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LaTeX Document
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1992-10-11
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% \iffalse meta-comment
% Copyright (C) 1989-1992 by Frank Mittelbach. All rights reserved.
% This file is part of the array package.
% IMPORTANT NOTICE:
% You are not allowed to change this file. You may however copy
% this file to a file with a different name and then change the copy
% if you obey the restrictions on file changes described in
% readme.mz.
% You are NOT ALLOWED to distribute this file alone. You are NOT
% ALLOWED to take money for the distribution or use of this file (or
% a changed version) except for a nominal charge for copying etc.
% You are allowed to distribute this file under the condition that
% it is distributed together with all files mentioned in readme.mz5.
% If you receive only some of these files from someone, complain!
% However, if these files are distributed by established suppliers
% as part of a complete TeX distribution, and the structure of the
% distribution would make it difficult to distribute the whole set
% of files, *those parties* are allowed to distribute only some of
% the files provided that it is made clear that the user will get a
% complete distribution-set upon request to that supplier (not me).
% Notice that this permission is not granted to the end user.
% For error reports in case of UNCHANGED versions see readme.mz
% \fi
\def\fileversion{v2.1b}
\def\filedate{92/07/06}
\def\docdate {92/09/12}
%% \CheckSum{1070}
%% \CharacterTable
%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%% Digits \0\1\2\3\4\5\6\7\8\9
%% Exclamation \! Double quote \" Hash (number) \#
%% Dollar \$ Percent \% Ampersand \&
%% Acute accent \' Left paren \( Right paren \)
%% Asterisk \* Plus \+ Comma \,
%% Minus \- Point \. Solidus \/
%% Colon \: Semicolon \; Less than \<
%% Equals \= Greater than \> Question mark \?
%% Commercial at \@ Left bracket \[ Backslash \\
%% Right bracket \] Circumflex \^ Underscore \_
%% Grave accent \` Left brace \{ Vertical bar \|
%% Right brace \} Tilde \~}
%\iffalse % this is a METACOMMENT !
%% Style-option `array' to use with LaTeX v2.09
%% Copyright (C) 1989-1992 Frank Mittelbach, all rights reserved.
% \fi
% \changes{v1.0b}{87/06/04}{`@classi (faster),
% `@classvi (new) A in preamble means
% \&\& in `halign.}
% \changes{v1.1a}{87/07/05}{New concept:
% preamblechar: c,l,r,C,L,R,A,p,t,|,@,!!}
% \changes{v1.1b}{87/09/21}{Again p like original \LaTeX{} and z for
% centered `parbox.}
% \changes{v1.2a}{87/09/27}{Completely new implementation.}
% \changes{v1.2b}{87/10/06}{!| does no longer generate space at start
% or end of the preamble. Otherwise `hline is
% too long.}
% \changes{v1.2b}{87/10/06}{Enlarged `@arstrutbox by 1pt (Test-Impl)
% with dimen `@strutheight.}
% \changes{v1.2c}{87/10/22}{New dimen parameter `extrarowheight
% (default: 0pt).}
% \changes{v1.2c}{87/10/22}{Enlarged `@arstrutbox by `extrarowheight.
% Thus you may avoid large characters to
% overprint a `hline.}
% \changes{v1.2c}{87/10/22}{Introduced `m@th in `@array to allow
% non-zero values of `mathsurround.}
% \changes{v1.2d}{87/11/02}{Completed the documentation.}
% \changes{v1.2e}{87/11/03}{Bug fixed: A at start of preamble resulted
% in an error since `@mkpream generated
% `@arstrut \& ... as a preamble.}
% \changes{v1.2f}{87/11/09}{`@testpach documented.}
% \changes{v1.3a}{87/11/11}{Again a new implementation, with a new
% concept (cf. the documentation).}
% \changes{v1.3b}{88/03/17}{`@decl expands now into `@empty, i.e. it
% disappears when the preamble is generated,
% except when the user specifies A{} or
% B{}.}
% \changes{v1.4a}{88/03/18}{Test implementation of use of token
% registers in order to do without `protect.}
% \changes{v1.4b}{88/03/19}{Changed erroneous class numbers:
% 5 -!> 6
% 6 -!> 7
% 7 -!> 5
% Corresponding changes in the macros.}
% \changes{v1.4c}{88/03/19}{Everything except p,z now works with token
% registers.}
% \changes{v1.9a}{88/03/20}{Last (so I hope) major change: 1) Options
% B,A now called !>,<. These options now point
% to the column they modify.}
% \changes{v1.9a}{88/03/20}{2) `protect is no longer necessary. But
% still the macro `@expast needs top be
% modified. `multicolumn still does not work.}
% \changes{v1.9b}{88/04/29}{inserted missing `fi in `@testpach.
% Corrected \LaTeX bug in `@tfor.}
% \changes{v1.9c}{88/05/07}{Re-introduced `@endpbox.
% `multicolumn now works! Version number still
% 1.9 since the documentation is still not
% finished.}
% \changes{v1.9c}{88/05/07}{1) `def `the@toks {`the ...} remaining only
% in `@mkpream. 2) Removed `@classiii and
% replaced by `save@decl.}
% \changes{v1.9c}{88/05/07}{3) `insert@column contains only `@tempcnta
% and `count@ counters. 4) `@@startpbox and
% `@@endpbox now totally obsolete.}
% \changes{v1.9d}{88/05/10}{Replaced `number by `the where the `toks
% registers' contents are used.}
% \changes{v1.9e}{88/05/11}{Re-introduced `@xargarraycr and
% `@yargarraycr, since `endtemplate seems to
% be `outer.}
% \changes{v1.9f}{88/05/20}{Small changes finally carried out:
% 1) `par!=`@empty.
% 2) {..ifnum0!=!`}... $\to$ `bgroup and
% analoguously `egroup.}
% \changes{v1.9g}{88/02/24}{Inserted again {..ifnum0!=!`}..,
% c.f. Appendix D of the \protect\TeX{}book.}
% \changes{v1.9h}{88/06/28}{No longer necessary to read in the file
% twice.}
% \changes{v1.9i}{88/06/28}{Corrected typo in german version.}
% \changes{v1.9j}{88/11/23}{In a `r' column an extra `kern`z@ is
% needed.}
% \changes{v1.9j}{88/11/23}{Otherwise the `hfil on the left side
% will be removed by the `unskip in
% `insert@column if the entry is empty.}
% \changes{v1.9k}{88/06/28}{Corrected typo in german version.}
% \changes{v1.9k}{89/01/16}{`begin{Macro} changed to `begin{macro} in
% documentation.}
% \changes{v2.0a}{89/05/12}{{\tt\protect\bslash @thetoks} changed to
% {\tt\protect\bslash the@toks}.}
% \changes{v2.0a}{89/05/12}{source changed to reflect new doc.sty
% conventions.}
% \changes{v2.0a}{89/05/12}{t option renamed to p to be compatible to
% the original.}
% \changes{v2.0a}{89/05/12}{File renamed from arraye.sty to array.sty.}
% \changes{v2.0b}{89/05/17}{Three forgotten end macro added.}
% \changes{v2.0b}{89/05/17}{All lines shortened to 72 or less.}
% \DoNotIndex{\@depth,\@ehc,\@fortmp,\@height,\@ifnextchar,\@ifstar}
% \DoNotIndex{\@ifundefined,\@latexerr,\@ne,\@nil,\@tempa,\@tempb}
% \DoNotIndex{\@tempcnta,\@tempd,\@tempdima,\@whilenum,\@width,\\}
% \DoNotIndex{\@tforloop}
% \DoNotIndex{\advance}
% \DoNotIndex{\baselineskip,\begingroup,\bgroup}
% \DoNotIndex{\cr,\crcr,\csname}
% \DoNotIndex{\def,\do,\docdate,\dp}
% \DoNotIndex{\edef,\egroup,\else,\endcsname,\endinput,\expandafter}
% \DoNotIndex{\fi,\filedate,\fileversion}
% \DoNotIndex{\gdef}
% \DoNotIndex{\hbox,\hfil,\hsize,\hskip,\ht}
% \DoNotIndex{\if,\ifcase,\ifdim,\ifnum,\ifx,\ignorespaces}
% \DoNotIndex{\kern}
% \DoNotIndex{\leavevmode,\let,\lineskip}
% \DoNotIndex{\m@ne,\multispan}
% \DoNotIndex{\newcount,\newdimen,\noalign}
% \DoNotIndex{\or}
% \DoNotIndex{\relax}
% \DoNotIndex{\setbox,\space,\strutbox}
% \DoNotIndex{\tabskip,\thr@@,\the,\toks,\toks@,\tw@,\typeout}
% \DoNotIndex{\unhcopy,\unskip}
% \DoNotIndex{\vbox,\vcenter,\vline,\vrule,\vtop,\vskip}
% \DoNotIndex{\xdef}
% \DoNotIndex{\z@}
% \title{A new implementation of \LaTeX's {\sf tabular}
% and {\sf array} environment\thanks{This file
% has version number \fileversion, last
% revised \filedate, documentation dated \docdate.}}
% \author{Frank Mittelbach
% \and
% David Carlisle\thanks{David kindly agreed on the inclusion
% of the {\tt\string\newcolumntype} implementation, formerly in
% {\tt newarray.sty} into this style option}}
% \date{Printed \today}
% \maketitle
% \MakeShortVerb{\=}
% \begin{abstract}
% This article describes a new implementation of the \LaTeX\
% {\sf array}-- and {\sf tabular}--environments. The special merits of
% this
% implementation are further options to format columns and the fact
% that fragile \LaTeX--commands don't have to be =\protect='ed any
% more within those environments.
% At the same time it shows a new --- and in our opinion sensible ---
% way of documenting \TeX\--macros: This article \underline{is the
% style--file} that is to be used. All we need in addition to it is a
% short \TeX--program which visualizes the comments and puts the
% definitions in verbatim mode.
% \end{abstract}
% \section{Introduction}
% This new implementation of the {\sf array}-- and {\sf
% tabular}--environments is part of a larger project in which we are
% trying to improve the \LaTeX\--code in some aspects and to make
% \LaTeX\ even easier to handle.
% The reader should be familiar with the general structure of the
% environments
% mentioned above. Further information can be found in {\sc Lamport}
% \cite{bk:lamport}. The additional options which can be used in the
% preamble as well as those which now have a slightly different meaning
% are described in table~\ref{tab:opt}.
% \DescribeMacro\extrarowheight
% Additionally we introduce a new
% parameter called =\extrarowheight=. If it takes a positive
% length, the value of the parameter is added to the normal height of
% every row of the table, while
% the depth will remain the same. This is important for tables
% with horizontal lines because those lines normally touch the
% capital letters.
% For example, we used =\setlength{\extrarowheight}{1pt}=
% in table~\ref{tab:opt}.
% \begin{table}[t]
% \begin{center}
% \setlength{\extrarowheight}{1pt}
% \begin{tabular}{|>{\tt}c|m{9cm}|}
% \hline
% \multicolumn{2}{|c|}{Unchanged options}\\
% \hline
% l & Left adjusted column. \\
% c & Centered adjusted column. \\
% r & Right adjusted column. \\
% p\{width\} & Equivalent to =\parbox[t]{width}=. \\
% @\{decl.\} & Suppresses inter-column space and inserts
% {\tt decl.}\ instead. \\
% \hline
% \multicolumn{2}{|c|}{New options}\\
% \hline
% m\{width\} & Defines a column of width {\tt width}.
% Every entry will be centered in proportion to
% the rest of the line. It is somewhat like
% =\parbox{width}=. \\
% \hline
% b\{width\} & Coincides with =\parbox[b]{width}=. \\
% \hline
% >\{decl.\} & Can be used before an {\tt l}, {\tt r},
% {\tt c}, {\tt p}, {\tt m} or a {\tt b}
% option. It inserts
% {\tt decl.}\ directly in front of the entry of
% the column. \\
% \hline
% <\{decl.\} & Can be used after an {\tt l}, {\tt r},
% {\tt c}, =p{..}=, =m{..}= or a
% =b{..}= option.
% It inserts {\tt decl.}\ right after the entry
% of the column. \\
% \hline
% | & Inserts a vertical line. The distance between
% two columns will be enlarged by the width of
% the line
% in contrast to the original definition of
% \LaTeX. \\
% \hline
% !\{decl.\} & Can be used anywhere and corresponds with the
% {\tt |} option. The difference is that
% {\tt decl.} is inserted instead of a vertical
% line, so this option doesn't suppress the
% normally inserted space between columns in
% contrast to =@{...}=.\\
% \hline
% \end{tabular}
% \end{center}
% \caption{The preamble options.} \label{tab:opt}
% \end{table}
% We will discuss a few examples using the new preamble options before
% dealing with the implementation.
% \begin{itemize}
% \item
% If you want to use a special font (for example =\bf=) in a
% flushed left column, this can be done with =>{\bf}l=. You
% do not have to begin every entry of the column with =\bf=
% any more.
% \item
% In columns which have been generated with {\tt p}, {\tt m}
% or {\tt b}, the default value of =\parindent= is
% {\sf 0pt}.
% This can be changed with \\
% =>{\setlength{\parindent}{1cm}}p=.
% \item
% The {\tt <}--option was originally developed for the following
% application:
% =>{$}c<{$}= generates a column in math mode in a
% {\sf tabular}--environment. If you use this type of a preamble
% in an
% {\sf array}--environment, you get a column in LR mode because
% the additional \$'s cancel the existing \$'s.
% \item
% One can also think of more complex applications. A problem
% which has
% been mentioned several times in \TeX{}hax can be solved with
% =>{\centerdots}c=\linebreak[0]=<{\endcenterdots}=.
% To center decimals at their
% decimal points you (only?) have to define the following macros:
% \begin{verbatim}
%{\catcode`\.\active\gdef.{\egroup\setbox2\hbox\bgroup}}
%\def\centerdots{\catcode`\.\active\setbox0\hbox\bgroup}
%\def\endcenterdots{\egroup\ifvoid2 \setbox2\hbox{0}\fi
% \ifdim \wd0>\wd2 \setbox2\hbox to\wd0{\unhbox2\hfill}\else
% \setbox0\hbox to\wd2{\hfill\unhbox0}\fi
% \catcode`\.12 \box0.\box2}
%\end{verbatim}
% Warning: The code is bad, it doesn't work with more than one
% dot in a cell and doesn't work when the tabular is used in the
% argument of some other command. A much better version is
% provided in the {\tt dcolumn.sty} by David Carlisle.
% \item
% Using =c!{\hspace{1cm}}c= you get space between two
% columns which is enlarged by one centimeter, while
% =c@{\hspace{1cm}}c= gives you exactly one centimeter
% space between two columns.
% \end{itemize}
% \subsection{Defining new column specifiers}
% \DeleteShortVerb{\=}
% \MakeShortVerb{\"}
% \DescribeMacro{\newcolumntype}
% Whilst it is handy to be able to type
% \begin{quote}
% ">{"\meta{some declarations}"}{c}<{"\meta{some more
% declarations}"}"
% \end{quote}
% if you have a one-off column in a table, it is rather inconvenient
% if you often use columns of this form. The new version allows you
% to define a new column specifier, say {\tt x}, which will expand to
% the primitives column specifiers.\footnote{This command was named
% {\tt\string\newcolumn} in the {\tt newarray.sty} option. At the
% moment {\tt\string\newcolumn} is still supported (but gives a
% warning). In later releases it will vanish.} Thus we
% may define
% \begin{quote}
% "\newcolumntype{x}{>{"\meta{some declarations}"}{c}<{"\meta{some
% more declarations}"}}"
% \end{quote}
% One can then use the {\tt x} column specifier in the preamble
% arguments of all {\tt array} or {\tt tabular} environments in which
% you want columns of this form.
% It is common to need math-mode and LR-mode columns in the same
% alignment. If we define:
% \begin{quote}
% "\newcolumntype{C}{>{$}c<{$}}" \\
% "\newcolumntype{L}{>{$}l<{$}}" \\
% "\newcolumntype{R}{>{$}r<{$}}"
% \end{quote}
% Then we can use {\tt C} to get centred LR-mode in an {\tt array}, or
% centred math-mode in a {\tt tabular}.
% The example given above for `centred decimal points' could be
% assigned to a {\tt d} specifier with the following command.
% \begin{quote}
% "\newcolumntype{d}{>{\centerdots}c<{\endcenterdots}}"
% \end{quote}
% The above solution always centres the dot in the
% column. This does not look too good if the column consists of large
% numbers, but to only a few decimal places. An alternative definition
% of a {\tt d} column is
% \begin{quote}
% "\newcolumntype{d}[1]{>{\rightdots{#1}}r<{\endrightdots}}"
% \end{quote}
% where the appropriate macros in this case are:\footnote{The style {\tt
% dcolumn.sty} contains more robust macros based on these ideas.}
% \begin{verbatim}
% \def\coldot{.}% Or if you prefer, \def\coldot{\cdot}
% {\catcode`\.=\active
% \gdef.{$\egroup\setbox2=\hbox to \dimen0 \bgroup$\coldot}}
% \def\rightdots#1{%
% \setbox0=\hbox{$1$}\dimen0=#1\wd0
% \setbox0=\hbox{$\coldot$}\advance\dimen0 \wd0
% \setbox2=\hbox to \dimen0 {}%
% \setbox0=\hbox\bgroup\mathcode`\.="8000 $}
% \def\endrightdots{$\hfil\egroup\box0\box2}
%\end{verbatim}
% Note that "\newcolumntype" takes the same optional argument as
% "\newcommand" which declares the number of arguments of the column
% specifier being defined. Now we can specify "d{2}" in our preamble
% for a column of figures to at most two decimal places.
% A rather different use of the "\newcolumntype" system takes
% advantage of the fact that the replacement text in the
% "\newcolumntype" command may refer to more than one column. Suppose
% that a document contains a lot of {\tt tabular} environments that
% require the same preamble, but you wish to experiment with different
% preambles. Lamport's original definition allowed you to do the
% following (although it was probably a mis-use of the system).
% \begin{quote}
% "\newcommand{\X}{clr}"\\
% "\begin{tabular}{\X}" \ldots
% \end{quote}
% {\tt array.sty} takes great care {\bf not} to expand the preamble, and
% so the above does not work with the new scheme. With the new version
% this functionality is returned:
% \begin{quote}
% "\newcolumntype{X}{clr}"\\
% "\begin{tabular}{X}" \ldots
% \end{quote}
% The replacement text in a "\newcolumntype" command may refer to any of
% the primitives of {\tt array.sty} see table \ref{tab:opt} on page
% \pageref{tab:opt}, or to any new letters defined in other
% "\newcolumntype" commands.
% \DescribeMacro{\showcols}A list of all the currently active
% "\newcolumntype" definitions is sent to the terminal and log file if
% the "\showcols" command is given.
% \section{Final Comments}
% \subsection{Comparisons with older versions of {\tt array.sty}}
% There are some differences in the way version 2.1 treat incorrect
% input, even if the source file does not appear to use any of the
% extra features of the new version.
% \begin{itemize}
% \item A preamble of the form "{wx*{0}{abc}yz}" was treated by
% versions prior to 2.1 as "{wx}". Version 2.1 treats it as "{wxyz}"
% \item An incorrect positional argument such as {\tt [Q]} is treated as
% {\tt [c]} by {\tt array.sty}, but is now treated as {\tt [t]}.
% \item A preamble such as "{cc*{2}}" with an error in a
% $*$-form will generate different errors in the new version. In both
% cases the error message is not particularly helpful to the casual
% user.
% \item Repeated {\tt <} or {\tt >} constructions did generate an error
% in earlier versions, but are new allowed in this style.
% ">{"\meta{decs1}"}>{"\meta{decs2}"}" is treated
% the same as ">{"\meta{decs2}\meta{decs1}"}".
% \item The "\extracolsep" command does not work with the old versions
% of {\tt array.sty},
% see the comments in {\tt array.bug}. With version 2.1
% "\extracolsep" may again be used in {\tt@}-expressions as in standard
% \LaTeX, and also in {\tt!}-expressions (but see the note below).
% \end{itemize}
% \subsection{Bugs and Features}
% \begin{itemize}
% \item Error messages generated when parsing the column specification
% refer to the preamble argument {\bf after} it has been re-written
% by the "\newcolumntype" system, not to the preamble entered by the
% user. This seems inevitable with any system based on
% pre-processing and so is classed as a {\bf feature}.
% \item The treatment of multiple {\tt<} or {\tt>} declarations may
% seem strange at first. Earlier implementations treated
% ">{"\meta{decs1}"}>{"\meta{decs2}"}" the same as
% ">{"\meta{decs1}\meta{decs2}"}". However this did not give the
% user the opportunity of overriding the settings of a
% "\newcolumntype" defined using these declarations. For example,
% suppose in an {\tt array} environment we use a {\tt C} column
% defined as above. The {\tt C} specifies a centred text column,
% however ">{\bf}C", which re-writes to ">{\bf}>{$}c<{$}" would not
% specify a bold column as might be expected, as the preamble would
% essentially expand to "\hfil$\bf$#$ $\hfil" and so the column
% entry would not be in the scope of the "\bf"\,! The present
% version switches the order of repeated declarations, and so the
% above example now produces a preamble of the form "\hfil$"
% "$\bf#$" "$\hfil", and the dollars cancel each other out without
% limiting the scope of the "\bf".
% \item The use of "\extracolsep" has been subject to the following
% two restrictions. There must be at most one "\extracolsep"
% command per "@", or "!" expression and the command must be
% directly entered into the "@" expression, not as part of a macro
% definition. Thus "\newcommand{\ef}{\extracolsep{\fill}}" \ldots
% "@{\ef}" does not work with this style. However you can use
% something like
% "\newcolumntype{e}{@{\extracolsep{\fill}}" instead.
% \end{itemize}
% \typeout{^^JEnd of the Introduction and Examples.}
% \typein[\answer]%
% {Do you want an annotated listing of the macro definitions (y/n) ?}
% \def\next{y}\ifx\answer\next\else\OnlyDescription\fi
% \StopEventually{
% \begin{thebibliography}{1}
% \bibitem{bk:knuth} {\sc D. E. Knuth}.
% \newblock The \TeX{}book (Computers \& Typesetting Volume A).
% \newblock
% Addison-Wesley, Reading, Massachusetts, 1986.
% \bibitem{cd:knuth} {\sc D. E. Knuth}.
% \newblock
% The \TeX{}program (Computers \& Typesetting Volume B).
% \newblock
% Addison-Wesley, Reading, Massachusetts, 1986.
% \bibitem{bk:lamport} {\sc L. Lamport}.
% \newblock
% \LaTeX\ -- A Document Preparation System.
% \newblock
% Addison-Wesley, Reading, Massachusetts, 1986.
% \bibitem{cd:lamport} {\sc L. Lamport}.
% \newblock
% {\tt latex.tex}, Version 2.09 of $\left\langle
% \mbox{15. Sept. 87}
% \right\rangle $.
% \end{thebibliography}
% } ^^A end of \StopEventually
% \section{The construction of the preamble}
% \DeleteShortVerb{\"}
% \MakeShortVerb{\=}
% It is obvious that those environments will consist mainly of an
% =\halign=, because \TeX\ typesets tables using this primitive.
% That is why we will now take a look at the algorithm which determines
% a preamble for a =\halign= starting with a given user preamble
% using the options mentioned above.
% First we will define the current version of this file:
% \begin{macrocode}
%<*style>
\@ifundefined{d@llarbegin}{}{\endinput}
\typeout{Style-Option: `array' \fileversion
\space\space <\filedate> (F.M.)}
\typeout{English documentation dated \space <\docdate> (F.M.)}
% \end{macrocode}
% The most interesting macros of this implementation are without doubt
% those
% which are responsible for the construction of the preamble
% for the =\halign=. The underlying algorithm was developed by
% {\sc Lamport} (resp.\ {\sc Knuth}, see texhax V87\#??), and it has
% been
% extended and improved.
% The user preamble will be read {\sf token} by {\sf token}.
% A {\sf token} is a single character like {\tt c} or a block enclosed
% ={...}=. For example the preamble of
% =\begin{tabular}=\linebreak[0]={lc||c@{\hspace{1cm}}}=
% consists of the {\sf token}
% {\tt l}, {\tt c}, {\tt |}, {\tt |}, {\tt @} and =\hspace{1cm}=.
% The currently used {\sf token} and the one, used before, are needed
% to decide on how the construction of the preamble has to be
% continued.
% In the example mentioned above the {\tt l} causes the preamble
% to begin with =\hskip\tabcolsep=. Furthermore
% =# \hfil= would be appended to define a flush left column.
% The next {\sf token} is a {\tt c}. Because it was preceded by an
% {\tt l} it generates a new column. This is done with
% =\hskip \tabcolsep & \hskip \tabcolsep=. The column which is to
% be centered will be appended with =\hfil # \hfil=.
% The {\sf token} {\tt |} would then add a space of
% =\hskip \tabcolsep=
% and a vertical line because the last
% {\sf tokens} was a {\tt c}.
% The following {\sf token} {\tt |} would only add a space
% =\hskip \doublerulesep= because it was preceded by the
% {\sf token} {\tt |}. We will not discuss our example further but
% rather take a look at the general case of constructing preambles.
% The example shows that the desired preamble for the
% =\halign= can be constructed as soon as the action of all
% combinations
% of the preamble {\sf tokens} are specified. There are 18 such
% {\sf tokens}
% so we have $19 \cdot 18 \string= 342$ combinations if we count the
% beginning of
% the preamble as a special {\sf token}. Fortunately, there are many
% combinations which generate the same spaces, so we can define
% {\sf token} classes. We will identify a
% {\sf token} within a class with a number, so we can insert the
% formatting (for example of a column).
% Table~\ref{tab:Klassen} lists all {\sf token} classes and
% their corresponding numbers.
% \begin{table}[ht]
% \begin{center}
% \begin{tabular}[t]{>{\tt}ccc}
% {\sf token} & =\@chclass= & =\@chnum= \\[2mm]
% c & 0 & 0 \\
% l & 0 & 1 \\
% r & 0 & 2 \\
% p-arg & 0 & 3 \\
% t-arg & 0 & 4 \\
% b-arg & 0 & 5 \\
% | & 1 & 0 \\
% !-arg & 1 & 1 \\
% <-arg & 2 & --- \\
% >-arg & 3 & ---
% \end{tabular}
% \kern3mm \vrule \kern3mm%
% \begin{tabular}[t]{>{\tt}ccc}
% {\sf token} & =\@chclass= & =\@chnum= \\[2mm]
% Start & 4 & --- \\
% @-arg & 5 & --- \\
% ! & 6 & --- \\
% @ & 7 & --- \\
% < & 8 & --- \\
% > & 9 & --- \\
% p & 10 & 3 \\
% t & 10 & 4 \\
% b & 10 & 5
% \end{tabular}
% \end{center}
% \caption{Classes of preamble {\sf tokens}}
% \label{tab:Klassen}
% \end{table}
% \begin{macro}{\@chclass}
% \begin{macro}{\@chnum}
% \begin{macro}{\@lastchclass}
% The class and the number of the current {\sf token} are saved in
% the
% {\sf count} registers =\@chclass=
% and =\@chnum=, while the class of the previous
% {\sf token} is stored in the
% {\sf count} register =\@lastchclass=.
% All of the mentioned registers are already allocated in
% {\tt latex.tex},
% which is the reason why the following three lines of code are
% commented out.
% Later throughout the text I will not mention it again explicitely
% whenever I use a =%= sign. These parts are already defined in
% {\tt latex.tex}.
% \begin{macrocode}
% \newcount \@chclass
% \newcount \@chnum
% \newcount \@lastchclass
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\@addtopreamble}
% We will save the already constructed preamble for
% the =\halign=
% in the global macro =\@preamble=. This will then be
% enlarged with
% the command =\@addtopreamble=.
% \begin{macrocode}
\def\@addtopreamble#1{\xdef\@preamble{\@preamble #1}}
% \end{macrocode}
% \end{macro}
% \subsection{The character class of a {\sf token}}
% \begin{macro}{\@testpach}
% \changes{v2.0a}{89/05/12}{p option renamed to m (middle).}
% \changes{v2.0a}{89/05/12}{t option renamed to p to be compatible to
% the original.}
% With the help of =\@lastchclass= we can now define a macro
% which determines the class and the number of a given preamble
% {\sf token}
% and assigns them to the registers
% =\@chclass= and =\@chnum=.
% \changes{v2.0f}{92/02/29}{Argument removed since implicitly known}
% \begin{macrocode}
\def\@testpach{\@chclass
% \end{macrocode}
% First we deal with the cases in which the {\sf token}
% (=#1=) is the argument of {\tt !}, {\tt @}, {\tt <} or
% {\tt >}. We can see this from the value of =\@lastchclass=:
% \begin{macrocode}
\ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
\ifnum \@lastchclass=7 5 \else
\ifnum \@lastchclass=8 \tw@ \else
\ifnum \@lastchclass=9 \thr@@
% \end{macrocode}
% Otherwise we will assume that the {\sf token} belongs to the
% class $0$
% and assign the corresponding number to =\@chnum= if our
% assumption is correct.
% \begin{macrocode}
\else \z@
% \end{macrocode}
% If the last {\sf token} was a {\tt p}, {\tt m} or a {\tt b},
% =\@chnum= already has the right value. This is the reason for
% the
% somewhat curious choice of the {\sf token} numbers in class $10$.
% \begin{macrocode}
\ifnum \@lastchclass = 10 \else
% \end{macrocode}
% Otherwise we will check if =\@nextchar= is either a {\tt c}, {\tt
% l} or an {\tt r}. Some applications change the catcodes of
% certain characters like ``{\tt@}'' in {\tt amstex.sty}. As a
% result the tests below would fail since they assume non-active
% character tokens. Therefore we evaluate =\@nextchar= once thereby
% turning the first token of its replacement text into a char. At
% this point here this should have been the only char present in
% =\@nextchar= which put into via a =\def=.
% \changes{v2.0f}{92/02/29}{Ensure to test a char which is not active}
% \begin{macrocode}
\edef\@nextchar{\expandafter\string\@nextchar}%
\@chnum
\if \@nextchar c\z@ \else
\if \@nextchar l\@ne \else
\if \@nextchar r\tw@ \else
% \end{macrocode}
% If it is a different {\sf token}, we know that the class was
% not $0$. We assign the
% value $0$ to =\@chnum= because this value is needed for the
% {\tt |}--{\sf token}. Now we must check the remaining classes.
% Note that the value of =\@chnum= is insignificant here for
% most classes.
% \begin{macrocode}
\z@ \@chclass
\if\@nextchar |\@ne \else
\if \@nextchar !6 \else
\if \@nextchar @7 \else
\if \@nextchar <8 \else
\if \@nextchar >9 \else
% \end{macrocode}
% The remaining permitted {\sf tokens} are {\tt p}, {\tt m} and
% {\tt b} (class $10$).
% \begin{macrocode}
\@chnum
\if \@nextchar m\thr@@\else
\if \@nextchar p4 \else
\if \@nextchar b5 \else
% \end{macrocode}
% Now the only remaining possibility is a forbidden {\sf token},
% so we choose class $0$ and number $0$ and give an error message.
% Then we finish the macro by closing all =\if='s.
% \begin{macrocode}
\z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
\fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi}
% \end{macrocode}
% \end{macro}
% \subsection{Multiple columns ($*$--form)}
% \begin{macro}{\@xexpast}
% \begin{macro}{\the@toks}
% \begin{macro}{\the@toksz}
% \label{@xexpast}
% Now we discuss the macro that deletes all forms of type
% =*{={\it N\/}=}{={\it String\/}=}= from a user
% preamble and replaces them with {\it N} copies of {\it String}.
% Nested $*$--expressions are dealt with correctly, that means
% $*$--expressions are not substituted if they are in explicit
% braces, as in =@{*}=.
% This macro is called via
% =\@xexpast=$\left\langle
% \it preamble
% \right\rangle$=*0x\@@=.
% The $*$--expression =*0x= is being used to terminate the
% recursion,
% as we shall see later, and =\@@= serves as an argument
% delimiter. =\@xexpast= has four arguments. The first
% one is the part of the
% user preamble before the first $*$--expression while the second
% and third ones are the arguments of the first $*$--expression
% (that is {\it N} and {\it String} in the notation mentioned
% above).
% The fourth argument is the rest of the preamble.
% \begin{macrocode}
\def\@xexpast#1*#2#3#4\@@{%
% \end{macrocode}
% The number of copies of {\it String} (=#2=) that are to be
% produced will be saved in a {\sf count} register.
% \begin{macrocode}
\@tempcnta #2
% \end{macrocode}
% We save the part of the preamble which does not
% contain a $*$--form (=#1=)
% in a \PlainTeX\ {\sf token} register.
% We also save {\it String} (=#3=) using a \LaTeX\
% {\sf token} register.
% \begin{macrocode}
\toks@={#1}\@temptokena={#3}%
% \end{macrocode}
% Now we have to use a little trick to produce {\it N} copies of
% {\it String}.
% We could try =\def\@tempa{#1}= and then
% {\it N} times =\edef\@tempa{\@tempa#3}=. This would have the
% undesired effect that all macros within =#1= and =#3=
% would be expanded, although, for example, constructions like
% =@{..}= are not supposed to be changed.
% That is why we =\let= two control sequences to
% be equivalent to =\relax=.
% \begin{macrocode}
\let\the@toksz\relax \let\the@toks\relax
% \end{macrocode}
% Then we ensure that =\@tempa= contains
% ={\the@toksz\the@toks...\the@toks}= (the macro
% =\the@toks= exactly {\it N\/} times) as substitution text.
% \begin{macrocode}
\def\@tempa{\the@toksz}%
\ifnum\@tempcnta >0 \@whilenum\@tempcnta >0\do
{\edef\@tempa{\@tempa\the@toks}\advance \@tempcnta \m@ne}%
% \end{macrocode}
% If {\it N\/} was greater than zero we prepare for another call of
% =\@xexpast=. Otherwise we assume we have reached the end of
% the user preamble, because we had appended
% =*0x\@@= when we first called
% =\@xexpast=.
% In other words: if the user inserts
% =*{0}{..}= in his preamble, \LaTeX\ ignores the rest of it.
% \begin{macrocode}
\let \@tempb \@xexpast \else
\let \@tempb \@xexnoop \fi
% \end{macrocode}
% Now we will make sure that the part of the user preamble, which
% was already dealt with, will be saved again in =\@tempa=.
% \begin{macrocode}
\def\the@toksz{\the\toks@}\def\the@toks{\the\@temptokena}%
\edef\@tempa{\@tempa}%
% \end{macrocode}
% We have now evaluated the first $*$--expression, and the user
% preamble up to this point
% is saved in =\@tempa=. We will put the contents of
% =\@tempa= and the rest of the user preamble together and work
% on the result with =\@tempb=. This macro either corresponds
% to =\@xexpast=, so that the next
% $*$--expression is handled, or to the macro =\@xexnoop=,
% which only ends the recursion by deleting its argument.
% \begin{macrocode}
\expandafter \@tempb \@tempa #4\@@}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\@xexnoop}
% So the first big problem is solved. Now it is easy to
% specify =\@xexnoop=.
% Its argument is delimited by =\@@= and it simply expands to
% nothing.
% \begin{macrocode}
% \def\@xexnoop#1\@@{}
% \end{macrocode}
% \end{macro}
% \section{The insertion of declarations
% ({\tt >}, {\tt <}, {\tt !}, {\tt @})}
% The preamble will be enlarged with the help of =\xdef=, but the
% arguments of {\tt >}, {\tt <},~{\tt !}\ and {\tt @} are not supposed
% to be expanded during the construction (we want an implementation
% that doesn't need a =\protect=). So we have to find a way to
% inhibit the expansion of those arguments.
% We will solve this problem with {\sf token} registers. We need one
% register for every {\tt !}\ and {\tt @}, while we need two for every
% {\tt c}, {\tt l}, {\tt r}, {\tt m}, {\tt p} or {\tt b}. This limits
% the number of columns of a table because there are only 256
% {\sf token} registers. But then, who needs tables with more
% than 100 columns?
% One could also find a solution which only needs two or three
% {\sf token} registers by proceeding similarly as in the macro
% =\@xexpast= (see page \pageref{@xexpast}). The advantage of our
% approach is the fact that we avoid some of the problems that arise
% with the other method\footnote{Maybe there are also historical
% reasons.}.
% So how do we proceed? Let us assume that we had =!{foo}= in the
% user preamble and say we saved {\tt foo} in
% {\sf token} register $5$. Then we call
% =\@addtopreamble{\the@toks5}= where
% =\the@toks= is defined in a way that it does not expand
% (for example it could be equivalent to =\relax=). Every
% following call
% of =\@addtopreamble= leaves =\the@toks5= unchanged in
% =\@preamble=. If the construction of the preamble is completed
% we change the definition of =\the@toks= to
% =\the\toks= and expand =\@preamble= for the last time.
% During this process all parts of the form
% =\the@toks=$\left\langle
% \it Number
% \right\rangle $
% will be substituted by the contents of the respective {\sf token}
% registers.
% As we can see from this informal discussion the construction of the
% preamble has to take place within a group, so that the
% {\sf token} registers we use will be freed later on. For that reason
% we keep all assignments to =\@preamble= global; therefore the
% replacement text of this macro will remain the same after we leave
% the group.
% \begin{macro}{\count@}
% We further need a {\sf count} register to remember which
% {\sf token} register is to be used next. This will be initialized
% with $-1$ if we want to begin with the
% {\sf token} register $0$. We use the
% \PlainTeX\ scratch register =\count@= because everything
% takes place locally. All we have to do is insert
% =\the@toks= =\the= =\count@= into the preamble.
% =\the@toks= will remain unchanged and
% =\the\count@= expands into the saved number.
% \end{macro}
% \begin{macro}{\prepnext@tok}
% The macro =\prepnext@tok= is in charge of preparing the next
% {\sf token} register. For that purpose we increase
% =\count@= by $1$:
% \begin{macrocode}
\def\prepnext@tok{\advance \count@ \@ne
% \end{macrocode}
% Then we locally delete any contents the
% {\sf token} register might have.
% \begin{macrocode}
\toks\count@{}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\save@decl}
% During the construction of the preamble the current {\sf token} is
% always saved in the macro =\@nextchar= (see the definition
% of =\@mkpream= on page \pageref{@mkpream}). The macro
% =\save@decl= saves it into the next free
% {\sf token} register, i.e.\ in =\toks\count@=.
% \changes{v2.0c}{90/08/14}{`relax removed and added elsewhere.}
% \begin{macrocode}
\def\save@decl{\toks\count@ \expandafter{\@nextchar}}
% \end{macrocode}
% The reason for the use of =\relax= is the following
% hypothetical situation in the preamble:
% \quad =..\the\toks1\the\toks2..= \quad \TeX\ expands
% =\the\toks2= first in order to find out if the digit =1=
% is followed by other digits. E.g.\ a =5= saved in the
% {\sf token} register $2$ would lead \TeX\ to insert the contents
% of {\sf token} register $15$ instead of $1$ later on.
% The example above referred to an older version of =\save@decl= which
% inserted a =\relex= inside the token register. This is now moved to
% the places where the actual token registers are inserted (look for
% =\the@toks=) because the old version would still make =@=
% expressions to moving arguments since after expanding the second
% register while looking for the end of the number the contents of the
% token register is added so that later on the whole register will be
% expanded. This serious bug was found after nearly two years
% international use of this style option by Johannes Braams.
% \end{macro}
% How does the situation look like, if we want to add another column
% to the preamble, i.e.\ if we have found a {\tt c}, {\tt l}, {\tt r},
% {\tt p}, {\tt m} or {\tt b} in the user preamble~?
% In this case we have the problem of the {\sf token} register from
% =>{..}= and =<{..}= having to be inserted at this moment
% because formating instructions like =\hfil= have to be set
% around them. On the other hand it is not known yet, if any
% =<{..}= instruction will appear in the user preamble at all.
% We solve this problem by adding two {\sf token} registers at a time.
% This explains, why we have freed the {\sf token} registers in
% =\prepnext@tok=.
% \begin{macro}{\insert@column}
% \begin{macro}{\@sharp}
% We now define the macro =\insert@column= which will do
% this work for us.
% \begin{macrocode}
\def\insert@column{%
% \end{macrocode}
% Here, we assume that the {\sf count} register
% =\@tempcnta= has saved the value $=\count@= - 1$.
% \begin{macrocode}
\the@toks \the \@tempcnta
% \end{macrocode}
% Next follows the =#= sign which specifies the place
% where the text of the column shall be inserted. To avoid
% errors during the expansions in
% =\@addtopreamble= we hide this sign in the command
% =\@sharp= which is temporarily occupied with
% =\relax= during the build-up of the preamble.
% To remove unwanted spaces before and after the column text, we set
% an =\ignorespaces= in front and a =\unskip= afterwards.
% \changes{v2.0e}{91/02/07}{Added {} around `@sharp for new ftsel}
% \changes{v2.0h}{92/06/22}{Removed {} again in favour of `d@llarbegin}
% \begin{macrocode}
\ignorespaces \@sharp \unskip
% \end{macrocode}
% Then the second {\sf token} register follows whose number should
% be saved in =\count@=.
% We make sure that there will be no further expansion after reading
% the number, by finishing with =\relax=. The case above is not
% critical since it is ended by =\ignorespaces=.
% \changes{v2.0c}{90/08/14}{`relax added to avoid problem
% `the`toks0`the`toks1.}
% \begin{macrocode}
\the@toks \the \count@ \relax}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \subsection{The separation of columns}
% \begin{macro}{\@addamp}
% In the preamble a =&= has to be inserted between any two
% columns; before the first column there
% should not be a =&=. As the user preamble may start with a
% {\tt |} we have to remember somehow if we have already inserted a
% =#= (i.e.\ a column). This is done with the boolean variable
% =\if@firstamp= that we test in =\@addamp=,
% the macro that inserts the =&=.
% \begin{macrocode}
% \newif \@iffirstamp
% \def\@addamp{\if@firstamp \@firstampfalse
% \else \@addtopreamble &\fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@acol}
% \begin{macro}{\@acolampacol}
% \begin{macro}{\col@sep}
% We will now define some abbreviations for the extensions,
% appearing most often in the preamble build-up.
% Here =\col@sep= is a {\sf dimen} register which is set
% equivalent to =\arraycolsep= in an {\sf array}--environment,
% otherwise it is set equivalent to =\tabcolsep=.
% \begin{macrocode}
\newdimen\col@sep
\def\@acol{\@addtopreamble{\hskip\col@sep}}
% \def\@acolampacol{\@acol\@addamp\@acol}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \subsection{The macro {\tt \protect\bslash @mkpream}}
% \begin{macro}{\@mkpream}
% \begin{macro}{\the@toks}
% \label{@mkpream}
% Now we can define the macro which builds up the preamble for the
% =\halign=.
% First we initialize =\@preamble=, =\@lastchclass=
% and the boolean variable =\if@firstamp=.
% \begin{macrocode}
\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
% \end{macrocode}
% During the build-up of the preamble we cannot directly use the
% =#= sign; this would lead to an error message in the next
% =\@addtopreamble= call.
% Instead, we use the command =\@sharp= at places where later
% a =#= will be.
% This command is at first given the meaning =\relax=;
% therefore it will not be expanded when the preamble
% is extended.
% In the macro =\@array=, shortly before the =\halign=
% is carried out, =\@sharp= is given its final meaning.
% In a similar way,
% we deal with the commands =\@startpbox= and
% =\@endpbox=, although the reason is different here: these
% macros expand in many {\sf tokens} which would delay the
% build-up of the preamble.
% \begin{macrocode}
\let\@sharp\relax \let\@startpbox\relax \let\@endpbox\relax
% \end{macrocode}
% Now we remove possible $*$-forms in the user preamble with the
% command =\@xexpast=. As we already know, this command saves
% its result in the macro =\@tempa=.
% \begin{macrocode}
\@xexpast #1*0x\@@
% \end{macrocode}
% Afterwards we initialize all registers and macros, that we need
% for the build-up of the preamble.
% Since we want to start with the {\sf token} register $0$,
% =\count@= has to contain the value $-1$.
% \begin{macrocode}
\count@\m@ne
\let\the@toks\relax
% \end{macrocode}
% Then we call up =\prepnext@tok= in order to prepare the
% {\sf token} register $0$ for use.
% \begin{macrocode}
\prepnext@tok
% \end{macrocode}
% To evaluate the user preamble (without stars) saved in
% =\@tempa= we use the \LaTeX--macro =\@tfor=.
% The strange appearing construction with =\expandafter= is
% based on the fact that we have to put the replacement text of
% =\@tempa= and not the macro =\@tempa= to this
% \LaTeX--macro.
% \begin{macrocode}
\expandafter \@tfor \expandafter \@nextchar
\expandafter :\expandafter =\@tempa \do
% \end{macrocode}
% The body of this loop (the group after the =\do=)
% is executed for one {\sf token} at a time, whereas
% the current {\sf token} is saved in =\@nextchar=.
% At first we evaluate the current {\sf token} with the already
% defined macro =\@testpach=, i.e.\ we assign to
% =\@chclass= the character class and to =\@chnum=
% the character number of this {\sf token}.
% \changes{v2.0f}{92/02/29}{`@testpach now without arg}
% \begin{macrocode}
{\@testpach
% \end{macrocode}
% Then we branch out depending on the value of =\@chclass= into
% different macros that extend the preamble respectively.
% \begin{macrocode}
\ifcase \@chclass \@classz \or \@classi \or \@classii
\or \save@decl \or \or \@classv \or \@classvi
\or \@classvii \or \@classviii \or \@classix
\or \@classx \fi
% \end{macrocode}
% Two cases deserve our special attention:
% Since the current {\sf token} cannot have the character class $4$
% (start) we have skipped this possibility. If the character class
% is $3$, only the content of =\@nextchar= has to be saved into
% the current {\sf token} register; therefore we call up
% =\save@decl= directly and save a macro name.
% After the preamble has been extended we assign the
% value of =\@chclass= to the counter =\@lastchclass= to
% assure that this information will be available during the next run
% of the loop.
% \begin{macrocode}
\@lastchclass\@chclass}%
% \end{macrocode}
% After the loop has been finished space must still be added to
% the created preamble, depending on the last {\sf token}.
% Depending on the value of =\@lastchclass= we perform
% the necessary operations.
% \begin{macrocode}
\ifcase\@lastchclass
% \end{macrocode}
% If the last class equals $0$ we add a
% =\hskip \col@sep=.
% \begin{macrocode}
\@acol \or
% \end{macrocode}
% If it equals $1$ we do not add any additional space so that the
% horizontal lines do not exceed the vertical ones.
% \begin{macrocode}
\or
% \end{macrocode}
% Class $2$ is treated like class $0$ because a =<{...}= can
% only directly follow after class $0$.
% \begin{macrocode}
\@acol \or
% \end{macrocode}
% Most of the other possibilities can only appear if the user
% preamble was defective. Class $3$ is not allowed since after
% a =>{..}= there must always follow a {\tt c}, {\tt l},
% { {\tt r}, {\tt p},\tt m} or {\tt b}. We report an error
% and ignore the declaration given by ={..}=.
% \begin{macrocode}
\@preamerr \thr@@ \or
% \end{macrocode}
% If =\@lastchclass= is $4$ the user preamble has been empty.
% To continue, we insert a =#= in the preamble.
% \begin{macrocode}
\@preamerr \tw@ \@addtopreamble\@sharp \or
% \end{macrocode}
% Class $5$ is allowed again. In this case
% (the user preamble ends with =@{..}=) we need not
% do anything.
% \begin{macrocode}
\or
% \end{macrocode}
% Any other case means that the arguments to
% =@=, {\tt !}, {\tt <}, {\tt >}, {\tt p}, {\tt m} or {\tt b}
% have been forgotten. So we report an error and ignore the last
% {\sf token}.
% \begin{macrocode}
\else \@preamerr \@ne \fi
% \end{macrocode}
% Now that the build-up of the preamble is almost finished we can
% insert the {\sf token} registers and therefore redefine
% =\the@toks=. The actual insertion, though, is performed
% later.
% \begin{macrocode}
\def\the@toks{\the\toks}}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \section{The macros {\tt \protect
% \bslash @classz} to {\tt \protect\bslash @classx}}
% The preamble is extended by the macros =\@classz= to
% =\@classx= which are called by =\@mkpream=
% depending on =\@lastchclass=
% (i.e. the character class of the last {\sf token}).
% \begin{macro}{\@classx}
% First we define =\@classx= because of its important r\^ole.
% When it is called we find that the current
% {\sf token} is {\tt p}, {\tt m} or {\tt b}.
% That means that a new column has to start.
% \begin{macrocode}
\def\@classx{%
% \end{macrocode}
% Depending on the value of =\@lastchclass= different actions
% must take place:
% \begin{macrocode}
\ifcase \@lastchclass
% \end{macrocode}
% If the last character class was $0$ we separate the columns by
% =\hskip\col@sep= followed by =&= and another
% =\hskip\col@sep=.
% \begin{macrocode}
\@acolampacol \or
% \end{macrocode}
% If the last class was class $1$ --- that means that a vertical
% line was
% drawn, --- before this line a =\hskip\col@sep= was inserted.
% Therefore there has to be only a =&= followed by
% =\hskip\col@sep=. But this =&= may be inserted only
% if this is not the first column. This process is controlled
% by =\if@firstamp= in the macro =\addamp=.
% \begin{macrocode}
\@addamp \@acol \or
% \end{macrocode}
% Class $2$ is treated like class $0$ because =<{...}= can only
% follow after class $0$.
% \begin{macrocode}
\@acolampacol \or
% \end{macrocode}
% Class $3$ requires no actions because all things necessary have
% been done by the preamble {\sf token} {\tt >}.
% \begin{macrocode}
\or
% \end{macrocode}
% Class $4$ means that we are at the beginning of the preamble.
% Therefore we start the preamble with =\hskip\col@sep= and
% then call =\@firstampfalse=. This makes sure that a later
% =\@addamp= inserts the character
% =&= into the preamble.
% \begin{macrocode}
\@acol \@firstampfalse \or
% \end{macrocode}
% For class $5$ {\sf tokens} only the character =&= is inserted
% as a column separator. Therefore we call =\@addamp=.
% \begin{macrocode}
\@addamp
% \end{macrocode}
% Other cases are impossible. For an example
% $=\@lastchclass= \string= 6$---as it might appear in a
% preamble of the form =...!p...=---{\tt p} would have
% been taken as an argument of {\tt !}\ by =\@testpach=.
% \begin{macrocode}
\fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classz}
% If the character class of the last {\sf token} is $0$
% we have {\tt c}, {\tt l}, {\tt r} or an argument of {\tt m},
% {\tt b} or\ {\tt p}. In the first three cases the preamble must be
% extended the same way as if we had class $10$. The remaining two
% cases do not require any action because the space needed was
% generated by the last {\sf token} (i.e.\ {\tt m}, {\tt b} or
% {\tt p}). Since =\@lastchclass= has the value $10$ at
% this point nothing happens when =\@classx= is called. So the
% macro =\@chlassz= may start like this:
% \begin{macrocode}
\def\@classz{\@classx
% \end{macrocode}
% According to the definition of =\insert@column= we must store
% the number of the {\sf token} register in which a preceding
% =>{..}= might have stored its argument into
% =\@tempcnta=.
% \begin{macrocode}
\@tempcnta \count@
% \end{macrocode}
% To have $=\count@= \string= =\@tmpcnta= + 1$ we prepare
% the next {\sf token} register.
% \begin{macrocode}
\prepnext@tok
% \end{macrocode}
% Now the preamble must be extended with the column whose format
% can be determinated by =\@chnum=.
% \begin{macrocode}
\@addtopreamble{\ifcase \@chnum
% \end{macrocode}
% If =\@chnum= has the value $0$ a centered column has to be
% generated.
% So we begin with stretchable space.
% \begin{macrocode}
\hfil
% \end{macrocode}
% The command =\d@llarbegin= follows expanding into =\begingroup=
% (in the {\sf tabular}--environment) or into =$=. Doing this
% (provided an appropriate setting of =\d@llarbegin=) we achieve
% that the contents of the columns of an {\sf array}--environment
% are set in math mode while those of a {\sf tabular}--environment
% are set in LR mode.
% \begin{macrocode}
\d@llarbegin
% \end{macrocode}
% Now we insert the contents of the two {\sf token} registers
% and the symbol
% for the column entry (i.e.\ =#= or
% more precise =\@sharp=) using =\insert@column=.
% \begin{macrocode}
\insert@column
% \end{macrocode}
% We end this case with =\d@llarend= and =\hfil= where =\d@llarend=
% again is either =$= or =\endgroup=.
% \begin{macrocode}
\d@llarend \hfil \or
% \end{macrocode}
% The templates for {\tt l} and {\tt r} (i.e.\ =\@chnum= $1$
% or $2$) are generated the same way. Since one =\hfil= is
% missing the text is moved to the relevant side.
% The =\kern\z@= is needed in case of an empty column
% entry. Otherwise
% the =\unskip= in =\insert@column= removes the
% =\hfil=.
% \begin{macrocode}
\d@llarbegin \insert@column \d@llarend \hfil \or
\hfil\kern\z@ \d@llarbegin \insert@column \d@llarend \or
% \end{macrocode}
% The templates for {\tt p}, {\tt m} and {\tt b} mainly consist
% of a {\sf box}. In case of {\tt m} it is generated by
% =\vcenter=.
% This command is allowed only in math mode. Therefore we start with
% a~=$=.
% \begin{macrocode}
$\vcenter
% \end{macrocode}
% The part of the templates which is the same in all three cases
% ({\tt p}, {\tt m} and {\tt b})
% is built by the macros =\@startpbox= and
% =\@endpbox=. =\@startpbox= has an argument:
% the width of the column which is stored in the current
% {\sf token} (i.e.\ =\@nextchar=).
% Between these two macros we find the well known
% =\insert@column=.
% \begin{macrocode}
\@startpbox{\@nextchar}\insert@column \@endpbox $\or
% \end{macrocode}
% The templates for {\tt p} and {\tt b} are generated in the same
% way though we do not need the
% =$= characters because we use =\vtop=
% or =\vbox=.
% \begin{macrocode}
\vtop \@startpbox{\@nextchar}\insert@column \@endpbox \or
\vbox \@startpbox{\@nextchar}\insert@column \@endpbox
% \end{macrocode}
% Other values for =\@chnum= are impossible. Therefore we
% end the arguments to =\@addtopreamble= and =\ifcase=.
% Before we come to the end of =\@classz= we have to
% prepare the next {\sf token} register.
% \begin{macrocode}
\fi}\prepnext@tok}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classix}
% In case of class $9$ ({\tt >}--{\sf token}) we first check
% if the character class of the last
% {\sf token} was $3$. In this case we have a
% user preamble of the form =..>{...}>{...}..= which
% is not allowed. We only give an error message and continue.
% So the declarations defined by the first =>{...}=
% are ignored.
% \begin{macrocode}
\def\@classix{\ifnum \@lastchclass = \thr@@
\@preamerr \thr@@ \fi
% \end{macrocode}
% Furthermore, we call up =\@class10=
% because afterwards always a new column is started by
% {\tt c}, {\tt l}, {\tt r}, {\tt p}, {\tt m} or {\tt b}.
% \begin{macrocode}
\@classx}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classviii}
% If the current {\sf token} is a {\tt <} the last
% character class must be $0$. In this case it is not necessary to
% extend the preamble. Otherwise we output an error message, set
% =\@chclass= to $6$ and call =\@classvi=.
% By doing this we achieve that {\tt <} is treated like {\tt !}.
% \begin{macrocode}
\def\@classviii{\ifnum \@lastchclass >\z@
\@preamerr 4\@chclass 6 \@classvi \fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@arrayrule}
% There is only one incompatibility with the original definition:
% the definition of =\@arrayrule=. In the original a line
% without width\footnote{So the space between {\tt cc} and {\tt c|c}
% is equal.}
% is created by multiple insertions of =\hskip .5\arrayrulewidth=.
% We only insert a vertical line into the preamble.
% This is done to prevent problems with \TeX's main
% memory when generating
% tables with many vertical lines in them (especially in the case of
% {\sf floats}).
% \begin{macrocode}
\def\@arrayrule{\@addtopreamble \vline}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classvii}
% As a consequence it follows that in case of class $7$
% (=@= {\sf token}) the preamble need not to be extended.
% In the original definition $=\@lastchclass= \string= 1$
% is treated by inserting =\hskip .5\arrayrulewidth=.
% We only check if the last {\sf token} was of class $3$ which is
% forbidden.
% \begin{macrocode}
\def\@classvii{\ifnum \@lastchclass = \thr@@
% \end{macrocode}
% If this is true we output an error message and
% ignore the declarations stored
% by the last =>{...}=, because these are overwritten
% by the argument of {\tt @}.
% \begin{macrocode}
\@preamerr \thr@@ \fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classvi}
% If the current {\sf token} is a regular {\tt !}\ and the last
% class
% was $0$ or $2$ we extend the preamble with =\hskip \col@sep=.
% If the last {\sf token} was of class $1$ (for instance {\tt |})
% we extend with =\hskip \doublerulesep= because the
% construction =!{...}= has to be treated like {\tt |}.
% \begin{macrocode}
\def\@classvi{\ifcase \@lastchclass
\@acol \or
\@addtopreamble{\hskip \doublerulesep}\or
\@acol \or
% \end{macrocode}
% Now =\@preamerr...= should follow because a
% user preamble of the form =..>{..}!..= is not allowed.
% To save memory we call =\@classvii= instead which also
% does what we want.
% \begin{macrocode}
\@classvii
% \end{macrocode}
% If =\@lastchclass= is $4$ or $5$ nothing has to be done.
% Class $6$ to $10$ are not possible.
% So we finish the macro.
% \begin{macrocode}
\fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classii}
% \begin{macro}{\@classiii}
% In the case of character classes $2$ and $3$ (i.e.\ the argument
% of {\tt <} or {\tt >}) we only have to store the current
% {\sf token} (=\@nextchar=) into the corresponding
% {\sf token} register since the preparation and
% insertion of these registers
% are done by the macro =\@classz=.
% This is equivalent to calling =\save@decl= in the case of
% class $3$. To save command identifiers we do this call up
% in the macro =\@mkpream=.
% Class $2$ exhibits a more complicated situation: the
% {\sf token} registers have already been inserted by
% =\@classz=. So the value of =\count@= is too high
% by one. Therefore we decrease =\count@= by $1$.
% \begin{macrocode}
\def\@classii{\advance \count@ \m@ne
% \end{macrocode}
% Next we store the current {\sf token} into the correct
% {\sf token} register by calling =\save@decl= and then
% increase the value of =\count@= again. At this point we
% can save memory once more (at the cost of time) if we use the
% macro =\prepnext@tok=.
% \begin{macrocode}
\save@decl\prepnext@tok}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\@classv}
% If the current {\sf token} is of class $5$ then it is an argument
% of a {\tt @} {\sf token}. It must be stored into a
% {\sf token} register.
% \begin{macrocode}
\def\@classv{\save@decl
% \end{macrocode}
% We extend the preamble with a command which inserts this
% {\sf token} register into the preamble when its construction is
% finished. The user expects that this argument is worked out in
% math mode if it was used in an {\sf array}--environment. Therefore
% we surround it with =\d@llar...='s.
% \changes{v2.0c}{90/08/14}{`relax added to avoid problem
% `the`toks0`the`toks1.}
% \begin{macrocode}
\@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
% \end{macrocode}
% Finally we must prepare the next {\sf token} register.
% \begin{macrocode}
\prepnext@tok}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classi}
% In the case of class $0$ we were able to generate the necessary
% space between columns by using the macro =\@classx=.
% Analogously the macro =\@classvi= can be used for class $1$.
% \begin{macrocode}
\def\@classi{\@classvi
% \end{macrocode}
% Depending on =\@chnum= a vertical line
% \begin{macrocode}
\ifcase \@chnum \@arrayrule \or
% \end{macrocode}
% or (in case of =!{...}=) the current {\sf token} --- stored
% in =\@nextchar= --- has to be inserted into the preamble.
% This corresponds to calling =\@classv=.
% \begin{macrocode}
\@classv \fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@startpbox}
% In =\@classz= the macro =\@startpbox= is used.
% The width of the {\sf parbox} is passed as an argument.
% =\vcenter=, =\vtop= or =\vbox= are already in the
% preamble. So we start with the braces for the wanted box.
% \begin{macrocode}
\def\@startpbox#1{\bgroup
% \end{macrocode}
% The argument is the width of the box. This information has to be
% assigned to =\hsize=.
% Then we assain default values to several parameters used in a
% {\sf parbox}.
% \begin{macrocode}
\hsize #1 \@arrayparboxrestore
% \end{macrocode}
% Our main problem is to obtain the same distance between succeeding
% lines of the {\sf parbox}.
% We have to remember that the distance between two {\sf parboxes}
% should be defined by =\@arstrut=. That means that it can be
% greater than the distance in a {\sf parbox}.
% Therefore it is not enough to set a =\@arstrut= at the
% beginning and at the end of the {\sf parbox}. This would
% dimension the distance
% between first and second line and the distance between the two
% last lines of the {\sf parbox} wrongly.
% To prevent this we set an invisible rule of height
% =\@arstrutbox=
% at the beginning of the {\sf parbox}. This has no effect on the
% depth of the first line. At the end of the {\sf parbox} we set
% analogously another invisible rule which only affects the depth
% of the last line.
% \begin{macrocode}
\vrule \@height \ht\@arstrutbox \@width \z@}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@endpbox}
% If there are any declarations defined by =>{...}=
% and =<{...}=
% they now follow in the macro =\@classz= --- the contents
% of the column in between.
% So the macro =\@endpbox= must insert the {\sf specialstrut}
% mentioned earlier and then close the group opened by
% =\@startpbox=.
% \begin{macrocode}
\def\@endpbox{\vrule \@width \z@ \@depth \dp \@arstrutbox \egroup}
% \end{macrocode}
% \end{macro}
% \section{Building and calling {\tt \protect\bslash halign}}
% \begin{macro}{\@array}
% After we have discussed the macros needed for the evaluation
% of the user preamble we can define the macro =\@array=
% which uses these macros to create a =\halign=.
% It has two arguments. The first one is a position argument
% which can be {\tt t}, {\tt b} or {\tt c}; the
% second one describes the wanted preamble,
% e.g.\ it has the form =|c|c|c|=.
% \begin{macrocode}
\def\@array[#1]#2{%
% \end{macrocode}
% First we define a {\sf strut} whose size basically corresponds
% to a normal {\sf strut} multiplied by the factor
% =\arraystretch=.
% This {\sf strut} is then inserted into every row and enforces
% a minimal distance between two rows.
% Nevertheless, when using horizontal lines, large letters
% (like accented capital letters) still collide with such lines.
% Therefore at first we add to the height of a normal {\sf strut}
% the value of the parameter =\extrarowheight=.
% \begin{macrocode}
\@tempdima \ht \strutbox
\advance \@tempdima by\extrarowheight
\setbox \@arstrutbox \hbox{\vrule
\@height \arraystretch \@tempdima
\@depth \arraystretch \dp \strutbox
\@width \z@}%
% \end{macrocode}
% Then we open a group, in which the user preamble is evaluated by
% the macro =\@mkpream=. As we know this must happen locally.
% This macro creates a preamble for a =\halign= and saves
% its result globally in the control sequence =\@preamble=.
% \begin{macrocode}
\begingroup
\@mkpream{#2}%
% \end{macrocode}
% We again redefine =\@preamble= so that a call up of
% =\@preamble= now starts the =\halign=. Thus also the
% arguments of {\tt >}, {\tt <}, {\tt @} and {\tt !}, saved in the
% {\sf token} registers are inserted into the preamble.
% The =\tabskip= at the beginning and end of the preamble
% is set to {\sf 0pt} (in the beginning by the use of
% =\ialign=). Also the command =\@arstrut= is build in,
% which inserts the =\@arstrutbox=, defined above. Of course,
% the opening brace after =\ialign= has to be implicit as it
% will be closed in =\endarray= or another macro.
% \begin{macrocode}
\xdef\@preamble{\ialign \@halignto
\bgroup \@arstrut \@preamble
\tabskip \z@ \cr}%
% \end{macrocode}
% What we have not explained yet is the macro =\@halignto=
% that was just used. Depending on its replacement text the
% =\halign= becomes a =\halign= {\tt to} \meta{dimen}.
% Now we close the group again. Thus
% =\@startpbox= and =\@endpbox= as well as all
% {\sf token} registers get their former meaning back.
% \begin{macrocode}
\endgroup
% \end{macrocode}
% To support the {\tt delarray.sty} style option we include a hook
% into this part of the code which is a no-op in the main style.
% \changes{v2.1a}{92/07/03}{Hook for delarray added}
% \begin{macrocode}
\@arrayleft
% \end{macrocode}
% Now we decide depending on the position argument in which {\sf
% box} the =\halign= is to be put. (=\vcenter= may be used
% because we are in math mode.)
% \changes{v2.1a}{92/07/03}{Wrong spec is now equiv to [t]}
% \begin{macrocode}
\if #1t\vtop \else \if#1b\vbox \else \vcenter \fi \fi
% \end{macrocode}
% Now another implicit opening brace appears; then definitions
% which shall stay local follow. While constructing the
% =\@preamble= in =\@mkpream= the =#= sign must be
% hidden in the macro =\@sharp= which is =\let= to
% =\relax= at that moment (see definition of =\@mkpream=
% on page~\pageref{@mkpream}).
% All these now get their actual meaning.
% \begin{macrocode}
\bgroup
\let \@sharp ##\let \protect \relax
% \end{macrocode}
% With the above defined {\sf struts} we fix down the distance
% between rows by setting =\lineskip= and =\baselineskip=
% to {\sf 0pt}. Since there have to be set =$='s
% around every column in the {\sf array}--environment
% the parameter =\mathsurround= should
% also be set to {\sf 0pt}. This prevents additional space between
% the rows. The
% \PlainTeX--macro =\m@th= does this.
% \begin{macrocode}
\lineskip \z@
\baselineskip \z@
\m@th
% \end{macrocode}
% Beside, we have to assign a special meaning (which we still have
% to specify) to the line separator =\\=. We also have to
% redefine the command =\par= in such a way that empty lines in
% =\halign= cannot do any damage. We succeed in doing so
% by choosing something that will disappear when expanding.
% After that we only have to call up =\@preamble= to
% start the wanted =\halign=.
% \begin{macrocode}
\let\\ \@arraycr \let\par\@empty \@preamble}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\extrarowheight}
% The {\sf dimen} parameter used above also needs to be allocated.
% As a default value we use {\sf 0pt}, to ensure compatibility with
% standard \LaTeX.
% \begin{macrocode}
\newdimen \extrarowheight
\extrarowheight=0pt
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@arstrut}
% Now the insertion of =\@arstrutbox= through =\@arstut=
% is easy since we know exactly in which mode \TeX\ is while working
% on the =\halign= preamble.
% \begin{macrocode}
\def\@arstrut{\unhcopy\@arstrutbox}
% \end{macrocode}
% \end{macro}
% \section{The line separator {\tt\protect\bslash\protect\bslash}}
% \begin{macro}{\@arraycr}
% In the macro =\@array= the line separator =\\= is
% =\let= to the command =\@arraycr=.
% Its definition starts with a special brace which I have directly
% copied from the original definition. It is
% necessary, because the =\futurlet= in =\@ifnextchar=
% might
% expand a following =&= {\sf token} in a construction like
% =\\ &=. This would otherwise end the alignment template at a
% wrong time. For further information see
% \cite[Appendix D]{bk:knuth}.
% \begin{macrocode}
\def\@arraycr{{\ifnum 0=`}\fi
% \end{macrocode}
% Then we test whether the user is using the star form and ignore
% a possible star (I also disagree with this procedure, because a
% star does not make any sense here).
% \begin{macrocode}
\@ifstar \@xarraycr \@xarraycr}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@xarraycr}
% In the command =\@xarraycr= we test if an optional argument
% exists.
% \begin{macrocode}
\def\@xarraycr{\@ifnextchar [%
% \end{macrocode}
% If it does, we branch out into the macro =\@argarraycr= if
% not we close the special brace (mentioned above) and end the row
% of the =\halign= with a =\cr=.
% \begin{macrocode}
\@argarraycr {\ifnum 0=`{\fi}\cr}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@argarraycr}
% If additional space is requested by the user this case is treated
% in the macro =\@argarraycr=. First we close the special brace
% and then we test if the additional space is positive.
% \begin{macrocode}
\def\@argarraycr[#1]{\ifnum0=`{\fi}\ifdim #1>\z@
% \end{macrocode}
% If this is the case we create an invisible vertical rule with a
% depth of $=\dp\@arstutbox= + \left\langle
% \it wanted\ space
% \right\rangle $.
% Thus we achieve that all vertical lines specified
% in the user preamble by a {\tt |} are now
% generally drawn.
% Then the row ends with a =\cr=.
% If the space is negative we end the row at once with a =\cr=
% and move back up with a =\vskip=.
% While testing these macros I found out that the
% =\endtemplate=
% created by =\cr= and =&= is something like an
% =\outer= primitive and therefore it should not appear in
% incomplete =\if= statements. Thus the following solution was
% chosen which hides the =\cr= in other macros when \TeX\
% is skipping conditional text.
% \begin{macrocode}
\@xargarraycr{#1}\else \@yargarraycr{#1}\fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@xargarraycr}
% \begin{macro}{\@yargarraycr}
% The following macros were already explained above.
% \begin{macrocode}
\def\@xargarraycr#1{\unskip
\@tempdima #1\advance\@tempdima \dp\@arstrutbox
\vrule \@depth\@tempdima \@width\z@ \cr}
\def\@yargarraycr#1{\cr\noalign{\vskip #1}}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \section{Spanning several columns}
% \begin{macro}{\multicolumn}
% If several columns should be held together with a special format
% the command =\multicolumn= must be used. It has three
% arguments: the number of columns to be covered; the format for
% the result column and the actual column entry.
% \begin{macrocode}
\def\multicolumn#1#2#3{%
% \end{macrocode}
% First we combine the given number of columns into a single one;
% then we start a new block so that the following definition is kept
% local.
% \begin{macrocode}
\multispan{#1}\begingroup
% \end{macrocode}
% Since a =\multicolumn= should only describe the format of a
% result column, we redefine =\@addamp= in such a way that one
% gets an error message if one uses more than one
% {\tt c}, {\tt l}, {\tt r}, {\tt p}, {\tt m} or {\tt b} in the
% second argument. One should consider that this definition is local
% to the build-up of the preamble; an {\sf array}-- or
% {\sf tabular}--environment in the third argument of the
% =\multicolumn= is therefore worked through correctly as well.
% \begin{macrocode}
\def\@addamp{\if@firstamp \@firstampfalse \else
\@preamerr 5\fi}%
% \end{macrocode}
% Then we evaluate the second argument with the help of
% =\@mkpream=.
% Now we still have to insert the contents of the {\sf token}
% register into the =\@preamble=, i.e.\ we have to say
% =\xdef\@preamble{\@preamble}=. This is achieved shorter by
% writing:
% \begin{macrocode}
\@mkpream{#2}\@addtopreamble\@empty
% \end{macrocode}
% After the =\@preamble= is created we forget all local
% definitions and occupations of the {\sf token} registers.
% \begin{macrocode}
\endgroup
% \end{macrocode}
% In the special situation of =\multicolumn= =\@preamble=
% is not needed as preamble for a =\halign= but it is directly
% inserted into our table. Thus instead of =\sharp=
% there has to be the column entry (=#3=) wanted by the user.
% \begin{macrocode}
\def\@sharp{#3}%
% \end{macrocode}
% Now we can pass the =\@preamble= to \TeX\ . For safety
% we start with an =\@arstrut=. This should usually be in the
% template for the first column however we do not know if this
% template was overwritten by our =\multicolumn=.
% \begin{macrocode}
\@arstrut \@preamble \ignorespaces}
% \end{macrocode}
% \end{macro}
% \section{The Environment Definitions}
% After these preparations we are able to define the environments. They
% only differ in the initialisations of =\d@llar...=, =\col@sep=
% and =\@halignto=.
% \begin{macro}{\@halignto}
% \begin{macro}{\d@llarbegin}
% \begin{macro}{\d@llarend}
% In order to relieve the {\sf save stack} we assign the replacement
% texts for =\@halignto= globally. =\d@llar= has to be local
% since otherwise nested {\sf tabular} and {\sf array} environments
% (via =\multicolumn=) are impossible.
% \changes{v2.0g}{92/06/18}{`d@llarbegin defined on toplevel.}
% When the new font selection scheme is in force we have to
% we surround all =\halign= entries
% with braces. See remarks in TUGboat 10\#2. Actually we are going
% to use =\begingroup= and =\endgroup=. However, this is only
% necessary when we are in text mode. In math the surrounding
% dollar signs will already serve as the necessary extra grouping
% level. Therefore we switch the settings of =\d@llarbegin= and
% =\d@llarend= between groups and dollar signs.
% \begin{macrocode}
\let\d@llarbegin\begingroup
\let\d@llarend\endgroup
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\array}
% Our new definition of =\array= then reads:
% \changes{v2.0d}{90/08/20}{`d@llar local to preamble.}
% \begin{macrocode}
\def\array{\col@sep\arraycolsep
\def\d@llarbegin{$}\let\d@llarend\d@llarbegin\gdef\@halignto{}%
% \end{macrocode}
% Since there might be an optional argument we call another
% macro which is also used by the other environments.
% \begin{macrocode}
\@tabarray}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@tabarray}
% This macro tests for a optional bracket and then calls up
% =\@array= or =\@array[c]= (as default).
% \begin{macrocode}
\def\@tabarray{\@ifnextchar[{\@array}{\@array[c]}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\tabular}
% \begin{macro}{\tabular*}
% The environments {\sf tabular} and {\sf tabular$*$} differ
% only in the initialisation of =\@halignto=. Therefore
% we define
% \begin{macrocode}
\def\tabular{\gdef\@halignto{}\@tabular}
% \end{macrocode}
% and analoguesly
% \begin{macrocode}
\expandafter\def\csname tabular*\endcsname#1{%
\gdef\@halignto{to#1}\@tabular}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\@tabular}
% The rest of the job is carried out by the =\@tabular= macro:
% \begin{macrocode}
\def\@tabular{%
% \end{macrocode}
% First of all we have to make sure that we start out in {\sf
% hmode}.
% Otherwise we might find our table dangling by itself on a line.
% \begin{macrocode}
\leavevmode
% \end{macrocode}
% It should be taken into consideration that the macro
% =\@array=
% must be called in math mode. Therefore we open a {\sf box}, insert
% a =$= and then assign the correct values to =\col@sep=
% and =\d@llar...=.
% \changes{v2.0d}{90/08/20}{`d@llar local to preamble.}
% \begin{macrocode}
\hbox \bgroup $\col@sep\tabcolsep \let\d@llarbegin\begingroup
\let\d@llarend\endgroup
% \end{macrocode}
% Now everything {\sf tabular} specific is done and we are able to
% call the =\@tabarray= macro.
% \begin{macrocode}
\@tabarray}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\endarray}
% When the processing of {\sf array} is finished we have to
% close the =\halign=
% and afterwards the surrounding {\sf box} selected by
% =\@array=. To save {\sf token} space we then redefine
% =\@preamble=
% because its replacement text isn't longer needed.
% \begin{macrocode}
\def\endarray{\crcr \egroup \egroup \gdef\@preamble{}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\endtabular}
% \begin{macro}{\endtabular*}
% To end a {\sf tabular} or {\sf tabular$*$} environment we call up
% =\endarray=, close the math mode and then the surrounding
% =\hbox=.
% \begin{macrocode}
\def\endtabular{\endarray $\egroup}
\expandafter\let\csname endtabular*\endcsname=\endtabular
% \end{macrocode}
% \end{macro}
% \end{macro}
% \section{Last minute definitions}
% If this file is used as a style file we should =\let= all macros
% to =\relax= that were used in the original but are no longer
% necessary.
% \begin{macrocode}
\let\@ampacol=\relax \let\@expast=\relax
\let\@arrayclassiv=\relax \let\@arrayclassz=\relax
\let\@tabclassiv=\relax \let\@tabclassz=\relax
\let\@arrayacol=\relax \let\@tabacol=\relax
\let\@tabularcr=\relax \let\@@endpbox=\relax
\let\@argtabularcr=\relax \let\@xtabularcr=\relax
% \end{macrocode}
% \begin{macro}{\@preamerr}
% We also have to redefine the error routine =\@preamerr= since
% new kind of errors are possible.
% The code for this macro is not perfect yet;
% it still needs too much memory.
% \begin{macrocode}
\def\@preamerr#1{\def\@tempd{{..} at wrong position: }%
\@latexerr{%
\ifcase #1 Illegal pream-token (\@nextchar): `c' used\or %0
Missing arg: token ignored\or %1
Empty preamble: `l' used\or %2
>\@tempd token ignored\or %3
<\@tempd changed to !{..}\or %4
Only one column-spec. allowed.\fi}\@ehc} %5
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@tfor}
% Testing this implementation an error was found in the definition
% of the \LaTeX{} macro =\@tfor=. It was not implemented
% according to
% its specification. The assignment to =\@fortmp= must not take
% place
% via =\xdef=. A =\def= has to be used because =#2= must
% not be expanded. Since this mistake does not show up when
% =\@tfor= is used in {\tt latex.tex}, it does not
% seem to have been noticed.
% \begin{macrocode}
\def\@tempa#1:=#2\do#3{\def\@fortmp{#2}\ifx\@fortmp\@empty
\else\@tforloop#2\@nil\@nil\@@#1{#3}\fi}
\ifx\@tempa\@tfor
\else
\errhelp{The bug fix for \@tfor was removed from
array.sty because it was^^J%
corrected in latex.tex <dec91>.^^J^^J%
Please update to a newer LaTeX release.}
\errmessage{Obsolete LaTeX release (older than Dec.91)}
\let\@tfor\@tempa
\let\@tempa\@empty
%</style>
% \end{macrocode}
% \end{macro}
% \section
% [Defining your own column specifiers]
% {Defining your own column specifiers\footnotemark}
% \footnotetext{The code and the documentation in this section was
% written by David. So far only the code from newarray was plugged
% into array so that some parts of the documentation still claim
% that this is newarray and even worse, some parts of the code are
% unnecessarily doubled. This will go away in a future release. For
% the moment we thought it would be more important to bring both
% styles together.}
% \changes{v2.1a}{92/07/03}{Newcolumn stuff added}
% \DeleteShortVerb{\=}
% \MakeShortVerb{\"}
% \begin{macro}{\newcolumn}
% In {\tt newarray.sty} the macro for specifying new columns was
% named "\newcolumn". When the functionality was added to {\tt
% array.sty} the name changed to "\newcolumntype". To allow
% prcessing older sources that made use of {\tt newarray.sty} we
% provide a definition for the old name.
% \begin{macrocode}
\def\newcolumn{%
\typeout{*** Obsolete command \string\newcolumn!
Please use \noexpand\newcolumntype ***}%
\newcolumntype
% \end{macrocode}
% \end{macro}
% \begin{macro}{\newcolumntype}
% \changes{v2.1b}{92/06/07}{Macro renamed from `newcolumn} As
% described above, the "\newcolumntype" macro gives users the chance
% to define letters, to be used in the same way as the primitive
% column specifiers, `c' `p' etc.
% \begin{macrocode}
%<*ncols>
\def\newcolumntype#1{%
% \end{macrocode}
% "\NC@char" was added in V2.01 so that active characters, like "@" in
% AMS\LaTeX\ may be used. This trick was stolen from {\tt array.sty}
% 2.0h. Note that we need to use the possibly active token,
% "#1", in several places, as that is the token that actually
% appears in the preamble argument.
% \begin{macrocode}
\edef\NC@char{\string#1}%
% \end{macrocode}
% First we check whether there is already a definition for this column.
% Unlike "\newcommand" we give a warning rather than an error if it is
% defined. If it is a new column, add "\NC@do" \meta{column} to
% the list "\NC@list".
% \begin{macrocode}
\@ifundefined{NC@find@\NC@char}%
{\@tfor\next:=<>clrmbp@!|\do{\if\next\NC@char
\@warning{Redefining primitive column \NC@char}\fi}%
\NC@list\expandafter{\the\NC@list\NC@do#1}}%
{\@warning{Column \NC@char\space is already defined}}%
% \end{macrocode}
% Now we define a macro with an argument delimited by the new column
% specifier, this is used to find occurences of this specifier in the
% user preamble.
% \begin{macrocode}
\@namedef{NC@find@\NC@char}##1#1{\NC@{##1}}%
% \end{macrocode}
% If an optional argument was not given, give a default argument of 0.
% \begin{macrocode}
\@ifnextchar[{\newcol@{\NC@char}}{\newcol@{\NC@char}[0]}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\newcol@}
% We can now define the macro which does the rewriting,
% "\@reargdef" takes the same arguments as "\newcommand", but
% does not check that the command is new. For a column, say `D' with
% one argument, define a command "\NC@rewrite@D" with one
% argument, which recursively calls "\NC@find" on the user preamble
% after replacing the first token or group with the replacement text
% specified in the "\newcolumntype" command. "\NC@find" will find the
% next occurrence of `D' as it will be "\let" equal to
% "\NC@find@D" by "\NC@do".
% \begin{macrocode}
\def\newcol@#1[#2]#3{\expandafter\@reargdef
\csname NC@rewrite@#1\endcsname[#2]{\NC@find#3}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@}
% Having found an occurence of the new column, save the preamble
% before the column in "\@temptokena", then check to see if we
% are at the end of the preamble. (A dummy occurrence of the column
% specifier will be placed at the end of the preamble by "\NC@do".
% \begin{macrocode}
\def\NC@#1{%
\@temptokena\expandafter{\the\@temptokena#1}\futurelet\next\NC@ifend}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@ifend}
% We can tell that we are at the end as "\NC@do" will place a "\relax"
% after the dummy column.
% \begin{macrocode}
\def\NC@ifend{%
% \end{macrocode}
% If we are at the end, do nothing. (The whole preamble will now be in
% "\@temptokena".)
% \begin{macrocode}
\ifx\next\relax
% \end{macrocode}
% Otherwise set the flag "\if@tempswa", and rewrite the column.
% "\expandafter" introduced 1n V2.01
% \begin{macrocode}
\else\@tempswatrue\expandafter\NC@rewrite\fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@do}
% If the user has specified `C' and `L' as new columns, the list of
% rewrites (in the token register "\NC@list") will look like
% "\NC@do *" "\NC@do C" "\NC@do L".
% So we need to define "\NC@do" as a one argument macro which
% initialises the rewriting of the specified column. Let us assume that
% `C' is the argument.
% \begin{macrocode}
\def\NC@do#1{%
% \end{macrocode}
% First we let "\NC@rewrite" and "\NC@find" be
% "\NC@rewrite@C" and "\NC@find@C" respectively.
% \begin{macrocode}
\expandafter\let\expandafter\NC@rewrite
\csname NC@rewrite@\string#1\endcsname
\expandafter\let\expandafter\NC@find
\csname NC@find@\string#1\endcsname
% \end{macrocode}
% Clear the token register "\@temptokena" after putting the present
% contents of the register in front of the token "\NC@find". At the
% end we place the tokens `"C\relax"' which "\NC@ifend" will use
% to detect the end of the user preamble.
% \begin{macrocode}
\expandafter\@temptokena\expandafter{\expandafter}%
\expandafter\NC@find\the\@temptokena#1\relax}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\showcols}
% This macro is useful for debugging "\newcolumntype" specifications,
% it is the equivalent of the primitive "\show" command for macro
% definitions. All we need to do is locally redefine "\NC@do" to take
% its argument (say `C') and then "\show" the (slightly modified)
% definition of "\NC@rewrite@C". Actually as the the list always
% starts off with "\NC@do *" and we do not want to print the
% definition of the $*$-form, define "\NC@do" to throw away the first
% item in the list, and then redefine itsef to print the rest of the
% definitions.
% \begin{macrocode}
\def\showcols{{\def\NC@do##1{\let\NC@do\NC@show}\the\NC@list}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@show}
% If the column `C' is defined as above, then
% "\show\NC@rewrite@C" would output\\
% "\long macro: ->\NC@find >{$}c<{$}".
% We want to strip the "long macro: ->" and the "\NC@find". So first we
% use "\meaning" and then apply the macro "\NC@strip" to the tokens so
% produced and then "\typeout" the required string.
% \begin{macrocode}
\def\NC@show#1{%
\typeout{Column #1\expandafter\expandafter\expandafter\NC@strip
\expandafter\meaning\csname NC@rewrite@#1\endcsname\@@}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@strip}
% Delimit the arguments to "\NC@strip" with `{\tt:}', `{\tt->}',
% a space, and "\@@" to pull out the required parts of the output from
% "\meaning".
% \begin{macrocode}
\def\NC@strip#1:#2->#3 #4\@@{#2 -> #4}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@list}
% Allocate the token register used for the rewrite list.
% \begin{macrocode}
\newtoks\NC@list
% \end{macrocode}
% \end{macro}
% \subsection{The $*$--form}
% We view the $*$-form as a slight generalisation of the system
% described in the previous subsection. The idea is to define a $*$
% column by a command of the form:
% \begin{verbatim}
% \newcolumntype{*}[2]{%
% \count@=#1\ifnum\count@>0
% \advance\count@ by -1 #2*{\count@}{#2}\fi}
% \end{verbatim}
% \begin{macro}{\NC@rewrite@*}\label{NC@rewrite@*}
% This does not work however as "\newcolumntype" takes great care not
% to expand anything in the preamble, and so the "\if" is never
% expanded. "\newcolumntype" sets up various other parts of the
% rewrite correctly though so we can define:
% \begin{macrocode}
\newcolumntype{*}[2]{}
% \end{macrocode}
% Now we must correct the definition of "\NC@rewrite@*". The
% following is probably more efficient than a direct translation of
% the idea sketched above, we do not need to put a $*$ in the preamble
% and call the rewrite recursively, we can just put "#1" copies of
% "#2" into "\@temptokena". (Nested $*$ forms will be expanded
% when the whole rewrite list is expanded again, see "\@mkpream")
% \begin{macrocode}
\long\@namedef{NC@rewrite@*}#1#2{%
% \end{macrocode}
% Store the number.
% \begin{macrocode}
\count@#1
% \end{macrocode}
% Put "#1" copies of "#2" in the token register.
% \begin{macrocode}
\loop
\ifnum\count@>\z@
\advance\count@\m@ne
\@temptokena\expandafter{\the\@temptokena#2}%
\repeat
% \end{macrocode}
% "\NC@do" will ensure that "\NC@find" is "\let" equal
% to "\NC@find@*".
% \begin{macrocode}
\NC@find}
% \end{macrocode}
% \end{macro}
% \subsection{Modifications to internal macros of {\tt array.sty}}
% \begin{macro}{\@xexpast}
% \begin{macro}{\@xexnoop}
% These macros are used to expand $*$-forms in {\tt array.sty}. "\let"
% them to "\relax" to save space.
% \begin{macrocode}
\let\@xexpast\relax
\let\@xexnoop\relax
% \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\save@decl}
% We do not assume that the token register is free, we add the new
% declarations to the front of the register. This is to allow user
% preambles of the form, ">{foo}>{bar}..". Users are not encouraged to
% enter such expressions directly, but they may result from the
% rewriting of "\newcolumntype"'s.
% \begin{macrocode}
\def\save@decl{\toks \count@ = \expandafter\expandafter\expandafter
{\expandafter\@nextchar\the\toks\count@}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@mkpream}
% The main modification to "\@mkpream" is to replace the call to
% "\@xexpast" (which expanded $*$-forms) by a loop which expands
% all "\newcolumntype" specifiers.
% \begin{macrocode}
\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
\let\@sharp\relax \let\@startpbox\relax \let\@endpbox\relax
% \end{macrocode}
% Now we remove possible $*$-forms and user-defined column
% specifiers in the user preamble by repeatedly executing the list
% "\NC@list" until the re-writes have no more effect. The
% expanded preamble will then be in the token register
% "\@temptokena". Actually we need to know at this point that
% this is not "\toks0".
% \begin{macrocode}
\@temptokena{#1}\@tempswatrue
\@whilesw\if@tempswa\fi{\@tempswafalse\the\NC@list}%
% \end{macrocode}
% Afterwards we initialize all registers and macros, that we need
% for the build-up of the preamble.
% \begin{macrocode}
\count@\m@ne
\let\the@toks\relax
\prepnext@tok
% \end{macrocode}
% Having expanded all tokens defined using "\newcolumntype" (including
% "*"), we evaluate the remaining tokens, which are saved in
% "\@temptokena". We use the \LaTeX--macro "\@tfor" to inspect each
% token in turn.
% \begin{macrocode}
\expandafter \@tfor \expandafter \@nextchar
\expandafter :\expandafter =\the\@temptokena \do
% \end{macrocode}
% "\@testpatch" does not take an argument since {\tt array.sty} 2.0h.
% \begin{macrocode}
{\@testpach
\ifcase \@chclass \@classz \or \@classi \or \@classii
\or \save@decl \or \or \@classv \or \@classvi
\or \@classvii \or \@classviii
% \end{macrocode}
% In {\tt newarray.sty} class 9 is equivalent to class 10.
% \begin{macrocode}
\or \@classx
\or \@classx \fi
\@lastchclass\@chclass}%
\ifcase\@lastchclass
\@acol \or
\or
\@acol \or
\@preamerr \thr@@ \or
\@preamerr \tw@ \@addtopreamble\@sharp \or
\or
\else \@preamerr \@ne \fi
\def\the@toks{\the\toks}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classix}
% {\tt array.sty} does not allow repeated {\tt>} declarations for the
% same column. This is allowed in {\tt newarray.sty} as documented in
% the introduction. Removing the test for this case makes class 9
% equivalent to class 10, and so this macro is redundant. It is
% "\let" to "\relax" to save space.
% \begin{macrocode}
\let\@classix\relax
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classviii}
% In {\tt newarray.sty} explicitly allow class 2, as repeated {\tt<}
% expressions are accepted by this style.
% \begin{macrocode}
\def\@classviii{\ifnum \@lastchclass >\z@\ifnum\@lastchclass=\tw@\else
\@preamerr 4\@chclass 6 \@classvi \fi\fi}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@classv}
% Class 5 is {\tt@}-expressions (and is also called by class 1)
% This macro was incorrect in Version~1. Now we do not expand the
% "@"-expression, but instead explicitly replace an
% "\extracolsep" command by an assignment to "\tabskip" by a
% method similar to the "\newcolumntype" system described above.
% "\d@llarbegin" "\d@llarend" were introduced in V2.01 to match
% {\tt array.sty} 2.0h.
% \begin{macrocode}
\def\@classv{\save@decl
\expandafter\NC@ecs\@nextchar\extracolsep{}\extracolsep\@@@
\@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
\prepnext@tok}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@ecs}
% Rewrite the first occurrence of "\extracolsep{1in}" to
% "\tabskip1in\relax". As a side effect discard any tokens after a
% second "\extracolsep", there is no point in the user entering two of
% these commands anyway, so this is not really a restriction.
% \begin{macrocode}
\def\NC@ecs#1\extracolsep#2#3\extracolsep#4\@@@{\def\@tempa{#2}%
\ifx\@tempa\@empty\else\toks\count@={#1\tabskip#2\relax#3}\fi}
%</ncols>
% \end{macrocode}
% \end{macro}
% \subsection{Support for the {\tt delarray.sty}}
% The {\tt delarray.sty} style option extends the array syntax by
% supporting the notation of delimiters. To this end we extend the
% array parsing mechanism to include a hook which can be used by this
% (or another) option to do some additional parsing.
% \begin{macro}{\@tabarray}
% This macro tests for an optional bracket and then calls up
% "\@@array" or "\@@array[c]" (as default).
% \begin{macrocode}
%<*style>
\def\@tabarray{\@ifnextchar[{\@@array}{\@@array[c]}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\@@array}
% This macro tests could then test an optional delimiter before the
% left brace of the main preamble argument. Here in the main style
% it simply is let to be "\@array".
% \begin{macrocode}
\let\@@array\@array
% \end{macrocode}
% \end{macro}
% \begin{macro}{\endarray}
% \begin{macro}{\@arrayright}
% We have to declare the hook we put into "\@array" above.
% A similar hook `"\@arrayright"' will be inserted into the
% "\endarray" to gain control. Both defaults to empty.
% \begin{macrocode}
\def\endarray{\crcr \egroup \egroup \@arrayright \gdef\@preamble{}}
\let\@arrayleft\@empty
\let\@arrayright\@empty
%</style>
% \end{macrocode}
% \end{macro}
% \end{macro}
% \section{The documentation driver file}
% The next bit of code contains the documentation driver file for
% \TeX{}, i.e., the file that will produce the documentation you are
% currently reading. It will be extracted from this file by the {\tt
% docstrip} program.
% \begin{macrocode}
%<+driver>\documentstyle[array,doc]{article}
%<+driver>
%<+driver>% dimensions from ltugboat.sty:
%<+driver>
%<+driver>\setlength\textwidth{31pc} \setlength\textheight{54pc}
%<+driver>\setlength{\parindent}{0pt}
%<+driver>\setlength{\parskip}{2pt plus 1pt minus 1pt}
%<+driver>\setlength{\oddsidemargin}{8pc}
%<+driver>\setlength{\marginparwidth}{8pc}
%<+driver>\setlength{\topmargin}{-2.5pc} \setlength{\headsep}{20pt}
%<+driver>\setlength{\columnsep}{1.5pc}
%<+driver>\setlength{\columnwidth}{18.75pc}
%<+driver>
%<+driver>% Allow large table at bottom
%<+driver>\renewcommand{\bottomfraction}{0.7}
%<+driver>
%<+driver>\EnableCrossrefs
%<+driver>%\DisableCrossrefs % Say \DisableCrossrefs if index is ready
%<+driver>
%<+driver>\RecordChanges % Gather update information
%<+driver>
%<+driver>\CodelineIndex % Index code by line number
%<+driver>
%<+driver>%\OnlyDescription % comment out for implementation details
%<+driver>%\OldMakeindex % use if your MakeIndex is pre-v2.9
%<+driver>\begin{document}
%<+driver> \DocInput{array.doc}
%<+driver>\end{document}
% \end{macrocode}
% \PrintIndex
% \PrintChanges
% \Finale
\endinput