Euclidean division of two counters

Question

I'd like to print the remainder of the Euclidean division by 4 of a latex counter. How do I do this?

Answer 1

In OpTeX, you can use \expr macro:

\def\remainderofdiv#1#2{\expr[0]{#1\%#2}}
\remainderofdiv{12}{5}
\bye

or, you can use \directlua directly:

\def\remainderofdiv#1#2{\directlua{tex.print(#1\%#2)}}

If you want to implement \mycountermodfour then you can use the previously defined macro:

\newcount\mycounter
\def\mycountermodfour{\remainderofdiv{\the\mycounter}{4}}
\mycounter=7
\mycountermodfour
\bye

Answer 2

I take it that you are actually looking for calculating a mod b. There is probably a wide range of options how to solve this. Using Expl3 syntax, you could do:

\documentclass{article}
\ExplSyntaxOn
    \NewDocumentCommand{\remainderofdiv}{ m m }{
        \int_mod:nn { #1 } { #2 }
    }
\ExplSyntaxOff
\begin{document}
\remainderofdiv{5}{2}

\remainderofdiv{12}{2}

\remainderofdiv{12}{5}


\end{document}

So, given that you have a counter that contains x and now you want to output x mod 4:

\documentclass{article}
\newcounter{mycounter}
\ExplSyntaxOn
    \NewDocumentCommand{\mycountermodfour}{ }{
        \int_mod:nn { \value{mycounter} } { 4 }
    }
\ExplSyntaxOff
\begin{document}
\setcounter{mycounter}{7}
\mycountermodfour


\end{document}