Big Parenthesis with a Vertical Line in it

Question

I need to type \big( but with a vertical line in it, either in the middle, or end-to-end (would prefer having both options). To clarify, I need something along the lines of \llparenthesis (package stmaryrd), but of exact size \big(. For some obscure reason about delimiters \big\llparenthesis fails to work, but \bigllbracket does work. I did find a temporary work-around using \scaleobj{1.1}{\llparenthesis} (package scalerel), which is visibly smaller in height than \big(. To summarize, below is a picture showing how things are, and how I want them to be. Obviously I need a right-parenthesis version as well. Thanks, Piotr.

Answer 1

Updated 2: This solution is meant to be used with Computer Modern and Latin Modern math fonts only.

\documentclass[12pt]{article}
\newcommand{\lstruck}{\mathopen{\Big(\kern-.475ex\Big\vert}}
\newcommand{\rstruck}{\mathclose{\Big\vert\kern-.475ex\Big)}}
\newcommand{\parstruck}[1]{\lstruck #1\rstruck}
\newcommand{\lmstruck}{\mathopen{\Big(\kern-.8ex\big\vert}}
\newcommand{\rmstruck}{\mathclose{\big\vert\kern-.8ex\Big)}}
\newcommand{\nparstruck}[1]{\lmstruck #1\rmstruck}
\begin{document}
\phantom{\texttt{n}}\verb|\parstruck|: $\parstruck{aBf(x)g}$
\verb|\nparstruck|: $\nparstruck{aBf(x)g}$
\end{document}

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Updated 1

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This is an improved of my previous answer:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\newcommand{\lstruck}{\Bigl(\mkern-4mu{\Big\lvert}}
\newcommand{\rstruck}{{\Big\rvert}\mkern-4mu\Bigr)}
\newcommand{\lmstruck}{\Bigl(\mkern-7.1mu{\bigl\lvert}}
\newcommand{\rmstruck}{{\bigr\rvert}\mkern-7.1mu\Bigr)}
\newcommand{\parstruck}[1]{{\lstruck{\mathbin #1}\rstruck}}
\newcommand{\nparstruck}[1]{{\lmstruck{\mathbin #1}\rmstruck}}
\begin{document}
\verb|\parstruck{...}| direct command where has been used \verb|\mathbin| for the first type of brackets:
[\parstruck{aBf(x)g}]
\verb|\nparstruck{...}| direct command where has been used \verb|\mathbin| for the second type of brackets:
[\nparstruck{rsg(x)hp}]
Classic \verb|\parstruck{...}| commands without \verb|\mathbin|:
[\lstruck pQr \rstruck, , \lmstruck pQr \rmstruck]
\end{document}

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Just as an exercise. You can create himself your parentesis.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\newcommand{\lstruck}{\Bigl(\mkern-4mu{\Big\lvert}}
\newcommand{\rstruck}{{\Big\rvert}\mkern-4mu\Bigr)}
\newcommand{\lmstruck}{\Bigl(\mkern-7.1mu{\bigl\lvert}}
\newcommand{\rmstruck}{{\bigr\rvert}\mkern-7.1mu\Bigr)}
\begin{document}
[\lstruck pQr \rstruck]
[\lmstruck pQr \rmstruck]
\end{document}