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%% $Id: multido.tex 317 2010-05-14 21:54:15Z herbert $
%% BEGIN multido.tex
%%
\def\fileversion{1.42}
\def\filedate{2010/05/14}
%%
%% COPYRIGHT 1993, 1994, 1999 by Timothy Van Zandt, tvz@nwu.edu.
%% Version 1.41 (2004) prepared by Rolf Niepraschk <Rolf.Niepraschk@gmx.de>
%% Herbert Voss <hvoss@tug.org>
%% COPYRIGHT 2010 by Herbert Voss <hvoss@tug.org>
%%
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN
%% archives in directory macros/latex/base/lppl.txt.
%%
%% 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.
%%
%% CODE:
% These macros use TeX primitives, plus the Plain TeX commands:
% \dimen@, \dimen@i, \count@, \newcount, \newtoks, \@ne, \tw@, \@z@.
%
% Check if file is loaded, announce file on terminal, and take care of @:
%
\message{ v\fileversion, \filedate\space <tvz>}
\csname MultidoLoaded\endcsname
\let\MultidoLoaded\endinput
\edef\TheAtCode{\the\catcode`\@}
\catcode`\@=11
% These are some useful hacks. "\multido@dimtonum" strips the value of "#1",
% a dimension register, of the "pt", and assigns the result to "#2",
% a command sequence.
\def\@empty{}
\def\@nnil{\@nil}
\def\multido@dimtonum#1#2{\edef#2{\multido@@dimtonum#1}}
\def\multido@@dimtonum#1{\expandafter\multido@@@dimtonum\the#1}
\edef\next{%
\noexpand\def\noexpand\multido@@@dimtonum##1\string p\string t{##1}}
\next
% "\multido@count" stores the number of repetitions. "\multidocount" keeps
% track of the iteration. These are also used locally as scratch counters
% by "\FPadd@". "\multido@stuff" is used to store the <stuff> that is
% to be repeated.
\newcount\multido@count
\newcount\multidocount
\newtoks\multido@stuff
\def\multido{\multido@{}{\begingroup}{\endgroup}}
\def\mmultido{\multido@{\multido@stepvar}{\begingroup}{\endgroup}}
\def\Multido{\multido@{}{}{}}
\def\MMultido{\multido@{\multido@stepvar}{}{}}
% "\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.
\long\def\multido@#1#2#3#4#5#6{%
#2%
\multido@count=#5\relax
\ifnum\multido@count=\z@\else\multido@@{#1}{#4}{#6}\fi
#3%
\ignorespaces}
\def\multido@@#1#2#3{%
\def\multido@stepvar{}%
\def\do{\noexpand\do\noexpand}%
\multido@initvar#2,\@nil,%
\let\do\noexpand
\edef\multido@stepvar{\multido@stepvar}%
\ifnum\multido@count<\z@\multido@count=-\multido@count\fi
\multidocount=1\relax
#1%
\multido@stuff{#3}%
\multido@loop}
\def\multido@loop{%
\the\multido@stuff
\ifnum\multidocount<\multido@count
\advance\multidocount\@ne
\multido@stepvar
\expandafter\multido@loop
\fi}
\def\multidostop{\multidocount=\multido@count}
\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}
\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}}
% For each variable type, we must now define \multido@init<vartype>.
% The syntax of these macros is:
%
% \multido@init@<vartype>{initial value}{increment}{variable}
%
% and the outcome should be:
%
% 1. Set <variable> to the initial value.
% 2. Invoke \multido@addtostep{step stuff}, where <step stuff> is
% whatever should be done to increment the variable. <step stuff> is
% expanded first, with expansion suppressed by "\do".
\def\multido@addtostep#1{\edef\multido@stepvar{\multido@stepvar#1}}
% Variable type for dimensions ("d", "D"):
\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}
% Variable type for integers ("i", "I"):
\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}
% Variable type for reals ("r", "R").
\def\multido@init@r#1#2#3{%
\dimen@=#1pt
\multido@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
\multido@dimtonum\dimen@#1}
\def\multido@init@R{\multido@init@r}
% Variable type for numbers ("n", "N").
\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}
% 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 close to 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.
% RN modification begin -- 2004/05/17; Rolf.Niepraschk@ptb.de
% \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\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}}
\ifx\FPadd\undefined\let\FPadd\fpAdd\let\FPsub\fpSub\fi
% RN modification end
\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}}
\catcode`\@=\TheAtCode\relax
\endinput
%%
%% END multido.tex