%\iffalse%%%%%%%%%%%%% BEGIN multido.doc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\fileversion{1.2} \def\filedate{92/10/12} % % DESCRIPTION: % multido.tex/multido.sty contains a loop macro, \multido, that supports % fixed point addition and has a nice interface. Among other things, it % is useful for pictures and putting numbers on axes. multido.tex % is compatible with most TeX macro packages, including Plain TeX, LaTeX, % AmSTeX, and Ams-LaTeX. % % INSTALLATION: % This file can be used as the input file. However, stripped input files % will load faster. To extract these files and typeset the documentation, % uncomment this line: %{}\let\endinput\relax % Plus one or more of the next three lines: %{}\let\PrintUsage\relax % To typeset Usage Notes. %{}\let\PrintCode\relax % To typeset Usage Notes and code. %{}\let\ExtractFiles\relax % To extract stripped multido.tex/multido.sty. % (Each line should still begin with {}) % To print Usage Notes and/or Code, you must use LaTeX. % To extract files only, you can use Plain TeX or LaTeX. % To typeset code, you must have Frank Mittelbach's doc.sty, preferably % v1.7k (or later?), and gind.ist to make an index with % makeindex -s gind.ist multido.idx , if desired. % % CHANGES: % % V1.1: Fixed bug in FPadd that gave wrong answer for, e.g., 3.4 + -0.2. % % V1.2: Make unit optional for dimension variables when using PSTricks. % %--------------------------- BEGIN DOCUMENTED CODE ------------------------- %% %% File multido.tex, for use with Generic TeX. %% %% COPYRIGHT 1992, by Timothy Van Zandt, tvz@Princeton.EDU %% %% Copying of part or all of this file is allowed under the following %% conditions only: %% (1) You may freely distribute unchanged copies of the file. Please %% include the documentation when you do so. %% (2) You may modify a renamed copy of the file, but only for personal %% use or use within an organization. %% (3) You may copy fragments from the file, for personal use or for %% distribution, as long as credit is given where credit is due. %% %% You are NOT ALLOWED to take money for the distribution or use of %% this file or modified versions or fragments thereof, except for %% a nominal charge for copying etc. %% % \fi % \CheckSum{528} % \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 \~} % % Yes, the documentation is pretty scimpy. % % These macros use \TeX{} primitives, plus the Plain \TeX{} commands: % \begin{quote} % "\dimen@", "\dimen@i", "\count@", "\newcount", "\newtoks", "\@ne", % "\tw@", and "\@z@". % \end{quote} % % Check whether file has been loaded already. % \begin{macrocode} \expandafter\ifx\csname multido@\endcsname\relax\else \expandafter\endinput \fi % \end{macrocode} % % Identify the file on the terminal: % \begin{macrocode} \message{\space\space v\fileversion\space\space \filedate\space\space } % \end{macrocode} % % Take care of the catcode of "@": % \begin{macrocode} \edef\MultidoAtCode{\the\catcode`\@} \catcode`\@=11 % \end{macrocode} % % These are some hacks borrowed from PSTricks, which are loaded if PSTricks is % not being used. "\@dimtonum" strips the value of "#1", a dimension register, % of the "pt", and assigns the result to "#2", a command sequence. % \begin{macrocode} \expandafter\ifx\csname @pstrickserr\endcsname\relax \def\@empty{} \def\@nnil{\@nil} \def\@dimtonum#1#2{\edef#2{\@@dimtonum#1}} \def\@@dimtonum#1{\expandafter\@@@dimtonum\the#1} {\let\@nnil\expandafter\catcode`\p=12\catcode`\t=12 \global\@nnil\def\csname @@@dimtonum\endcsname#1pt{#1}} \fi % \end{macrocode} % % \begin{macro}{\multido@count,\multidocount} % "\multido@count" stores the number of repetitions. "\multidocount" keeps % track of the iteration. These are also used locally as scratch counters by % "\FPadd@". % \begin{macrocode} \newcount\multido@count \newcount\multidocount % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@stuff} % "\multido@stuff" is used to store the \m{stuff} that is to be repeated. % \begin{macrocode} \newtoks\multido@stuff % \end{macrocode} % \end{macro} % % \begin{macro}{\multido,\mmultido,\Multido,\MMultido} % \begin{macrocode} \def\multido{\multido@{}{\begingroup}{\endgroup}} \def\mmultido{\multido@{\multido@stepvar}{\begingroup}{\endgroup}} \def\Multido{\multido@{}{}{}} \def\MMultido{\multido@{\multido@stepvar}{}{}} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@} % "\multido@initvar" processes the variable declarations, initializing the % value of the variables and defining "\multido@stepvar" to increment the % variables with each repetition. "\multido@count" is set to the number of % repetitions. % \begin{macrocode} \def\multido@#1#2#3#4#5#6{%\ #2% \multido@count=#5\relax \def\multido@stepvar{}% \def\do{\noexpand\do\noexpand}% \multido@initvar#4,\@nil,% \let\do\noexpand \edef\multido@stepvar{\multido@stepvar}% \ifnum\multido@count<\z@\multido@count=-\multido@count\fi \multidocount=1\relax #1% \multido@stuff{#6}% \multido@loop #3% \ignorespaces} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@loop} % "\multido@loop" does the repetition. % \begin{macrocode} \def\multido@loop{% \the\multido@stuff \ifnum\multidocount<\multido@count \advance\multidocount\@ne \multido@stepvar \expandafter\multido@loop \fi} % \end{macrocode} % \end{macro} % % \begin{macro}{\multidostop} % \begin{macrocode} \def\multidostop{\multidocount=\multido@count} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@initvar,\multido@@initvar,\multido@getvartype} % "\multido@initvar" passes each variable declaration to "\multido@@initvar". % \begin{macrocode} \def\multido@badvar{% \multido@count=0 \errhelp{\multido command will be skipped.}% \errmessage{Bad \string\multido\space variable declaration}} \def\multido@initvar#1,{% \def\multido@temp{#1}% \ifx\multido@temp\@nnil\else \ifx\multido@temp\@empty\else \multido@@initvar#1\@nil=+\@nil\relax \fi \expandafter\multido@initvar \fi} \def\multido@@initvar#1=#2+#3\@nil#4\relax{% \ifx\@empty#4\@empty \multido@badvar \else \multido@vartype#1\@empty \ifx\multido@temp\relax \multido@badvar \else \multido@temp{#2}{#3}#1% \fi \fi} \def\multido@vartype#1{% \ifcat\noexpand\@nil\noexpand#1% \expandafter\multido@@vartype\string#1\@nil \else \let\multido@temp\relax \fi} \def\multido@@vartype#1#2#3\@nil{% \expandafter\let\expandafter\multido@temp \csname multido@init@#2\endcsname} % \end{macrocode} % \end{macro} % % \begin{macro}{\MultidoCheckNames} % \begin{macrocode} \def\MultidoCheckNames{% \let\multido@@@vartype\multido@vartype \def\multido@vartype##1{% \ifx\undefined##1% \multido@@@vartype{##1}% \else \errhelp{\multido command will be skipped.}% \errmessage{Multido variable \string##1 already defined}% \let\multido@temp\relax \fi}} % \end{macrocode} % \end{macro} % % For each variable type, we must now define "\multido@init"\m{vartype}. The % syntax of these macros is: % \begin{quote}\tt % "\multido@init@"\m{vartype}\M{initial value}\M{increment}\M{variable} % \end{quote} % and the outcome should be: % \begin{enumerate} % \item Set \m{variable} to the initial value. % \item Invoke "\multido@addtostep"\M{step stuff}, where \m{step stuff} is % whatever should be done to increment the variable. \M{step stuff} is % expanded first, with expansion suppressed by "\do". % \end{enumerate} % % \begin{macro}{\multido@addtostep} % \begin{macrocode} \def\multido@addtostep#1{\edef\multido@stepvar{\multido@stepvar#1}} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@init@d,\multido@init@D,\multido@step@d} % We start with the variable type for dimensions ("d", "D"). % \begin{macrocode} \def\multido@init@d#1#2#3{% \expandafter\ifx\csname pssetlength\endcsname\relax \dimen@=#1\relax\dimen@i=#2\relax \else \pssetlength\dimen@{#1}\pssetlength\dimen@i{#2}% \fi \edef#3{\number\dimen@ sp}% \ifnum\multido@count<\z@\dimen@i=-\dimen@i\fi \multido@addtostep{\do\multido@step@d{\do#3}{\number\dimen@i sp}}} \def\multido@step@d#1#2{% \dimen@=#1\advance\dimen@#2 \edef#1{\number\dimen@ sp}}% \def\multido@init@D{\multido@init@d} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@init@i,\multido@init@I,\multido@step@i} % Now the variable type for integers ("i", "I"). % \begin{macrocode} \def\multido@init@i#1#2#3{% \count@=#1\relax \edef#3{\the\count@}% \count@=#2\relax \ifnum\multido@count<\z@\count@=-\count@\fi \multido@addtostep{\do\multido@step@i{\do#3}{\the\count@}}} \def\multido@step@i#1#2{% \count@=#1\advance\count@ by #2 \edef#1{\the\count@}} \def\multido@init@I{\multido@init@i} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@init@r,\multido@init@R,\multido@step@r} % Now the variable type for reals ("r", "R"). % \begin{macrocode} \def\multido@init@r#1#2#3{% \dimen@=#1pt \@dimtonum\dimen@#3% \dimen@=#2pt \ifnum\multido@count<\z@\dimen@=-\dimen@\fi \multido@addtostep{\do\multido@step@r{\do#3}{\number\dimen@ sp}}} \def\multido@step@r#1#2{% \dimen@=#1pt\advance\dimen@#2 \@dimtonum\dimen@#1} \def\multido@init@R{\multido@init@r} % \end{macrocode} % \end{macro} % % \begin{macro}{\multido@init@n,\multido@step@n} % Now the variable type for numbers ("n", "N"). % \begin{macrocode} \def\multido@init@n#1#2#3{% \edef#3{#1}% \ifnum\multido@count<\z@\expandafter\FPsub\else\expandafter\FPadd\fi {0}{#2}\multido@temp \multido@addtostep{\do\FPadd{\do#3}{\multido@temp}{\do#3}}} \def\multido@init@N{\multido@init@n} % \end{macrocode} % \end{macro} % % \begin{macro}{\FPadd,\FPsub} % Simple fixed-point addition couldn't be harder. "\dimen@" and "\dimen@i" are % used as scratch {\em counters} (to avoid creating a new counter). "\count@", % "\multido@count" and "\multidocount" are also used as scratch counters. % % This is probably pretty optimal, given the requirements that leading and % trailing spaces be OK in the arguments, and that there need not be any % numbers to the left of the decimal. % \begin{macrocode} \def\FPadd#1#2#3{% \edef\multido@temp{#1..\noexpand\@nil#2}% \expandafter\FPadd@\multido@temp..\@nil \let#3\multido@temp} \def\FPsub#1#2{% \edef\multido@temp{\noexpand\FPsub@#2\noexpand\@empty}% \FPadd{#1}{\multido@temp}} \def\FPsub@#1{\ifx-#1\else-#1\fi} \def\FPadd@#1.#2.#3\@nil#4.#5.#6\@nil{% \begingroup \def\multido@temp{\let\next\relax}% \let\next\z@ \afterassignment\multido@temp\count@=#1\next \dimen@i=0#2sp\relax \let\next\z@ \afterassignment\multido@temp\multido@count=#4\next \multidocount=0#5\relax \dimen@=\number\count@ sp \count@=\@ne \FPadd@@@#500000000\@nil \ifnum#11<\z@ \count@=-\tw@ \dimen@=-\dimen@ \fi \ifnum#41<\z@ \count@=-\count@ \multido@count=-\multido@count \fi \ifnum\count@>\z@ \advance\multido@count\dimen@ \advance\multidocount\dimen@i \ifnum\multidocount<\multido@temp\relax \advance\multidocount\multido@temp\relax \else \advance\multido@count\@ne \fi \advance\count@-3 \else \advance\multido@count-\dimen@ \advance\multidocount-\dimen@i \ifnum\multido@count<\z@ \multido@count=-\multido@count \multidocount=-\multidocount \advance\count@\@ne \else \ifnum\multido@count=\z@ \ifnum\multidocount<\z@ \multidocount=-\multidocount \advance\count@\@ne \fi \fi \fi \ifnum\multidocount<\z@ \advance\multidocount\multido@temp \advance\multido@count-\@ne \fi \advance\multidocount\multido@temp\relax \fi \expandafter\FPadd@@\the\multidocount\@empty\@nil \endgroup} \def\FPadd@@#1#2#3\@nil{\xdef\multido@temp{% \ifnum\count@=-1-\fi \the\multido@count\ifx#2\@empty\else.#2#3\fi}} \def\FPadd@@@#1#2#3#4#5#6#7#8#9\@nil{\def\multido@temp{1#9}} % \end{macrocode} % % \end{macro} % \begin{macrocode} \catcode`\@=\MultidoAtCode\relax % \end{macrocode} % % \Finale % \Endinput % \endinput % %%%%%%%%%%%%%%%%%%%%%%%% END DOCUMENTED CODE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \catcode`\@=11 %%%%%%%%%%%%%%%%%%%%%%%% INPUT FILE EXTRACTION %%%%%%%%%%%%%%%%%%%%%%%%%%% \ifx\ExtractFiles\relax\else \begingroup \catcode`\*=0 *catcode`*\=12 *long*def*next#1\relax\relax\relax{*endgroup} *def*do#1{*catcode`#1=12}*dospecials*expandafter*next*fi \fi \def\infile{multido.doc} \def\outfile{multido.tex} \def\styfile{multido.sty} \newread\Infile \newwrite\Outfile \def\typeout{\immediate\write16} \newif\ifflag \def\CheckOK#1#2+{\ifx#1y\flagtrue\else\flagfalse\fi} \def\CheckFile#1{% \typeout{} \typeout{Preparing to make file `#1'.} \immediate\openin1=#1\relax \ifeof1\else \typeout{% File `#1' exists and will be overwritten if in current directory!!!} \fi \typeout{Make `#1'? (y=yes, n=no)} \read16 to\OK \expandafter\CheckOK\OK+} \begingroup \catcode`\{=12 \catcode`\}=12 \catcode`\(=1 \catcode`\)=2 \catcode`\%=12 \gdef\%(%) \gdef\Percent(%%) \gdef\Braces({}) \endgroup \def\temp#1{} \edef\Endinput{\expandafter\temp\string\\endinput} \def\ProcessLine{\expandafter\ProcessLINE\inline\relax\relax\nil} \def\ProcessLINE#1#2#3\nil{% \def\tempa{#1}% \def\tempb{#1#2}% \ifx\tempa\% \ifx\tempb\Percent\owrite\inline\fi \else \ifx\tempb\Braces\else\owrite\inline\fi \fi} \def\owrite#1{\immediate\write\Outfile{#1}} \def\stripfile{% \begingroup \def\do##1{\catcode`##1=12\relax} \dospecials \endlinechar-1 \flagtrue \loop \read\Infile to\inline \ifx\inline\Endinput\flagfalse\fi \ifeof\Infile\flagfalse\fi \ifflag \ProcessLine \repeat \endgroup} \CheckFile{\outfile} \ifflag \immediate\openout\Outfile\outfile\relax \owrite{\%\% This is file `\outfile' generated on \the\year/\the\month/\the\day.} \owrite{\%\% The original source file was `\infile'.} \owrite{\%\%} \immediate\openin\Infile\infile\relax \stripfile \immediate\closein\Infile \owrite{\Endinput} \owrite{\%\%} \owrite{\%\% End of file `\outfile'.} \immediate\closeout\Outfile \fi \expandafter\ifx\csname styfile\endcsname\relax\flagfalse\else \CheckFile{\styfile} \fi \ifflag \immediate\openout\Outfile\styfile\relax \immediate\write\Outfile{\string\input\space \outfile} \immediate\write\Outfile{\Endinput} \immediate\closeout\Outfile \fi \relax\relax\relax %%%%%%%%%%%%%%%%%%% END INPUT FILE EXTRACTION %%%%%%%%%%%%%%%%%%%%%%%%%%% \ifx\PrintUsage\relax \let\next\relax \else \ifx\PrintCode\relax \let\next\relax \else \expandafter\ifx\csname @latexerr\endcsname\relax \let\next\end\else\let\next\@@end \fi \fi \fi \next %%%%%%%%%%%%%% BEGIN PREAMBLE FOR DOCUMENATION %%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% \let\FileVersion\fileversion \let\FileDate\filedate %% \documentstyle[12pt]{article} \makeatletter %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% DOC? STUFF %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Check whether doc.sty has been input. If not, code won't be printed. %% \CodeLineIndex can only be used in preamble. Other code-specific %% preamble stuff has been left to the end of this file. %% \ifx\PrintCode\relax\@input{doc.sty}\CodelineIndex\else \def\StopEventually{\end{document}} \fi %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%% PAGE PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \setlength{\parindent}{0pt} % paragraph indent \setlength{\parskip}{4pt plus 1pt minus 1pt} \setlength{\oddsidemargin}{4pc} \setlength{\evensidemargin}{4pc} \setlength{\topmargin}{-2.5pc} \setlength{\headheight}{12pt} % height of running head \setlength{\headsep}{20pt} % distance between header and text \setlength{\textheight}{54pc} % height of text on page \setlength{\textwidth}{35pc} % total width of a page %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% VERBATIM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% This is good for examples, using \verb or whatever explicitly. \def\Ex{\quote\tt} \def\endEx{\endquote} %% %% In the verbatim environment, \trivlist is changed to \list, so that %% verbatim code is offset from the left margin. %% \def\@verbatim{% \list{}{} \item[]% \leftskip\@totalleftmargin\rightskip\z@ \parindent\z@\parfillskip\@flushglue \@@par\leavevmode\parskip=\z@ \def\par{\leavevmode\null\@@par}% \obeylines \let\do\@makeother \dospecials\catcode`\>=14\tt} \def\endverbatim{\endlist} %% \def\m#1{{\rm\it #1}} % For just putting things in italics (m=>meta>) \def\M#1{{\tt\{}\m{#1}{\tt\}}} % Argument is in italic, enclosed in tt braces. \def\N#1{{\tt\string#1}} % For in-line macro names \catcode`\>=13\def>{} % Now we can write \LaTeX> without problem. %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% SECTIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Section headings use customizable fonts, leave less space above %% and below, and may overhang on left. %% \def\section{\@startsection{section}{1}{\sechang}{-3ex plus -1ex minus -.2ex}{1.5ex plus .2ex}{\secfont}} \def\subsection{\@startsection{subsection}{2}{\subsechang}{-2.75ex plus -1ex minus -.2ex}{1.25ex plus .2ex}{\subsecfont}} \newdimen\sechang \newdimen\subsechang \sechang=-.6in \subsechang=-.375in \def\secfont{\Large\bf} % Section headings \def\subsecfont{\tt\large} % Subsection heading %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%% DATES, VERSIONS AND TITLES %%%%%%%%%%%%%%%%%%%%%%%%%%% %% \def\expanddate#1/#2/#3/{\number#3{} \month=#2 \ifcase\month\or January \or February \or March \or April \or May \or June \or July \or August \or September \or October \or November \or December \fi 19#1} \def\thefiledate{\expandafter\expanddate\FileDate/} \date{Version \FileVersion\\ \thefiledate} \def\@maketitle{\newpage \null \begin{center} {\Large\bf \@title \par} \vskip 1.2em {\lineskip .5em \begin{tabular}[t]{c}\@author\end{tabular}\par} \vskip .8em {\@date}% \end{center} \par \vskip .5em} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% PAGE STYLE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \pagestyle{myheadings} \markright{Documentation for multido.tex \hfill v.\FileVersion\hskip 1em \thefiledate\hfill}% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%% END PREAMBLE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \catcode`\"=13 \def"{\verb"} \catcode`\@=12 \begin{document} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title{Documentation for multido.tex:\\[2pt] A loop macro for Generic \protect\TeX} \author{Timothy Van Zandt% \thanks{Author's address: Department of Economics, Princeton University, Princeton, NJ 08544-1021, USA. Internet: {\tt tvz@Princeton.EDU}}} \maketitle \section{Usage notes} "multido.tex"/"multido.sty" contains the \N\multido> macro, which is a loop facility for Generic TeX. This macro happens to be useful for drawing pictures, and was originally developed for the PSTricks package,\footnote{PSTricks is an extensive collection of PostScript-based macros for Generic TeX. It is available from the /pub directory at Princeton.EDU, and \TeX> archives.} but you can use it for other purposes as well. A special feature is support of fixed-point addition. For example, PSTricks uses the \N\multido> to put numbers on axes, much like in the following \LaTeX> example: \begin{verbatim}> \setlength{\unitlength}{1cm} \small \begin{picture}(8,1)(0,-.5) \put(0,0){\vector(1,0){8}} \multido{\i=0+1,\n=0+0.25}{8}{% \put(\i,-.1){\line(0,1){.2}} \put(\i,-.2){\makebox(0,0)[t]{\n}}} \end{picture} \end{verbatim} \begin{center}\leavevmode \setlength{\unitlength}{1cm} \small \begin{picture}(8,1)(0,-.5) \put(0,0){\vector(1,0){8}} \multido{\i=0+1,\n=0+0.25}{8}{% \put(\i,-.1){\line(0,1){.2}} \put(\i,-.2){\makebox(0,0)[t]{\n}}} \end{picture} \end{center} The general syntax for \N\multido> is: \begin{Ex} "\multido"\M{variables}\M{repetitions}\M{stuff} \end{Ex} \m{stuff} is whatever you want repeated; it can be any balanced \TeX{} input. \m{repetitions} is the number times \m{stuff} is repeated. The first argument is the interesting one. \m{variables} is a comma-separated list of variable declarations.\footnote{Don't use commas to mark the decimal point within the \protect\m{variables} argument, as they will be confused for delimiters.} Each variable declaration is of the form: \begin{center}\em variable "=" initial value "+" increment \end{center} \m{variable} is a command sequence that can be used in \m{stuff}. It is initially set to {\em initial value}, and is then incremented by {\em increment} with each repetition. The first letter of the variable name determines the variable type. There are four variable types: \begin{description} \item[Dimension (d or D)] The initial value and the increment should be dimensions (lengths, in \LaTeX> parlance). The substitution text is a dimension, with "sp" units. E.g., "\dx=4cm+5pt".\footnote{For PSTricks users, the unit is optional.} \item[Number (n or N)] The initial value and increment should be integers or numbers with the same number of digits to the right of the decimal. The one exception is that it is always OK for the initial value to be an integer. There can be at most 8 digits on each side of the decimal. The substitution text is a number, with fixed-point addition. E.g., "\n=3+7.05", "\Nx=5.30+-1.25". \item[Integer (i or I)] The initial value and increment should be integers. This gives the same result as using a number variable, but it is faster. E.g., "\I=2+-1". \item[Real (r or R)] The initial value and increment should be integers or numbers with at most 4 digits on each side of the decimal. The substitution text is a number, but with floating point addition and occasional small errors. This gives a less satisfactory result than using a number variable, but it is faster. E.g., "\ry=4.2+1.05". \end{description} Here are some examples that illustrate how the substitution text is determined: \begin{quote} "\multido{}{10}{\TeX\ }"\\[3pt] \hbox to 2em{}\multido{}{10}{\TeX\ }{}\\[8pt] "\multido{\d=2pt+3pt}{5}{\d, }"\\[3pt] \hbox to 2em{}\multido{\d=2pt+3pt}{5}{\d, }{}\\[8pt] "\multido{\n=2+3}{10}{\n, }"\\[3pt] \hbox to 2em{}\multido{\n=2+3}{10}{\n, }{}\\[8pt] "\multido{\i=2+-3}{10}{\i, }"\\[3pt] \hbox to 2em{}\multido{\i=2+-3}{10}{\i, }{}\\[8pt] "\multido{\r=2+3.05}{6}{\r, }"\\[3pt] \hbox to 2em{}\multido{\r=2+3.05}{6}{\r, }{}\\[8pt] "\multido{\n=2.00+-3.05}{8}{\n, }"\\[3pt] \hbox to 2em{}\multido{\n=2.00+-3.05}{8}{\n, }{} \end{quote} Here are some details about the choice of names: \begin{itemize} \item Your computer won't explode if you use names that conflict with \TeX> internal commands, but you might want to check name conflicts if you get inexplicable errors. The command "\MultidoCheckNames" can be useful in this case. It causes \N\multido> to report an error whenever you use a variable name that is already defined. But see the next item. \item The whole \N\multido> loop is grouped. This means, e.g., that although "\i" is a Plain \TeX{} command sequence (giving a dotless ``\i''), you can use the variable "\i" if you do not use any dotless i's in \m{stuff} (and if you do not use "\MultidoCheckNames"). \end{itemize} Here are a few more details: \begin{itemize} \item \N\Multido> commands can be nested. \item Spaces after a \N\multido> command are ignored. This makes \N\multido> more hospitable for pictures. \item Spaces between the various parts of the \m{variables} argument are ignored. \end{itemize} And finally here a few special features, some of which are of interest mainly macro writers and other \TeX nicians: \begin{itemize} \item The material that is repeated is not grouped, so that you can insert your own recursive routines. \item There is a variant, "\mmultido", which works just like "\multido" except that the variables are all incremented once before starting. \item There are variants, "\Multido" and "\MMultido" of "\multido" and "\mmultido", resp., that do not group the whole loop. This can be useful, e.g., for making entries in an alignment environment. However, these cannot be nested within any "\multido" macro. \item If the number of repetitions is a negative number, the variables are incremented backwards. \item The count register "\multidocount" keeps track of the number of current iteration. \item The command "\multidostop" causes the "\multido" loop to quit at the end of the current iteration. \item Fixed point addition is performed by \N\FPadd> and \N\FPsub: \begin{Ex} "\FPadd"\M{num1}\M{num2}\M{\string\cs}\\ "\FPsub"\M{num1}\M{num2}\M{\string\cs} \end{Ex} \m{num2}\/ is added to or subtracted from \m{num1}, and the answers is stored in the command sequence given as the third argument. The rules about decimals and so on that apply to number variables apply here as well. E.g., after \begin{Ex} "\FPsub{1.75}{-0.15}{\answer}" \end{Ex} the definition of "\answer" is 1.90. \end{itemize} \clearpage %%%%%%%%%%%%%%%%%% STOP HERE IF DOC.STY NOT INPUT%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \StopEventually{} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%% BEGIN CODE-SPECIFIC PREAMBLE %%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \catcode`\@=11 %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%% CHANGE TO MACRO ENVIRONMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% A change to the doc.sty's macro environment. %% Prints macro names like subsections, instead of as marginal notes. %% Argument is comma separated list of macro names. %% No nested macro environments. %% %% WHY: Don't need as many \begin{macro} ... \end{macro}. %% Works even there isn't anything between \begin{macro} and %% \begin{macrocode}. %% \newif\iffirst@macroname \newif\ifnestedmacro \def\macro{% \ifnum\macro@level=\z@ \def\next{\MakePrivateLetters \m@cro@}% \else \def\next{\@latexerr{Nested \string\begin{macro}}\@eha \endgroup\end{macro}\macro@level=\z@\begin{macro}} \fi \next} \def\m@cro@#1{% \first@macronametrue \m@@cro@@#1,\@nil,} \def\m@@cro@@#1,{% \def\@tempa{#1}\def\@tempb{\@nil}% \ifx\@tempa\@tempb \let\next\finishm@@cro@@ \else {\advance\c@CodelineNo\@ne\SpecialMainIndex{#1}\nobreak}% \DoNotIndex{#1}% \iffirst@macroname \edef\saved@macronames{\string#1}% \first@macronamefalse \else \def\comma{\noexpand\comma}% \edef\saved@macronames{\saved@macronames\comma\string#1}% \fi \let\next\m@@cro@@ \fi \next} \def\finishm@@cro@@{% \advance\macro@level\@ne \def\comma{{\rm, }}% \subsection*{\tt\saved@macronames}} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%% DO NOT INDEX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \DoNotIndex{\ ,\!,\[,\\,\],\^,\`,\{,\},\~} \DoNotIndex{\@ifundefined,\@namedef,\@spaces,\@tempa,\@tempb} \DoNotIndex{\@warning,\active} \DoNotIndex{\begingroup,\catcode,\char,\csname,\def,\do} \DoNotIndex{\docdate,\dospecials,\edef,\else,\endcsname,\endgroup} \DoNotIndex{\expandafter,\fi,\filedate,\fileversion} \DoNotIndex{\gdef,\if,\ifcat} \DoNotIndex{\ifx,\immediate,\lccode,\let} \DoNotIndex{\lowercase,\next,\noexpand} \DoNotIndex{\relax,\space,\the} \DoNotIndex{\toks@,\count@,\dimen@,\dimen@ii} \DoNotIndex{\theatcode,\string,\t,\@empty,\@nil,\@nnil,\advance} \DoNotIndex{\dimen@i,\@,\endinput,\errhelp,\errmessage,\global,ifnum} \DoNotIndex{\p,\number,\newtoks,\ignorespaces,\message,\multido@temp} \DoNotIndex{\newcount,\xdef,\z@,\@ne,\tw@,\number,\undefined,\ifnum} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%% OTHER DOC PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \setcounter{IndexColumns}{2} % two column index; %\DisableCrossrefs \EnableCrossrefs \IndexPrologue{This index is only for the documented code. Underlined numbers refer roughly to the line number of the entry's definition, and all others indicate code lines where it is used.} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%% END CODE-SPECIFIC PREAMBLE %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% \catcode`\@=12 %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Documented code} \def\Endinput{\clearpage\PrintIndex\end{document}} \DocInput{multido.doc} %%%%%%%%%%%%%%%%%%% END DOCUMENTATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% END multido.doc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%