[Tex/LaTex] Underarrow with smaller depth, shorter minimum length, and smaller arrow head

amsmatharrowsmath-modespacingtext-decorations

I am using underarrows from amsmath to decorate messages with their direction, as in $\underleftarrow{\mathsf{msg}}$ () and $\underrightarrow{\mathsf{msg}}$ (). I am looking for a better underarrow, in several senses:

Smaller depth of entire construction. The underarrows add depth to the message names. I often use these in multiline constructions, such as align*, and the extra depth affects the apparent spacing. For example, compare the following versions that use underarrows and underlines.

Using \smash[b] does eliminate the added depth but also, for some reason, shifts the arrow down:
Shorter minimum arrow length. With the standard underarrows, message names that consist of a single letter are overpowered by the arrow. For example, $\underleftarrow{\mathsf{p}}$ produces .
Smaller arrow head. To my eye, the arrow head looks too large for my use case.

Are there left and right underarrows that better meet these three criteria? Is there a way that I can construct my own underarrows?

Here is a MWE, in case it is useful:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
  \begin{aligned}[t]
    &\mathsf{bit_0} \bullet \underleftarrow{\mathsf{inc}} \\
    &\mathsf{bit_1} \bullet \underleftarrow{\mathsf{p}}
  \end{aligned}\quad
  \begin{aligned}[t]
    &\mathsf{bit_0} \bullet \smash[b]{\underleftarrow{\mathsf{inc}}} \\
    &\mathsf{bit_1} \bullet \smash[b]{\underleftarrow{\mathsf{p}}}
  \end{aligned}
\end{equation*}
\end{document}

Best Answer

I don’t know how much amsmath’s \underleftarrow slows the compilation down or how it would with TikZ, but here is a solution that uses PGF and avoids the parsing process of TikZ.

The proposed solution uses only one \pgfpicture which measured the under-arrowed math content after typesetting it in an box using

\edef\pgf@math@fam{\the\fam}%

and later

\sbox\pgfutil@tempboxa{$\fam\pgf@math@fam#1#2$}%

where the saved font setting is set again, combined with \mathpalette which forwards the current math style to \@pgfunderleftarrow.

The box’s width is stored in \pgfutil@tempdimb which is then used in drawing the line (where we have used \wd\pgfutil@tempboxa directly, too).

This makes it possible to let TeX typeset the math content as it is but also measure it as precise as possible. As I realized later, even the original \underleftarrow doesn’t kepp the math family font settings (like \mathsf) so maybe you want to change this again.

This \the\fam trick was provided by egreg in a chat message from 2013-07-31:

For a single symbl it should work.

It seems also to work for more than one symbol.

The original definition of the to arrow is

\pgfarrowsdeclare{to}{to}
{ … }{
  \pgfutil@tempdima=0.28pt%
  \advance\pgfutil@tempdima by.3\pgflinewidth%
  \pgfsetlinewidth{0.8\pgflinewidth}
  \pgfsetdash{}{+0pt}
  \pgfsetroundcap
  \pgfsetroundjoin
  \pgfpathmoveto{\pgfqpoint{-3\pgfutil@tempdima}{4\pgfutil@tempdima}}
  …
}

The important part is the setup of \pgfutil@tempdima as the y value of the \pgfpathmoveto coordinate is 4\pgfutil@tempdima which makes up the vertical height of the arrow. \pgfutil@tempdima in the definition of \@pgfunderleftarrow is used to calculate this height (we cannot extract it from some macro like the left and right extend).

To let the arrow arc touch the bottom of the math content we would use:

\pgfutil@tempdima=0.28pt%
\advance\pgfutil@tempdima by.3\pgflinewidth%
\pgfutil@tempdima-4\pgfutil@tempdima
\advance\pgfutil@tempdima-.4\pgflinewidth

The last line adds half the line width of the arrow line (which is set to 0.8\pgflinewidth).

So why did I do something differently, namely \pgfutil@tempdima=0.28pt% \advance\pgfutil@tempdima by.8\pgflinewidth% \pgfutil@tempdima-4\pgfutil@tempdima

Because I haven’t done it right (.5 instead of .4 of the line width added and before the multiplication of the factor 4), but it looks right.

Of course, you can change the factors and addition if you think it looks better.

The unstarred version of \pgfunderleftarrow doesn’t add any depth to the line (other than the depth of the math content itself). If this depth is needed (take a look at a \fraction), the starred version \pgfunderleftarrow* can be used.

Code

\documentclass{article}
\usepackage{amsmath}
\usepackage{pgf}
\makeatletter
\newcommand*{\pgfunderleftarrow}{%
  \@ifstar
    {\let\ifpgf@depth\iftrue\mathpalette\@pgfunderleftarrow}
    {\let\ifpgf@depth\iffalse\mathpalette\@pgfunderleftarrow}%
}
\newcommand*{\@pgfunderleftarrow}[2]{%
  #2%
  \edef\pgf@math@fam{\the\fam}%
  \pgfpicture
    \pgfsetbaseline{0pt}%                 % "baseline = 0pt"
    \pgf@relevantforpicturesizefalse      % "overlay"
    \pgfsetroundcap                       % "line cap = round"
    \pgfsetarrowsend{to}%                 % "arrows = -to"
    \pgfutil@tempdima=0.28pt%
    \advance\pgfutil@tempdima by.8\pgflinewidth%
    \pgfutil@tempdima-4\pgfutil@tempdima
    \sbox\pgfutil@tempboxa{$\m@th\fam\pgf@math@fam#1#2$}%
    \advance\pgfutil@tempdima-\dp\pgfutil@tempboxa
    \pgfutil@tempdimb\wd\pgfutil@tempboxa
    \pgfpathmoveto{\pgfqpoint{0pt}{\pgfutil@tempdima}}%
    \pgfpathlineto{\pgfqpoint{-\pgfutil@tempdimb}{\pgfutil@tempdima}}%
    \pgfusepath{stroke}%                  % "draw"
    \ifpgf@depth
      \pgf@relevantforpicturesizetrue
      \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfutil@tempdimb}}%
      \pgfusepath{use as bounding box}%
    \fi
  \endpgfpicture
}
\makeatother
\begin{document}
\begin{gather*}
  \mathsf{bit_0} \bullet \underleftarrow{\mathsf{inc}} \\
  \mathsf{bit_1} \bullet \underleftarrow{\mathsf{p}}  \\
  \mathsf{bit_2} \bullet \underleftarrow{\mathsf{f}} \\
  \mathsf{bit_2} \bullet \mathsf{\underleftarrow{f}} \rlap{$\to$ \texttt{\char`\\mathsf} lost?}
\end{gather*}
\begin{gather*}
  \mathsf{bit_0} \bullet \pgfunderleftarrow{\mathsf{inc}} \bullet \mathsf{\pgfunderleftarrow{inc}}\\
  \mathsf{bit_1} \bullet \pgfunderleftarrow{\mathsf{p}} \bullet \mathsf{\pgfunderleftarrow{p}}\\
  \mathsf{bit_2} \bullet \pgfunderleftarrow{\mathsf{f}} \bullet \mathsf{\pgfunderleftarrow{f}}
\end{gather*}
\begin{equation*}
  \frac{\pgfunderleftarrow*{f}}{f} \neq \frac{\pgfunderleftarrow{f}}{f} \neq \frac{\underleftarrow{f}}{f}
\end{equation*}
\end{document}