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% \iffalse
% +AMDG This document was begun on 1 May 1202, the
% feast of St. Joseph the Worker, and it
% is humbly dedicated to him and to the Immaculate Heart of
% Mary for their prayers, and to the Sacred Heart of Jesus
% for His mercy.
%
% This document is copyright 2018 by Donald P. Goodman, and is
% released publicly under the LaTeX Project Public License. The
% distribution and modification of this work is constrained by the
% conditions of that license. See
% http://www.latex-project.org/lppl.txt
% for the text of the license. This document is released
% under version 1.3c of that license, and this work may be distributed
% or modified under the terms of that license or, at your option, any
% later version.
%
% This work has the LPPL maintenance status 'maintained'.
%
% The Current Maintainer of this work is Donald P. Goodman
% (dgoodmaniii@gmail.com).
%
% This work consists of modulus.dtx, modulus.ins, and
% derived files modulus.sty and modulus.pdf.
% \fi
% \iffalse
%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
%<package>\ProvidesPackage{modulus}[2018/05/07 v1.0 Modulus/modulo operator in plain TeX]
%<*driver>
\documentclass{ltxdoc}
\usepackage{doc}
\usepackage{modulus}
\usepackage{booktabs}
\begin{document}
\DocInput{modulus.dtx}
\end{document}
%</driver> \fi
%
% \title{The |modulus| Package, v1.0}
% \author{Donald P.\ Goodman III}
% \date{\today}
%
% \maketitle
%
% \begin{abstract}
% \noindent
% \TeX\ (traditional \TeX, not even $\epsilon$-\TeX) has the four
% basic functions with |\advance|, |\multiply|, and
% |\divide|, though these are all integer operations. This
% tiny package makes a modulus operator usable with \TeX\
% (or \LaTeX, and probably most flavors). It also provides a
% non-destructive way of
% getting at the integer quotient of two numbers.
% \end{abstract}
%
% \tableofcontents
%
% \section{The Operators}
%
% One question immediately occurs to me: why bother with
% such a package, when $\epsilon$-\TeX\ already has
% |\numexpr|, and there are so many advanced packages
% providing real math, and even floating-point operations
% and bignums? The answer is twofold: (1) an interesting
% project, and (2) \TeX\ is the archival format, as Knuth
% has always emphasized, and so doing things in ordinary
% \TeX, where possible, should be preferred, to keep it
% such.
%
% The core of the package is \DescribeMacro{\modulo}|\modulo|:
%
% \begin{center}
% \cmd{\modulo} \marg{dividend} \marg{divisor}
% \end{center}
%
% Running this will assign the remainder of the integer
% division of \textit{dividend} and \textit{divisor} to the
% counter \DescribeMacro{\remainder}|\remainder|. The
% values of \textit{dividend} and \textit{divisor} will not
% be changed, if they are changeable (e.g., if they are
% counters).
%
% Note that the package works with plain \TeX\ counters,
% \emph{not} \LaTeX-style counters created and set with
% |\newcounter{counter}| and friends. If you try to
% use it with |\thecounter| or |\value{counter}| in the
% \LaTeX\ style, it will not work. Fortunately, plain-\TeX\
% counters are perfectly usable within \LaTeX.
%
% We can use the macro as such:
%
% \begin{quote}
% |\modulo{\the\dividend}{\the\divisor}\the\remainder|
% \end{quote}
%
% This will execute the macro and print the resulting
% remainder. We can also use simple number tokens in the
% same way:
%
% \begin{quote}
% |\modulo{8}{3}\the\remainder|: \modulo{8}{3}\the\remainder
% \end{quote}
%
% In the table above, the divisor is always the
% value of a counter |\testdivisor|, which is 4; the
% dividend is the value of a counter |\testdividend|, which
% is reset as indicated in each line. We then do the
% modulus operation and print the value of |\remainder| in
% the ``Modulus'' column. We then reprint the values of
% |\testdividend| and |\testdivisor|, to show that we have
% not altered them by taking the remainder.
%
% \newcount\testdivisor\testdivisor=4
% \newcount\testdividend
%
% \begin{table}[t]
% \centering
% \begin{tabular}{ccccc}
% \toprule
% Dividend & Divisor & Modulus & Dividend & Divisor \\
% \midrule
% \global\testdividend=1\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=2\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=3\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=4\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=5\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=6\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=7\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=8\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \global\testdividend=9\leavevmode\the\testdividend & \the\testdivisor &
% \modulo{\the\testdividend}{\the\testdivisor}\the\remainder &
% \the\testdividend & \the\testdivisor \\
% \bottomrule
% \end{tabular}
% \caption{A few example modulos, dividend and divisor both
% before and after the operation.}
% \label{tab:ex}
% \end{table}
%
% Plain \TeX\ can also very simply take the integer quotient
% of a counter, with the |\divide| operator, like so:
%
% \begin{quote}
% |\divide\thiscounter by4|
% \end{quote}
%
% However, this destroys the original value of
% |\thiscounter| (or whatever else one is dividing). The
% |modulus| package therefore also provides another macro,
% \DescribeMacro{\quotient}|\quotient|, which
% non-destructively takes the integer quotient of two
% numbers and stores it in the counter
% \DescribeMacro{\intquotient}|\intquotient|:
%
% \begin{quote}
% |\quotient{365}{4}\leavevmode\the\intquotient|: \quotient{365}{4}\leavevmode\the\intquotient\\
% |\modulo{365}{4}\leavevmode\the\remainder|: \modulo{365}{4}\leavevmode\the\remainder
% \end{quote}
%
% Note that if |\the\thecounter| doesn't print as expected,
% it may be because you're still in vertical mode (the
% |\the| operator only works in horizontal mode), so try
% |\leavevmode| before printing the counter.
%
% \section{Implementation}
%
% Not much to this one. We define our counter to hold the
% eventual modulus:
% \begin{macrocode}
\newcount\remainder%
% \end{macrocode}
% Then we define the macro which will assign the modulus to
% that counter:
% \begin{macrocode}
\def\modulo#1#2{%
\remainder=#1%
\divide\remainder by#2%
\multiply\remainder by#2%
\multiply\remainder by-1%
\advance\remainder by#1\relax%
}%
% \end{macrocode}
% Then, for good measure, we also have a macro which will
% non-destructively take the integer quotient of a division, and
% store it in the counter |\intquotient|:
% \begin{macrocode}
\newcount\intquotient%
\def\quotient#1#2{%
\intquotient=#1%
\divide\intquotient by#2%
}%
% \end{macrocode}
% Happy \TeX{}ing!
|
