!}\marg{len}]\mbox{}\par
+% \changes{v1.3-5}{2013/09/17}
+%	{Add description of \cs{ensurevspace}.}

+% 

+% The command tells the first \sync{}ing \cswitch{} command (i.e.,
+% \!\switchcolumn!\oarg{col}|*|) or environment (i.e., \env{column*}, etc.\@)
+% following this command that the page must be broken before \sync{}ation
+% unless the \sync{}ation point has the space of \meta{len} or more below it
+% in the page.  If a \sync{}ation does not have the command after the
+% previous \sync{}ation, it is assumed that
+% \!\ensurevspace!|{|\!\baselineskip!|}| is given.
+% 

+% \begin{itemize}
+% \item
+% This command is to be used when a \sync{}ation point would be placed near
+% the bottom of a page $p$ and the space below it is not sufficient for a column
+% $c$ to put anything in the page, while another column $c'$ can have a few
+% lines in the page.  If this happens, the first line after the \sync{}ation
+% should start at the top of the page $p+1$ in the column $c$, while that of
+% $c'$ is still in the page $p$, giving you an impression that the
+% \sync{}ation fails to align the top of all columns below it.  The fact is,
+% however, the \sync{}ation point is properly established near at the bottom
+% of the page but the first line of $c$ needs some large space due to, for
+% example, the followings.
+% 

+% \begin{itemize}
+% \item
+% The line has unusually tall stuff including larger font letters.
+% 
+% \item
+% The line has a footnote reference which is hardly apart from the
+% footnote, and thus the line and the footnote go to the next page together.
+% 
+% \item
+% The parameter \!\clubpenalty! is too large (e.g., 10000) to break the
+% first and second lines into separate pages.
+% 
+% \item
+% The first line follows a vertical space.
+% \end{itemize}
+% 
+% \item
+% This manual itself has some instances of \!\ensurevspace! command in the
+% page \pageref{page:bfreude} and \pageref{page:efreude} in which each German
+% stanza is enclosed in \env{verse} and then \env{leftcolumn*} environments
+% and has \!\ensurevspace!|{2|\!\baselineskip!|}| before the \!\begin!ing of
+% the outer \env{leftcolumn*} because the first line of the stanza is
+% preceded by a vertical space inserted by \!\begin!|{|\env{verse}|}|.  In
+% fact without \!\ensurevspace!, the first two lines of the sixth English
+% stanza would be in the page \pageref{page:bfreude}, while corresponding
+% German stanza go to the next page \pageref{page:efreude} as a whole, due
+% to the difference of the height of footnotes in each column, i.e., German
+% ones are taller than English ones to narrow the space for the German
+% column.
+% 
+% \item
+% As the author does in the ``An die Freude/To Joy'' example, it is a good
+% tactics to have an \!\ensurevspace! with some vertical space larger than the
+% default \!\baselineskip! if it is sure that a column has a feature shown
+% above regardless of the position of the \sync{}ation point in question,
+% because the point goes up or down with revisions of your document and
+% using an \!\ensurevspace! for a \sync{}ation far above the page bottom is
+% perfectly harmless.  Similarly, if you find a problem in a \sync{}ation
+% and add an \!\ensurevspace! to solve it, keeping the command attached is
+% recommended even when the \sync{}ation point moves up or down to make the
+% command unnecessary.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Commands for Column and Gap Width}
+% \label{sec:ref-colwidth}
+% 
+% \begin{description}
+% \item[\Midx{\!\columnratio!}\Arg{$r_0,r_1,\cdots,r_k$}

+%                              {|[|$r'_0,r'_1,\cdots,r'_{k'}$|]|}]\mbox{}\par
+% \changes{v1.1}{2012/05/11}
+% 	{Add description of \cs{columnratio}.}

+% \changes{v1.3-2}{2013/09/17}
+%	{Add descriptino of the optional argument of \cs{columnratio} for
+%	 parallel-paging.}
+% 

+% The command defines the width of each column by the fraction $r_i$ to
+% specify the portion which $i$-th ($i=0$ for the leftmost) column
+% occupies.  More specifically, the width $\Midx{\w}_i$ of the $i$-th column
+% is defined as follows, where $W$ is \!\textwidth!, $S$ is \!\columnsep!,
+% and $n$ is the number of columns given to \beginparacol.
+% 

+% \begin{eqnarray*}
+% W'&=&W-(n-1)S\\
+% w_i&=&\cases{
+%   r_iW'
+%     \vrule height1.5\ht\strutbox depth1.5\dp\strutbox width0pt&$i\leq k$\cr
+%   \displaystyle{(1-\sum_{j=0}^k r_j)W'\over n-(k+1)}&$i>k$}
+% \end{eqnarray*}
+% 

+% For a \env{paracol} environment with \parapag{}ing, $n$ is replaced with
+% $n_l$ for the columns in left \parapag{}es, while $n$ and $w_i$ are
+% replaced with $n_r$ and $w_{n_r+i}$ for those in right \parapag{}es.
+% Moreover, if the optional argument having $r'_0,r'_1,\cdots,r'_{k'}$ is
+% provided, $w_{n_r+i}$ for a column in right \parapag{}es is determined
+% by $r'_i$ and $k'$ instead of $r_i$ and $k$.
+% 

+% \begin{itemize}
+% \item
+% The equations above imply that $k<n-1$, $r_i>0$ and $\sum_{j=0}^k
+% r_j<1$.  If $k\geq n-1$, $k$ is assumed to be $n-2$ and all $r_i$ such
+% that $i\geq n-1$ are ignored.  If $r_i$ or its sum does not satisfy the
+% conditions, you will have an ugly result with ``Overfull'' messages.
+% 
+% \item
+% The argument $r_0,r_1,\cdots,r_k$ can be empty to mean $k=-1$ to let all
+% column widths be $W'/n$ as default.
+% 
+% \item
+% The setting of column width by the command takes effect in the |paracol|
+% environments following the command\footnote{

+% 

+% If the command is in a \texttt{paracol} environment, the command does not
+% affect the column widths of the environment but does the next ones, though
+% such usage is very unusual.}.
+% 

+% Therefore, though placing the command in the preamble is the most natural
+% way\footnote{

+% 

+% Or second most to not using it at all, of course.},
+% 

+% you may place this command between two |paracol| environments to change
+% the column layout for the second one even when they appear in a page as
+% shown in Section~\ref{sec:man-close}.
+% 
+% \item
+% \changes{v1.2-5}{2013/05/11}
+% 	{Modify the description about \cs{linewidth} reflecting the fact
+%	 that \string\texttt{paracol} may be included in a
+%	 \string\texttt{list}-like environment.}

+% 

+% In the $i$-th column, \!\columnwidth! has $w_i$ and, for outermost
+% paragraphs in the column, \!\hsize! has $w_i$ as well.  As for
+% \!\linewidth!, it has $w_i-(\!\textwidth!-l)$ where $l$ is what
+% \!\linewidth! had at \beginparacol{}, i.e., the \!\linewidth! for the
+% \env{list}-like environment surrounding \env{paracol} if any, or
+% \!\textwidth! otherwise.
+% 
+% \item
+% You can specify width of each column and that of each {\em gap} between
+% two columns more detailedly by \!\setcolumnwidth! shown below.  If your
+% document has both of \!\columnratio! and \!\setcolumnwidth! prior to a
+% \env{paracol} environment, the command given later is effective for the
+% environment.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\setcolumnwidth!}\Arg{$s_0,s_1,\cdots,s_k$}

+%                              {|[|$s'_0,s'_1,\cdots,s'_{k'}$|]|}]\mbox{}\par
+% \changes{v1.3-2}{2013/09/17}
+%	{Add descriptino of \cs{setcolumnwidth}.}

+% 

+% The command defines the width of each column and that of each {\em gap}
+% between two columns by the column/gap specification $s_i$ for the $i$-th
+% column and the gap between it and the $(i{+}1)$-th column.  More
+% specifically, $s_i$ has the form of $\hat w_i$ or $\hat w_i\,|/|\,\hat g_i$
+% where each of $\hat w_i$ and $\hat g_i$ is a proper glue including a
+% proper dimension, or an empty string to mean $\hat w_i=\!\fill!$ and $\hat
+% g_i=\!\columnsep!$, to determine the width of $i$-th column $\w_i$ and that
+% of $i$-th gap $\Midx{\gap}_i$ as follows, where $\mathit{nat}(x)$ is the
+% natural width of the glue $x$, $\mathit{str}(x)$ is the infinite stretch
+% factor of $x$, $W$ is \!\textwidth!, and $n$ is the number of columns
+% given to \beginparacol.
+% 

+% \begin{eqnarray*}
+% W'&=&\sum_{i=0}^{n-2}\big(\mathit{nat}(\hat w_i)+\mathit{nat}(\hat g_i)\big)+
+%      \mathit{nat}(\hat w_{n-1})\\
+% F&=&\sum_{i=0}^{n-2}\big(\mathit{str}(\hat g_i)+\mathit{str}(\hat g_i)\big)+
+%      \mathit{str}(\hat w_{n-1})\\
+% x_i&=&\cases{(W/W')\mathit{nat}(\hat x_i)&$W'\geq W\;\lor\;F\leq0$\cr
+%              \mathit{nat}(\hat x_i)+(\mathit{str}(\hat x_i)/F)(W-W')&
+%                                           $W'< W\;\land\;F>0$}
+%     \qquad(x\in\{w,g\})
+% \end{eqnarray*}
+% That is, if the total of natural widths $W'$ is larger than \!\textwidth!
+% $W$ or there are no infinite stretch factors in the specification, given
+% widths are scaled down or up so that the scaled total is equal to $W$.
+% Otherwise, each width with an infinite stretch factor is extended
+% according to its ratio in the total stretch so that the stretched total is
+% equal to $W$.
+% 
+% For a \env{paracol} environment with \parapag{}ing, $n$ is replaced with
+% $n_l$ for the columns in left \parapag{}es, while $n$, $w_i$ and $g_i$ are
+% replaced with $n_r$, $w_{n_r+i}$ and $g_{n_r+i}$ for those in right
+% \parapag{}es.  Moreover, if the optional argument having
+% $s'_0,s'_1,\cdots,s'_{k'}$ is provided, $w_{n_r+i}$ and $g_{n_r+i}$ for a
+% column in right \parapag{}es are determined by $s'_i$ instead of $s_i$.
+% 

+% \begin{itemize}
+% \item
+% In \env{paracol} environments having $n$ columns, $s_i$ s.t.\ $i\geq n$
+% and $\hat g_{n-1}$ are ignored.  On the other hand if $k<n-1$, it is
+% assumed $s_i$ is an empty string for all $i>k$.
+% 
+% \item
+% Finite stretch factors and finite or infinite shrink factors in $\hat w_i$
+% and $\hat g_i$ are ignored.
+% 
+% \item
+% Unlike \TeX's genuine glue addition, all infinite unit |fil|, |fill| and
+% |filll| are not distinguished in the summation for $F$.  Also unlike
+% \TeX's genuine scaling of a glue primitive, 
+% $f\!\fill!$ means $0\,|pt|\ |plus|\ f\,|fill|$ for convenience\footnote{

+% 

+% In \TeX's grammar, $f\!\fill!$ means a dimension rather than a glue and is
+% $0\,|pt|$ because the natural component of \!\fill! is 0.}.
+% 
+% \item
+% The division $W/W'$ and $\mathit{str}(\hat x_i)/F$ can have some
+% arithmetic errors and thus the total of $w_i$ and $g_i$ may not be equal to
+% $W$ exactly but can be a little bit less than $W$.  This small error is,
+% however, equally distributed to $g_i$ in typesetting of a page to make the
+% total width of columns and gaps is exactly $W$\footnote{

+% 

+% If we may ignore the arithmetic error inherent in \TeX.}.
+% 
+% \item
+% All the specifications shown in the table below give us same results for a
+% \env{paracol} environment having three columns, providing
+% $\!\textwidth!=360\,|pt|$ and $\!\columnsep!=S=20\,|pt|$.
+% 

+% \par\hbox to\textwidth\bgroup\hfil
+% \nosv \def\|{\verb|}\small\arraycolsep0pt\def\arraystretch{1.1}
+% $\begin{array}[b]{l|ccccc}
+% s_0,s_1,s_2&w_0&g_0&w_1&g_1&w_2\rlap{ (in \texttt{pt})}\\\hline
+% \|50pt/20pt,100pt/40pt,150pt|&50&20&100&40&150\\
+% \|50pt,100pt/2\columnsep,150pt|&50&S&
+%                                100&2S&150\\
+% \|50pt/\fill,100pt/2\fill,150pt|&50&(1/3)\cdot60&100&(2/3)\cdot60&150\\
+% \|,2\fill/2\columnsep,3\fill|&\ (1/6)\cdot300&S&
+%                              (2/6)\cdot300&2S&
+%                              (3/6)\cdot300\\
+% \|50pt/20,50pt plus 1fil/40pt,50pt plus 2fil |&
+%                              50&20&50+(1/3)\cdot150&40&
+%                              50+(2/3)\cdot150\\
+% \|5pt/2pt,10pt/4pt,15pt|&10\cdot5&10\cdot2&10\cdot10&10\cdot4&
+%                         10\cdot15\\
+% \|100pt/40pt,200pt/80pt,300pt|&0.5\cdot100&0.5\cdot40&
+%                               0.5\cdot200&0.5\cdot80&
+%                               0.5\cdot300
+% \end{array}$\hfil\egroup
+% 
+% \item
+% If your document has both of \!\columnratio! and \!\setcolumnwidth! prior
+% to a \env{paracol} environment, the command given later is effective for
+% the environment.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Commands for Two-Sided Typesetting and Marginal Note Placement}
+% \label{sec:ref-twoside}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add the sub-section ``Commands for Two-Sided Typesetting and Marginal
+%	 Note Placement''.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add the sub-section ``Commands for Two-Sided Typesetting and Marginal
+%	 Note Placement''.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Add the sub-section ``Commands for Two-Sided Typesetting and Marginal
+%	 Note Placement''.}

+% 
+% \begin{description}
+% \item[\Midx{\!\twosided!}{$|[|t_1t_2\cdots t_k|]|$}]\mbox{}\par
+% \changes{v1.3-3}{2013/09/17}
+%	{Add description of \cs{twosided}.}

+% \changes{v1.3-4}{2013/09/17}
+%	{Add description of \cs{twosided}.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Add description of \cs{twosided}.}

+% 

+% The command enables a set of two-sided typesetting features
+% $\Set{t_i}{t_i\in\{|p|,|c|,|m|,|b|\},\ 1\leq i\leq k}$ explicitly by the
+% optional argument, or all of the following four features as a whole
+% without the argument, in even-numbered pages.
+% 

+% \begin{description}
+% \item[|p|\rm(\textit{age})]
+% for ordinary two-sided paging, letting the left side margin be
+% \!\evensidemargin!, page headers be different from those in odd-numbered
+% pages with |headings| or |myheadings| page style, and \!\cleardoublepage!
+% leave an even-numbered page blank if it is used in an odd-numbered page.
+% 
+% \item[|c|\rm(\textit{olumn})]
+% for {\em\Uidx\cswap} to \emph{print} columns in even-numbered pages in
+% reverse order.  This feature is sometimes preferable in typesetting
+% especially with unbalanced parallel columns to make, for example, a wider
+% columns are always \emph{inside} while narrower ones are \emph{outside}.
+% 
+% \item[|m|\rm(\textit{arginal text})]
+% to place marginal notes in the side margin opposite to that specified by
+% the command \!\marginparthreshold! discussed shortly.
+% 
+% \item[|b|\rm(\textit{ackground painting})]
+% to make \bgpaint, shown in Section~\ref{sec:ref-bgpaint},
+% \emph{\mirror{}ed} so that, for example, a color specified for the left
+% margin is used to paint the right margin instead.
+% \end{description}
+% 

+% \begin{itemize}
+% \item
+% The feature |p| is also enabled by the |twoside| option of
+% \!\documentclass! with almost all classes including |article|, |book|,
+% |report|, etc.  Though it is strongly recommended to make both settings by
+% \!\documentclass! and this command consistent, they can be inconsistent
+% resulting in lack of some expected functions.  For example, enabling |p|
+% feature by \!\twosided! without |twoside| option in \!\documentclass!
+% makes the format of headers and footers in all pages same even with
+% \!\pagestyle!|{headings}|.
+% 
+% \item
+% The \cswap{} enabled by the feature |c| is ineffective in \npaired{}
+% \parapag{}ing because it is meaningless\footnote{

+% 

+% Unless somebody tells the author it is meaningful.},
+% 

+% and thus silently ignored.
+% 
+% \item
+% In ordinary single-column typesetting, marginal note swapping in
+% even-numbered pages is enabled by the |twoside| option, while it never takes
+% place in ordinary two-column typesetting.  For marginal notes given in
+% \env{paracol} environments, however, swapping of them in
+% even-numbered pages is enabled by giving the feature |m| to \!\twosided!.
+% 
+% \item\label{page:cswap}
+% The command has to be outside of \env{paracol} environments to decide the
+% action in the environments following them.  If it appears in a
+% \env{paracol} environment, you will have a warning message saying it is
+% ignored.
+% 
+% \twosided[c]\columnratio{0.6}\columnsep0pt
+% \begin{paracol}{2}
+% \hfuzz2pt
+% \item
+% Here is an example of column swapping.  Since this page
+% \pageref{page:cswap} is odd, this wider column-0 with roman font is placed
+% in left side and thus inside at the begining, but now we are in an even
+% page in which this column is in right side.
+% 
+% \switchcolumn
+% \item\it
+% This narrower, outside and italicized column-1 is at first in right
+% side but the page break has changed the position to the left.
+% \end{paracol}
+% 
+% \item
+% \changes{v1.2-4}{2013/05/11}
+% 	{Add description of \cs{[no]swapcolumninevenpages}.}

+% \changes{v1.3-5}{2013/09/17}
+% 	{Remove description of \cs{[no]swapcolumninevenpages} but mention
+%	 they are still available.}

+% 

+% In old versions of \Paracol, namely 1.2 and its minor revisions 1.2x,
+% \cswap{} was controlled by lengthy commmands
+% \Midx{\!\swapcolumninevenpages!} and \Midx{\!\noswapcolumninevenpages!}.
+% Though they are still available and will be so forever for backward
+% compatibility, it is recommended to use \!\twosided! with or without the
+% feature |c|.  The old versions also have a problem that \spanning{}
+% crossing a page boundary is placed incorrectly after the page break in it,
+% but this problem is solved by a fix incorporated in version 1.3.
+% 
+% \item
+% It must be $t_i\in\{|p|,|c|,|m|,|b|\}$, or you will have an error message
+% of illegal two-siding feature.
+% 
+% \item
+% Section~\ref{sec:ppts} shows examples of two-sided typesetting together
+% with related issues on \parapag{}ing.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\marginparthreshold!}$\Arg{k}{|[|k'|]|}$]\mbox{}\par
+% \changes{v1.3-4}{2013/09/17}
+%	{Add description of \cs{marginparthreshold}.}

+% 

+% The command specifies the minimum ordinal $k$ of columns whose marginal
+% notes are placed in right margin.  That is, marginal notes given in a
+% column-$i$ go to left margin if $i<k$, while they go to right if $i\geq
+% k$.  The optional argument $k'$, if given, is for columns in right
+% \parapag{}es to decide the margin where their marginal notes are placed.
+% In default, $k=1$ is assumed to let marginal notes from the leftmost
+% column-0 go to left margin while those from other columns go to right.
+% 

+% \begin{itemize}
+% \item
+% You may specify $k=0$ to let all marginal notes go to right margin, or may
+% give the command a large number, say 100, to place all of them in left
+% margin.
+% 
+% \item
+% The setting $k=0$ or $k=100$ above makes a side margin \emph{shared} by
+% marginal notes from different columns, and sharing is inevitable when a
+% (parallel-) page has three or more columns.  When a margin is shared by
+% marginal notes from two or more columns, it can happen that two marginal
+% notes from different columns conflict over the space to be occupied by each
+% of them.  This conflict is solved by \Paracol{} to push down the note
+% given later in your source |.tex| until an available space for it is
+% found.  Note that the marginal note to be pushed down is determined by the
+% position in the source rather than that in the printed result.  Also note
+% that \Paracol{} exploits space between two marginal notes having been
+% already placed in the placement of other note coming later to place it at
+% the natural position if possible or to minimize the amount of pushing down
+% otherwise.
+% 
+% \item
+% In the decision of the real margin in which a marginal note is placed,
+% other two factors are involved;  |m| feature of \!\twosided! command and
+% the parity of the page; and \LaTeX's genuine command \!\reversemarginpar!.
+% More specifically, after the first preliminary decision is made according
+% to the threshold given to \!\marginparthreshold!, we have the following
+% two steps to modify the decision;  if |m| feature has been specified in
+% \!\twosided! command and the marginal note belongs to an even-numbered
+% page, the decision is reversed to have the second preliminary result;  and
+% then if \!\reversemarginpar! has been specified, the second result is
+% reversed (again) to have the final result.
+% 
+% \item
+% In old versions of \Paracol, namely older than 1.3, marginal note
+% placement was not only uncontrollable but also gave ugly results when your
+% document has three or more columns because the marginal notes from a column
+% not being leftmost or rightmost were placed in the gap following the
+% column rather than a margin.  This miserable {\em gap note} placement does
+% not happen any more, or in other words this is no more available because
+% the author believes nobody loves it.
+% 
+% \item
+% Section~\ref{sec:ppts} shows examples of marginal note placement together
+% with related issues on \parapag{}ing and two-sided typesetting.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\marginnote!}\oarg{left}\marg{right}\oarg{voffset}]\mbox{}\par
+% \changes{v1.35-3}{2018/12/31}
+% 	{Add description of \cs{marginnote}.}

+% You may use the package \textsf{marginnote} and its command \!\marginnote!
+% in \env{paracol} environments as a replacement of \!\marginpar!.  However,
+% the command is \emph{emulated} with \!\marginpar! and \textsf{paracol}'s
+% own mechanism of marginal note placement.  Therefore, some of
+% \textsf{marginnote}'s functionality are not effective in \env{paracol}
+% environment except for the following features.
+% 

+% \begin{itemize}
+% \item
+% Shifting up/down a marginal note by the optional \meta{voffset}.
+%
+% \item
+% Defining fonts (and others) for marginal notes by \!\marginfont!.
+% 
+% \item
+% Controlling the holizontal paragraph alignment by \!\raggedleftmarginnote!
+% and |\raggedright|\~|marginnote|\SpecialIndex{\raggedrightmarginnote}.
+% \end{itemize}
+% 

+% Note that you will see a warning message ``|\margninnote| is emulated by
+% |\marginpar|'' at the first in-\env{paracol} occurrence of the command to
+% let you know the imperfection.
+% \end{description}
+% 
+% 
+% 
+% \subsection{Commands for Counters}
+% \label{sec:ref-counter}
+% 
+% \begin{description}
+% \item[\Midx{\!\globalcounter!}\marg{ctr}]\mbox{}
+% \Item[\Midx{\!\globalcounter!}\texttt{*}]\mbox{}\par
+% \changes{v1.32-1}{2015/10/10}
+% 	{Add descriptions of \cs{globalcounter*}.}
+% 

+% The command \!\globalcounter!\marg{ctr} declares that the counter
+% \meta{ctr} is global to all columns, while \!\globalcounter!|*| does so
+% for all counters.  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 inconsistent result, as you
+% might have in ordinary \LaTeX{} documents.}.
+% 
+% \item
+% All counters except for \counter{page} are local by default.  This feature
+% may cause a problem with some packages including \textsf{marginnote} and
+% \textsf{(auto-)pst-pdf} having their own counters which must be global.
+% Since it is tough to find the name of such counters from package sources,
+% if you have something wrong with these (or other) packages, try to put
+% \!\globalcounter!|*| in your preamble and use \!\localcounter! shown below
+% to localize specific counters which you need to be local.
+% 
+% \item
+% Globalizing a \meta{ctr} being already global is just ignored without any
+% complaints.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\localcounter!}\marg{ctr}]\mbox{}\par
+% The command declares that the counter \meta{ctr} is local for each column.
+% 

+% \begin{itemize}
+% \item
+% Though this command is intended for localizing a \meta{ctr} which is once
+% globalized, localizing a local counter does not causes any error but is
+% just ignored.  Localizing the permanently global \counter{page} is also
+% just ignored without any complaints.
+% \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{Page-Wise Footnotes}
+% \label{sec:ref-scfnote}
+% \changes{v1.2-2}{2013/05/11}
+% 	{Add the sub-section ``Single-Columned Footnotes'' to describe newly
+%	 introducerd commands for page-wise footnotes.}

+% \changes{v1.3-5}{2013/09/17}
+%	{Rename the sub-section title from ``Single-Columned Footnotes'' to
+% 	``Page-Wise Footnotes'' following new naming.}

+% 
+% \begin{description}
+% \item[\Midx{\!\footnotelayout!}\marg{layout}]\mbox{}\par
+% The command specifies the \meta{layout}${}\in\{|c|,|p|,|m|\}$ of footnotes
+% in \env{paracol} environments as follows.
+% 

+% \begin{description}
+% \item[|c|\rm(\textit{olumn})] makes footnotes {\em\Uidx\mcfnote} (aka
+% multi-columned) being default to place footnotes in each column at the
+% bottom of the column and separating them from \Preenv{} and \Postenv{}
+% footnotes.
+% 
+% \item[|p|\rm(\textit{age})] makes footnotes {\em\Uidx\scfnote} (aka
+% single-columned) so that footnotes in all columns are gathered, typeset
+% spanning all columns, and placed at the bottom of the page in which they
+% appear or at the end of the \env{paracol} environment they belong to, so
+% that they are separated from \Preenv{} and \Postenv{} footnotes.
+% 
+% \item[|m|\rm(\textit{erge})] makes \Scfnote{}s {\em\Uidx\mgfnote} with
+% footnotes in outside of the environment but in the same page, i.e., those
+% in \Preenv{} and \postenv.
+% \end{description}
+% 
+% 

+% \begin{itemize}
+% \item
+% An example of \Mgfnote{} is found in p.~\pageref{sec:ref-paracol} while
+% you will see many of them in Section~\ref{sec:fnnp}\footnote{

+% 

+% The left-column footnote \ref{fn:flush} in p.~\pageref{fn:flush} looks like
+% a merged footnote because it is at the bottom of the page and the marked
+% text is above the single-column text.  However, it is an ordinary
+% \mcfnote{} one produced by a trick with \cs{footnotemark} and
+% \cs{footnotetext} in different \env{paracol} environments.}.
+% 
+% \item
+% In any layouts, a footnote cannot have page breaks in it, i.e., a footnote
+% is always put in a page as a whole.  This makes it impossible to have a
+% footnote taller than \!\textheight! and thus you will see a warning
+% message if you give a very long footnote which will be printed intruding
+% into the area for page footer (or out of the paper bound).
+% 
+% \item
+% Choosing the layout |p|age-wise or |m|erged makes \counter{footnote}
+% counter global and \!\fncounteradjustment!  shown below performed inside
+% \!\footnotelayout!.  Choosing |c|olumn-wise let the command do the
+% operations oppositely, i.e., localizes \counter{footnote} and does
+% \!\nofncounteradjustment!.  Though these settings are usually appropriate
+% for each footnote layout but you can override them by explicitly using
+% commands like \!\localcounter!|{footnote}|.
+% 
+% \item
+% The command has to be outside of \env{paracol} environments to decide the
+% action in the environments following them.  If it appears in a
+% \env{paracol} environment, you will have a warning message saying it is
+% ignored.
+% 
+% \item
+% \changes{v1.3-5}{2013/09/17}
+% 	{Remove description of \cs{multicolumnfootnotes},
+%	 \cs{singlecolumnfootnotes}, \cs{mergedfootnotes} but mention they
+%	 are still available.}

+% 

+% In old versions of \Paracol, namely 1.2 and its minor revisions 1.2x,
+% footnote layout was controlled by a set of lengthy commands
+% \Midx{\!\multicolumnfootnotes!} for |c|, \Midx{\!\singlecolumnfootnotes!}
+% for |p|, and \Midx{\!\mergedfootnotes!} for |m|.
+% Though they are still available and will be so forever for backward
+% compatibility, it is recommended to use \!\footnotelayout!\footnote{

+% 

+% Not only for type saving but also for being familiar with this command
+% which could have some advanced feature, for example to put gathered
+% footnotes into a specific column, someday.}.
+% 
+% % \item
+% It must be $\meta{layout}\in\{|c|,|p|,|m|\}$, or you will have an error
+% message of illegal layout specifier.
+% \end{itemize}
+% 
+% 
+% 
+% \KeepSpace{5}
+% \item[\Midx{\!\footnote!}\texttt{*}\oarg{num}\marg{text}]\mbox{}
+% \Item[\Midx{\!\footnotemark!}\texttt{*}\oarg{num}]\mbox{}
+% \Item[\Midx{\!\footnotetext!}\texttt{*}\oarg{num}\marg{text}]\mbox{}\par
+% The starred version of \!\footnote!, \!\footnotemark! and \!\footnotetext!
+% are for the adjustment of the footnote numbering, the order of footnote
+% marks in main texts, and the stacking order of footnotes at page
+% bottom.  Their usages with various examples are given in
+% Section~\ref{sec:fnnp}.
+% 
+% 
+% 
+% \KeepSpace{3}
+% \item[\Midx{\!\fncounteradjustment!}]\mbox{}
+% \Item[\Midx{\!\nofncounteradjustment!}]\mbox{}\par
+% The maintenance of \counter{footnote} with the starred footnote commands
+% such as \!\footnote!|*| shown above causes out-of-order progress of the
+% counter to make it hard to have a consistent counter value at
+% \Endparacol.  The command \!\fncounteradjustment! is to let \Endparacol{}
+% adjust the value of the counter based on its value at
+% \beginparacol{} and the number of footnote commands in the environment.
+% The command \!\nofncounteradjustment! is to tell \Endparacol{} to do
+% nothing as in default.
+% 
+% \begin{itemize}
+% \item
+% Though \!\footnotelayout! with |p|(age-wise) or |m|(erged) argument does
+% \!\fncounteradjustment! while that with |c|(olumn) does
+% \!\nofncounteradjustment! inside of it, you can override these settings by
+% explicitly putting a counter adjustment command after \!\footnotelayout!.
+% 
+% \item
+% The effect of \!\fncounteradjustment! is shown in Section~\ref{sec:fnnp}.
+% \end{itemize}
+% 
+% 
+% \item[\Midx{\!\belowfootnoteskip!}]\mbox{}\par
+% \changes{v1.35-4}{2018/12/31}
+% 	{Add description of \cs{belowfootnoteskip}.}

+% The typesetting parameter specifies the amount of the space inserted below
+% footnotes of single-column \preenv{} if it does not have bottom floats.  The
+% default amount is 0\,pt, i.e., no space is added.
+% 
+% \end{description}
+% 
+% 
+% \KeepSpace{6}
+% \subsection{Commands for Coloring Texts and Column-Separating Rules}
+% \label{sec:ref-tcolor}
+% \changes{v1.3-3}{2013/09/17}
+%	{Rename the sub-sectoin title from ``Commands for Text Coloring'' to
+%	 ``Commands for Coloring Texts and Column-Separating Rules'' to
+%	 add description of the rule coloring together with the rule
+%	 drawing itself.}

+% 
+% \begin{description}
+% \item[\Midx{\!\columncolor!}\oarg{mode}\marg{color}\oarg{col}]\mbox{}
+% \Item[\Midx{\!\normalcolumncolor!}\oarg{col}]\mbox{}\par
+% \changes{v1.2-1}{2013/05/11}
+%	{Add description of \cs{columncolor} and \cs{normlcolumncolor}.}

+% 

+% The command \!\columncolor! declares that the \emph{default color} of a
+% column is \meta{color} or what it specifies by the combination with the
+% optional \meta{mode}.  The command \!\normalcolumncolor! declares the
+% default color is what \!\normalcolor! specifies, i.e., black usually.  The
+% target column of these commands is that in which the commands reside, or
+% \meta{col} if it specified.
+% 

+% \begin{itemize}
+% \item
+% The command may be outside of \env{paracol} environment.  If so and
+% \meta{col} is not provided, the target column is the leftmost 0.
+% 
+% \item
+% The default color declaration is \emph{global}.  Therefore, even if the
+% command appears in a \env{paracol} environment (and even in some grouping
+% structure in it), the declaration will be kept effective after
+% \Endparacol{} to determine the default color of the specified column in
+% succeeding \env{paracol} environments.
+% 
+% \item
+% To give a color to texts (and maybe other stuff) in a column correctly,
+% you need to load \textsf{color} package or its relative (e.g.,
+% \textsf{xcolor}) which the implementation of coloring in \textsf{paracol}
+% relies on.
+% 
+% \item
+% Coloring with \!\color!\oarg{mode}\marg{color} and other coloring commands
+% in \env{paracol} environments is of course allowed.  One caution is that
+% the \!\color! decides the color for following texts until other
+% specification is given or the group surrounding the command is closed.
+% Therefore, \!\switchcolumn! does not affect the coloring but a color given
+% to the texts in a column is also applied to the texts in the column to be
+% switched to.  This irrelativeness of coloring and \cswitch{} is shown in
+% the example below.
+% 
+% \twosided[]\columnratio{0.5}\columnsep0pt
+% \tolerance5000\hbadness5000
+% \begin{paracol}{2}
+% \columncolor{blue}
+% This column is colored blue because\\
+% \mbox{}\qquad \!\columncolor!|{blue}|\\
+% is specfied.  Here we have a \!\switchcolumn!.
+% \switchcolumn
+% \columncolor{red}
+% This column is colored red because\\
+% \mbox{}\qquad\!\columncolor!|{red}|\\
+% is specified.
+% 
+% \begin{color}{green}
+% Now the color of the right column is changed to green because\\
+% \mbox{}\qquad\!\begin!|{color}{green}|\\
+% is given prior to this paragraph.  Now we have another \!\switchcolumn! to
+% go back to the left.
+% \switchcolumn
+% The color of this paragraph is green because we are still in the
+% environment of green coloring, which we are now closing.\par
+% \end{color}%
+% 
+% Since the coloring environment has been closed, the color of this
+% paragraph is the default blue.  Now we have yet another and the last
+% \!\switchcolumn! to the right.
+% \switchcolumn
+% Since this paragraph is outside of the coloring environment, its color is
+% the default red.
+% \end{paracol}
+% 
+% \normalcolumncolor[0]\normalcolumncolor[1]
+% The default coloring of columns does not affect anything outside of
+% \env{paracol} environment of course, and thus this sentence is not
+% colored\footnote{

+% 

+% Or colored black as \cs{normalcolor} specifies.}.
+% \end{itemize}
+% 
+% 
+% 
+% \KeepSpace{4}
+% \item[\Midx{\!\coloredwordhyphenated!}]\mbox{}
+% \Item[\Midx{\!\nocoloredwordhyphenated!}]\mbox{}\par
+% \changes{v1.3-3}{2013/09/17}
+%	{Add description of \cs{coloredwordhyphenated} and
+%	 \cs{nocoloredwordhyphenated}.}
+% 

+% The command \!\coloredwordhyphenated! allows the first word following a
+% coloring command such as \!\color! to be hyphenated, but at the same time
+% make it possible that a line is broken before the word.  The command
+% \!\nocoloredwordhyphenated! acts oppositely and thus line breaking before
+% the first word and hyphenating it are inhibited.  By default,
+% \!\coloredwordhyphenated! is effective.
+% 

+% \begin{itemize}
+% \item
+% The implementation of \textsf{color} package and its relatives makes it
+% impossible that \meta{word} is hyphenated when it appears like
+% |{|\!\color!|{red}|\meta{word} \ldots|}| or
+% \!\textcolor!|{|\meta{word} \ldots|}|.  This inhibition of the hyphenation
+% is sometimes annoying especially when the document is multi-columned and
+% thus a line is narrow and a column is written in a language having long
+% words such as German.  Therefore in \Paracol{} package, a trick is used to
+% allow the \meta{word} is hyphenated.  However this trick being insertion
+% of a null horizontal space has a side effect that the word can have a line
+% break before it.  Though this line break is usually unharmful, in a
+% special occasion the break is undesirable and
+% in\textcolor{red}{appropriate} by making it possible that the
+% \emph{half-colored} word `inappropriate' is broken between `in' and
+% `appropriate' without hyphenation.  Therefore, if you find such a
+% inappropriate break, use \!\nocoloredwordhyphenated! as follows, for example.
+% \begin{quote}
+% |{\nocoloredwordhyphenated in\textcolor{red}{appropriate}}|
+% \end{quote}
+% \end{itemize}
+% 
+% 
+% \KeepSpace{4}
+% \item[\Midx{\!\colseprulecolor!}\oarg{mode}\marg{color}\oarg{col}]\mbox{}
+% \Item[\Midx{\!\normalcolseprulecolor!}\oarg{col}]\mbox{}\par
+% \changes{v1.3-3}{2013/09/17}
+%	{Add description of \cs{colseprulecolor} and
+%	 \cs{normalcolseprulecolor}.}
+% 

+% The command \!\colseprulecolor! declares the color for
+% {\em\Uidx\cseprule{}s}, being the vertical rules drawn at the center of
+% gaps between columns, is \meta{color} or what it specifies by the
+% combination with the optional \meta{mode}.  The command
+% \!\normalcolseprulecolor! declares the color of rules is what
+% \!\normalcolor! specifies, i.e., black usually.  If the optional argument
+% \meta{col} is given, these commands specifies the color of the rule in the
+% gap following the column whose ordinal is \meta{col}, rather than all rules.
+% 

+% \begin{itemize}
+% \item
+% The rules are drawn if \LaTeX's typesetting parameter \!\columnseprule!
+% for the rule width has non-zero value, e.g., 0.4\,|pt| to obey the
+% standard rule thickness.  The rules are \emph{not} drawn on \pwstuff{},
+% i.e., \Preenv{} and \postenv, \pwise{} floats or (\mgfnote{} or
+% non-merged) \Scfnote{}s of course but also \mctext{}s.  Therefore, if a
+% page has \mctext{}s, the rules are {\em broken} by them as shown in the
+% red rule example below.
+% \global\unitlength\@totalleftmargin
+% \end{itemize}
+% \end{description}
+% 
+% \columnseprule0.4pt\colseprulecolor{red}[1]\colseprulecolor{white}[0]
+% \setcolumnwidth{\unitlength/0pt}
+% \begin{paracol}{3}\switchcolumn\noindent 
+% This is a left column paragraph preceding a \mctext.  Of cource the rule
+% separating this and the next column starts from the top of this paragraph.
+% \switchcolumn\noindent
+% This is a right column paragraph preceding a \mctext{} given by the
+% \!\switchcolumn!|*| at its end.
+% \switchcolumn[1]*[\subsubsection*{\hbox to\unitlength{}

+% An Example of Spanning Text Given by \cs{subsubsection}|*| Command}]
+% Since we have a \mctext{} above, the red rule separating this and the next
+% column is broken by the text.
+% \switchcolumn
+% It is also natural that the rule separating this and the previous column is
+% terminated at the end of this \env{paracol} environment.
+% \end{paracol}
+% \columnseprule0pt\columnratio{}
+% 

+% \begin{description}
+% \Item[]\mbox{}
+% \begin{itemize}
+% \Item
+% To give a color to rules correctly, you need to load \textsf{color}
+% package or its relative (e.g., \textsf{xcolor}) which the implementation
+% of coloring in \textsf{paracol} relies on.
+% 
+% \item
+% Once you give a color to rules in a specific gap with the optional
+% \meta{col}, another \!\colseprulecolor! or \!\normalcolseprulecolor!
+% without \meta{col} does \emph{not} change the color of the rule in the
+% gap.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \KeepSpace{7}
+% \subsection{Commands for Background Painting}
+% \label{sec:ref-bgpaint}
+% \changes{v1.3-3}{2013/09/17}
+%	{Add the sub-section ``Commands for Background Painting.}
+% 
+% \begin{description}
+% \item[\Midx{\!\backgroundcolor!}\marg{region}\oarg{mode}\marg{color}]
+%     \mbox{}\par
+% \Item[\Midx{\!\backgroundcolor!}

+%     \Arg{\meta{region}$|(|x_0|,|y_0|)|$}\oarg{mode}\marg{color}]
+%     \mbox{}\par
+% \Item[\Midx{\!\backgroundcolor!}

+%     \Arg{\meta{region}$|(|x_0|,|y_0|)||(|x_1|,|y_1|)|$}

+%     \oarg{mode}\marg{color}]
+%     \mbox{}\par
+% \changes{v1.3-3}{2013/09/17}
+%	{Add description of \cs{backgroundcolor}.}

+% 

+% The command declares that {\em\Uidx\bgpaint} of \meta{region} is performed
+% with \meta{color} or what it specifies by the combination of the optional
+% \meta{mode}.  The \meta{region} whose \bground{} is painted is one of the
+% following.
+% 

+% \begin{description}
+% \item[|c|\rm(\textit{olumn})] for all columns, or particular one if
+% \meta{region} is |c|\oarg{col} to specify its ordinal \meta{col}.
+% 
+% \item[|g|\rm(\textit{ap})] for all gaps between columns, or particular one
+% if \meta{region} is |g|\oarg{col} to specify the ordinal \meta{col} of the
+% column preceding the gap.
+% 
+% \item[|s|\rm(\textit{panning})] for \mctext{}s.
+% 
+% \item[|f|\rm(\textit{loat})] for \pwise{} floats.
+% 
+% \item[|n|\rm(\textit{ote})] for (\mgfnote{} or non-merged) \Scfnote{}s.
+% 
+% \item[|p|\rm(\textit{re/post})] for \Preenv{} and \postenv.
+% 
+% \item[|t|\rm(\textit{op})] for top margin.
+% 
+% \item[|b|\rm(\textit{ottom})] for bottom margin.
+% 
+% \item[|l|\rm(\textit{eft})] for left margin.
+% 
+% \item[|r|\rm(\textit{ight})] for right margin.
+% \end{description}
+% 

+% In addition, capitals of the keys above, i.e., |C|, |G|, \ldots, |L|, are
+% also legitimate for {\em under painting}.  For example, you may specify to
+% paint the \bground{} of a region, say top margin, by two
+% \!\backgroundcolor! with |t| and |T| and with different color arranging the
+% size of the region of either |t| or |T| (or both of them) by the
+% \emph{\bgext} option shown below.
+% 
+% The optional $|(|x_0|,|y_0|)|$ is to enlarge the region to be painted
+% shifting its left-top and right-bottom corner outside by
+% the dimension $x_0$ horizontally and $y_0$ vertically, or to shrink it
+% with negative dimensions.  This {\em\Uidx\bgext} can be asymmetric giving
+% another optional $|(|x_1|,|y_1|)|$ so that it acts on the right-bottom
+% corner while let $|(|x_0|,|y_0|)|$ shift only the left-top corner.
+% Moreover, you may make each \bgext{} {\em infinite} by giving 10000\,|pt|
+% (about 3.5\,m) to $x_0$, $y_0$, $x_1$ and/or $y_1$ so that the
+% corresponding region edge is shifted to the paper edge.  Furthermore, this
+% {\em\Uidx\bginfext{}} can be terminated at the point $\alpha$ inside the
+% corresponding paper edge by giving $10000\,|pt|-\alpha$
+% ($\alpha\leq1000\,|pt|$) to an extension parameter $x_0$, etc.
+% 

+% \begin{itemize}
+% \item
+% A region whose color is not specified is not painted and thus left blank
+% (or kept as painted by \!\pagecolor! if you specify it).
+% 
+% \item
+% Under-painting of columns and gaps by |C| and |G| is made for regions
+% different from those over-painting |c| and |g|.  That is, under-painting
+% is done ignoring all \pwstuff{} and thus the height of the regions is
+% always $\!\textheight!+\!\maxdepth!$.  On the other hand, over-painting is
+% only for chunks shrunk or separated by \pwstuff.
+% 
+% \item
+% You may exploit the following painting order, where $x_i$
+% is the $i$-th \mctext{} ($x\in\{|s|,|S|\}$) or $i$-th chunk followed by
+% the $i$-th \mctext, $m$ and $n$ is the number of \mctext{}s and columns in
+% a page respectively, to overlay a preceding region with a succeeding
+% region, if your \emph{printer} allows overlaid color painting.
+% 

+% \begin{eqnarray*}
+% |T|&\to&|B|\to|L|\to|R|
+%     \to|G[|0|]|\to\cdots\to|G[|n{-}1|]|\to|C[|0|]|\to\cdots\to|C[|n{-}1|]|\\
+% &\to&|t|\to|b|\to|l|\to|r|\to|N|\to|n|\to\{|F|,|P|\}\to\{|f|,|p|\}
+%  \to|S|_1\to\cdots\to|S|_m\\
+% &\to&|g|_1|[|0|]|\to\cdots|g|_1|[|n{-}2|]|\to
+%      |c|_1|[|0|]|\to\cdots|c|_1|[|n{-}1|]|\to|s|_1\\
+% &\to&\cdots\\
+% &\to&|g|_m|[|0|]|\to\cdots|g|_m|[|n{-}2|]|\to
+%      |c|_m|[|0|]|\to\cdots|c|_m|[|n{-}1|]|\to|s|_m\\
+% &\to&|g|_{m+1}|[|0|]|\to\cdots|g|_{m+1}|[|n{-}2|]|\to
+%      |c|_{m+1}|[|0|]|\to\cdots|c|_m|[|n{-}1|]|
+% \end{eqnarray*}
+% 
+% \item
+% If you specify |b| feature by \!\twosided!, \bgpaint{} is
+% {\em\Uidx\mirror{}ed} in even-numbered pages so that |l| and |L| mean
+% right margin, |r| and |R| mean left margin, and asymmetric extensions are
+% applied to right-top and left-bottom corners.
+% 
+% \item
+% To give a color for \bgpaint{} correctly, you need to load \textsf{color}
+% package or its relative (e.g., \textsf{xcolor}) which the implementation
+% of coloring in \textsf{paracol} relies on.
+% 
+% \item
+% To paint margins and regions having infinite extension correctly, the
+% parameters \!\paperwidth! and \!\paperheight! should be set properly by,
+% for example, a paper selection option of \!\documentclass!.
+% 
+% \item
+% Section~\ref{sec:bgpaint} shows examples of \bgpaint{} to give you more
+% intutive explanations of \!\backgroundcolor! and its region specifications.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\nobackgroundcolor!}\marg{region}]\mbox{}
+% \Item[\Midx{\!\resetbackgroundcolor!}]\mbox{}\par
+% \changes{v1.3-3}{2013/09/17}
+%	{Add description of \cs{nobackgroundcolor} and
+%	 \cs{resetbackgroundcolor}.}

+% 

+% The command \!\nobackgroundcolor! declares that the \bground{} of
+% \meta{region} is not painted, where \meta{region} is one of legitimate
+% region specifiers of \!\backgroundcolor!.  The command
+% \!\resetbackgroundcolor! declares no regions are painted and thus gives
+% you the default state.
+% 

+% \begin{itemize}
+% \item
+% If you specified the \bgpaint{} of |c|\oarg{col} or |g|\oarg{col} by
+% \!\backgroundcolor!, the painting is \emph{not} canceled by
+% \!\nobackgroundcolor! with |c| or |g| but without \oarg{col}.  Similarly,
+% once you made declarations of \bgpaint{} of both |c| and |c|\oarg{col}
+% (resp.\ |g| and |g|\oarg{col}), \!\nobackgroundcolor! with |c|\oarg{col}
+% (resp.\ |g|\oarg{col}) cancels the painting of |c|\oarg{col} (resp.\
+% |g|\oarg{col}) but the region will still be painted by the color you gave
+% to |c| (resp.\ |g|).
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\pagerim!}]\mbox{}\par
+% \changes{v1.3-3}{2013/09/17}
+%	{Add description of \cs{pagerim}.}

+% 

+% This is a (kind of) \emph{length command}\footnote{

+% 

+% In reality, it is a \cs{dimen} register rather than a \cs{skip} register.}
+% 

+% to have the width of the \emph{rim} area placed at each paper edge to 
+% inhibit \bgpaint{} in the area.  That is, the inner edges of the area are
+% considered as virtual paper edges to block painting of all margins and
+% regions having \bginfext{} to the edges, for example in order to
+% avoid printing troubles caused by painting the rim area too close to the
+% real paper edges.  The default value of \!\pagerim! is 0 to allow paint
+% anywhere in a paper.
+% \end{description}
+% 
+% 
+% 
+% \subsection{Control of Contents Output}
+% \label{sec:ref-contents}
+% 
+% \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}
+% \item
+% For example, this manual has \!\addcontentsonly!|{toc}{0}| to
+% inhibit the contents information output from \!\subsection! commands
+% in the right column in Section~\ref{sec:env} and~\ref{sec:float},
+% or the table should have duplicated entries of sub-sections.
+% 
+% \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}
+% \label{sec:ref-flush}
+% 
+% \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 \cwise{} ones creating \fcolumn{}s for them, and
+% then for \pwise{} ones creating {\em\Uidx\fpage{}s} only with
+% \pwise{} floats, as \LaTeX's \!\clearpage! does outside \env{paracol}
+% environment.
+% 
+% \item[\Midx{\!\cleardoublepage!}]\mbox{}\par
+% \changes{v1.3-5}{2013/09/17}
+%	{Add description of \cs{cleardoublepage}.}
+% The command does what \LaTeX's \!\cleardoublepage! does outside
+% \env{paracol}.  That is, it does \!\clearpage! always and then leaves a
+% blank page if it is even-numbered and two-sided |p|(age) feature is
+% enabled by |twoside| option of \!\documentclass! or \Paracol's own
+% \!\twosided! command shown in Section~\ref{sec:ref-twoside}.
+% 

+% \begin{itemize}
+% \item
+% This command is equivalent to \!\clearpage! in \env{paracol} environments
+% for \npaired{} \parapag{}ing because \!\clearpage! flushes \emph{both}
+% left and right \parapag{}es.
+% \end{itemize}
+% \end{description}
+\endinput