%%%%%%%%%%%%%%%%%%%%%%%%  md-doc.tex  Version 1.0, 92/09/28  %%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%% COPYING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% 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.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DESCRIPTION: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% multido.tex contains a loop macro, \multido, that supports floating
%% 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. Name a copy of the file
%% multido.sty if you want to use as a LaTeX style option.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% GETTING MULTIDO %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% The complete multido.tex distribution is available in .tar.Z form from
%% the /pub directory at Princeton.EDU. multido.tex is also available
%% at various TeX archives. However, all you really need is multido.tex
%% and md-doc.tex.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 %%%%%%%%%%%%%%%%%%%%%%%%%% PRINTING THE DOCUMENTATION
%%%%%%%%%%%%%%%%%%%%%%%% %%
%% multido.tex is also distributed with the documentation already
%% typeset. Check the /pub directory at Princeton.EDU if you can
%% handle  .tar.Z  files.
%%
%% This file contains the Usage Notes, Run with LaTeX with or without NFSS.
%%
%% If you include the doc style option, the documented code
%% in multido.doc is also printed at the end. For this,
%% you must have the files  doc.sty  and  gind.ist  from Frank
%% Mittelbach's doc package (try the /soft/tex/latex-supported/doc
%% directory at  ftp.uni-stuttgart.de ). This documented was originally
%% prepared using v1.7k (92/08/24) of doc.sty.
%%
%% To make an index on UNIX using makeindex, resolve cross-references and
%% give the command:
%%      makeindex -s gind.ist multido.idx
%% and run the file again. The index is only for the documented code.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%  BEGIN PREAMBLE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
\documentstyle[12pt]{article}
\input multido.tex
\catcode`\@=11
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% 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.
%%
\@ifundefined{StopEventually}%
  {\def\StopEventually{\end{document}}}%
  {\CodelineIndex}
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%  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.
%%
%% This is adapted from Mittelbach's doc.sty:
\def\MyShortVerb#1{%
  \expandafter
  \xdef\csname cc\string#1\endcsname{\the\catcode`#1}%
  \begingroup
    \catcode`\~\active  \lccode`\~`#1%
    \lowercase{%
    \global\expandafter\let
       \csname ac\string#1\endcsname~%
    \gdef~{\verb~}}%
  \endgroup
  \global\catcode`#1\active}
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%% 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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
\MyShortVerb\"
\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:
 PSTricks uses "\multdo" internally to put numbers on axes, much like in this
\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[t](0,0){\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".

 \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 the
iterations.
 \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{cs}\\
"\FPsub"\M{num1}\M{num2}\M{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}

\DocInput{multido.doc}

\clearpage

\PrintIndex 

\end{document}