\mapstochar without the protuberance on the right side (i.e., a rounded vertical bar)

Question

The \mapstochar character is a vertical bar, with borders slightly rounded and a protuberance on its right-side, in the middle:

I'm trying to get the same symbol, but without the protuberance on the right-side.

I have been through the The Comprehensive LaTeX Symbol List, looked up the definition of \mapstochar (\mathchar"3237), searched this website high and low (for instance, Creating a smaller vertical bar ), but could not find any way of getting a rounded vertical bar.

Answer 1

Picture mode.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}
\makeatletter
\NewDocumentCommand{\smallbar}{}{%
  \mathrel{\mathpalette\smallbar@\relax}%
}
\newcommand{\current@math@font}[1]{%
  \ifx#1\displaystyle\textfont\else
  \ifx#1\textstyle\textfont\else
  \ifx#1\scriptstyle\scriptfont\else
  \scriptscriptfont\fi\fi\fi
}
\newcommand{\smallbar@factor}[1]{%
  \ifx#1\displaystyle 1.135\else
  \ifx#1\textstyle 1.128\else
  \ifx#1\scriptstyle 1.09\else
  1.06\fi\fi\fi
}
\newcommand{\smallbar@}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1\mapstochar$}%
  \dimen0=\smallbar@factor{#1}\ht\z@
  \dimen2=\dimeval{2\fontdimen22\current@math@font{#1} 2 - \dimen0}%
  \mbox{%
    $\m@th#1\mkern1mu
    \begin{picture}(0,\dimen0)
    \roundcap
    \linethickness{\fontdimen8\current@math@font{#1}3}
    \Line(0,\dimen2)(0,\dimen0)
    \end{picture}%
    \mkern1mu$%
  }%
  \endgroup
}
\makeatother
\begin{document}
$\mapstochar,\smallbar$
$\scriptstyle\mapstochar,\smallbar$
$\scriptscriptstyle\mapstochar,\smallbar$
\end{document}