How can I make 'git diff' aware of Emacs Lisp functions?

Question

When diffing with Git, for most languages, it provides a function name in the chunk header, allowing to get a better grasp on the context, e.g.,

@@ -7,5 +7,6 @@ int main() {
   if(condition()) {
     task4();
     task5();
+    task6();
   }
 }

For Emacs Lisp, git diff seems to use some sort of fall-back mode, where apparently the closest line without indentation is used; which usually is part of a docstring, not something like (defun ...

@@ -9,4 +9,5 @@ Last docstring line."
   (run-task3)
   (when (run-condition)
     (run-task4)
-    (run-task5)))
+    (run-task5)
+    (run-task6)))

Is it possible to make Git aware of how to identify a useful line to use for the @@ line?

Complete example source

For reference I attach the full source used to produce the examples.

/// run.c
int main() {
// foo
  task1();
  task2();
  task3();
  if(condition()) {
    task4();
    task5();
    task6();
  }
}

;;; run.el
(defun run-main ()
  "1st docstring line.
2nd docstring line.
Last docstring line."
  (run-task1)
  (run-task2)
  (run-task3)
  (when (run-condition)
    (run-task4)
    (run-task5)
    (run-task6)))

Answer 1

Is it possible to make Git aware of how to identify a useful line to use for the @@ line?

Yes, quoth section "Defining a custom hunk-header" in man 5 gitattributes:

Defining a custom hunk-header
    Each group of changes (called a "hunk") in the textual diff output
    is prefixed with a line of the form:

        @@ -k,l +n,m @@ TEXT

    This is called a hunk header. The "TEXT" portion is by default a
    line that begins with an alphabet, an underscore or a dollar sign;
    this matches what GNU diff -p output uses. This default selection
    however is not suited for some contents, and you can use a
    customized pattern to make a selection.

    First, in .gitattributes, you would assign the diff attribute for
    paths.

        *.tex   diff=tex

    Then, you would define a "diff.tex.xfuncname" configuration to
    specify a regular expression that matches a line that you would
    want to appear as the hunk header "TEXT". Add a section to your
    $GIT_DIR/config file (or $HOME/.gitconfig file) like this:

        [diff "tex"]
                xfuncname = "^(\\\\(sub)*section\\{.*)$"

So, to teach Git about Elisp files, you could first add the following to your $XDG_CONFIG_HOME/git/attributes file (which defaults to ~/.config/git/attributes):

*.el diff=elisp

Then, you can configure the exact header-matching regexp in your $XDG_CONFIG_HOME/git/config file (which defaults to ~/.config/git/config), e.g. as follows:

[diff "elisp"]
  xfuncname = ^\\([^[:space:]]+[[:space:]]+([^()[:space:]]+)

This is the relatively liberal regexp that I use globally. The Emacs repository itself uses a slightly more restricted one:

[diff "elisp"]
  xfuncname = ^\\([^[:space:]]*def[^[:space:]]+[[:space:]]+([^()[:space:]]+)

You can find it by searching for xfuncname in the script autogen.sh.