Wrong date format if datenumber is loaded after datetime

Question

The date format is wrong when datetime and datenumber are used at the same time, datenumber being loaded after datetime.

As can be tested with the following MWE:

\documentclass{article}
\usepackage{datetime}
\usepackage[english]{datenumber}
\begin{document}
\section{Package datenumber}
\begin{itemize}
  \item \setdate{2015}{1}{21}
    \datedate
  \item \setdate{2015}{1}{22}
    \datedate
  \item \setdate{2015}{1}{23}
    \datedate
  \item \setdate{2015}{1}{31}
    \datedate
\end{itemize}

\section{Package datetime}
\begin{itemize}
\item \newdate{21}{21}{1}{2015}
  \displaydate{21}
\item \newdate{22}{22}{1}{2015}
  \displaydate{22}
\item \newdate{23}{23}{1}{2015}
  \displaydate{23}
\item \newdate{31}{31}{1}{2015}
  \displaydate{31}
\end{itemize}
\end{document}

• when datenumber is not loaded, datetime displays the ordinal for 21, 22, 23 and 31 as 21^st, 22^nd, 23^rd and 31^st, as expected with UKenglish;

• when datetime is not loaded, datenumber displays the ordinal for 21, 22, 23 and 31 as 21st, 22nd, 23rd and 31st, as (almost) expected with UKenglish;

• when datenumber and datetime are loaded in this order, the error:

   ! You can't use `the character 2' after \advance.
   <argument> 2
               015
   l.9 \item \setdate{2015}{1}{21}
  

  already reported in datetime and datenumber package conflict? arises;

• when datetime and datenumber are loaded in this order, the ordinal for 21, 22, 23 and 31 are displayed as:

  • 21st, 22nd, 23rd and 31st by datenumber, as (almost) expected with UKenglish;
  • 21^th, 22^th, 23^th and 31^th by datetime, and that's wrong.

Answer 1

Both packages define a \@modulo macro. More precisely datetime requires package fmtcount and get it from there, while datenumber gives its own definition.

$ latexdef -p datetime @modulo

\@modulo:
macro:#1#2->\@DT@modctr =#1\relax \divide \@DT@modctr by #2\relax \multiply \@DT@modctr by #2\relax \advance #1 by -\@DT@modctr 

$ latexdef -p datenumber @modulo

\@modulo:
macro:#1#2->\@nom =#1\relax \@den =#2\relax \divide \@nom by \@den \multiply \@nom by \@den \@den =#1\advance \@den by -\@nom 

This is presumably the source of the incompatibility.

Wrap the loading of datenumber as:

\makeatletter
\let\@modulo@SAVED\@modulo
\usepackage[english]{datenumber}
\let\DATENUMBER@modulo\@modulo
\def\setdaynamebynumber#1{%
  \@tempcnta=#1\relax
  \ifnum\the@startyear=1800\advance \@tempcnta by 1\fi
  \ifnum\the@startyear=1900\advance \@tempcnta by 6\fi
  \ifnum\the@startyear=2000\advance \@tempcnta by 4\fi
  \DATENUMBER@modulo{\the\@tempcnta}{7}%
  \setcounter{datedayname}{\the\@den}%
  \addtocounter{datedayname}{1}%
  \setdayname{\thedatedayname}%
}
\def\ifleapyear#1{%#1 year
  \ifnum#1>1500
    \DATENUMBER@modulo{#1}{100}%
    \ifnum\@den=0
      \DATENUMBER@modulo{#1}{400}%
    \else
      \DATENUMBER@modulo{#1}{4}%
    \fi
  \else
    \DATENUMBER@modulo{#1}{4}%
  \fi
  \ifnum\@den=0
}
\let\@modulo\@modulo@SAVED
\makeatother

It then doesn't matter if you load it before or after datetime.

Answer 2

Define own modulo functions:

\documentclass{article}
\usepackage[english]{datenumber}
\makeatletter 
\let\dn@modulo\@modulo
\makeatother
\usepackage{datetime}
\makeatletter 
\let\dt@modulo\@modulo
\makeatother

\begin{document}
\section{Package datenumber}
\makeatletter 
\let\@modulo\dn@modulo
\makeatother
\begin{itemize}
  \item \setdate{2015}{1}{21}
    \datedate
  \item \setdate{2015}{1}{22}
    \datedate
  \item \setdate{2015}{1}{23}
    \datedate
  \item \setdate{2015}{1}{31}
    \datedate
\end{itemize}

\makeatletter 
\let\@modulo\dt@modulo
\makeatother
\section{Package datetime}
\begin{itemize}
\item \newdate{21}{21}{1}{2015}
  \displaydate{21}
\item \newdate{22}{22}{1}{2015}
  \displaydate{22}
\item \newdate{23}{23}{1}{2015}
  \displaydate{23}
\item \newdate{31}{31}{1}{2015}
  \displaydate{31}
\end{itemize}
\end{document}