Shaoxuan Yuan wrote:

Originally, <destination> is assumed to be in the working tree. If it is
not found as a directory, then it is determined to be either a regular file
path, or error out if used under the second form (move into a directory)
of 'git-mv'. Such behavior is not ideal, mainly because Git does not
look into the index for <destination>, which could potentially be a
SKIP_WORKTREE_DIR, which we need to determine for the later "moving from
in-cone to out-of-cone" patch.

Change the logic so that Git first check if <destination> is a directory
with all its contents sparsified (a SKIP_WORKTREE_DIR).

If <destination> is such a sparse directory, then we should modify the
index the same way as we would if this were a non-sparse directory. We
must be careful to ensure that the <destination> is marked with
SKIP_WORKTREE_DIR.

Also add a `dst_w_slash` to reuse the result from `add_slash()`, which
was everywhere and can be simplified.

This all makes sense. Stepping through the code...

...you pre-compute a reusable 'dst_w_slash' here...

...then remove the in-place 'add_slash()' of 'dest_path[0]' and use
'dst_w_slash' in 'internal_prefix_pathspec()'. Makes sense.

 	} else {

Then, this block is reached if 'dest_path' is not '.' and it is not a
directory that exists on disk.

Previously, reaching this point meant that 'dest_path' *must* refer to a
file, not a directory. However, you want to add handling for the case where
'dst_w_slash' doesn't exist on disk because all of its contents are sparse:

-		if (argc != 1)
+		if (!path_in_sparse_checkout(dst_w_slash, &the_index) &&
+		    empty_dir_has_sparse_contents(dst_w_slash)) {
+			destination = internal_prefix_pathspec(dst_w_slash, argv, argc, DUP_BASENAME);

so the above condition identifies whether 'dest_path[0]' is non-empty in the
index, and sets 'destination' accordingly. 

It took me some time to understand what all of these (nested) conditions are
doing; one suggestion I have (feel free to ignore it, since it's really just
a matter of stylistic preference) is reduce some duplicate code/simplify the
change a bit by moving the sparse directory check into the main "if-else"
block:

------------->8------------->8------------->8------------->8------------->8-------------

diff --git a/builtin/mv.c b/builtin/mv.c
index 4729bb1a1a..1c1b9559f6 100644
--- a/builtin/mv.c
+++ b/builtin/mv.c

@@ -203,10 +203,11 @@ int cmd_mv(int argc, const char **argv, const char *prefix)
 	if (dest_path[0][0] == '\0')
 		/* special case: "." was normalized to "" */
 		destination = internal_prefix_pathspec(dest_path[0], argv, argc, DUP_BASENAME);
-	else if (!lstat(dest_path[0], &st) &&
-			S_ISDIR(st.st_mode)) {
-		dest_path[0] = add_slash(dest_path[0]);
-		destination = internal_prefix_pathspec(dest_path[0], argv, argc, DUP_BASENAME);
+	else if ((!lstat(dest_path[0], &st) && S_ISDIR(st.st_mode)) ||
+		 (!path_in_sparse_checkout(dst_w_slash, &the_index) &&
+		  empty_dir_has_sparse_contents(dst_w_slash))) {
+		/* directory dest_path[0] exists on-disk or in the index */
+		destination = internal_prefix_pathspec(dst_w_slash, argv, argc, DUP_BASENAME);
 	} else {
 		if (argc != 1)
 			die(_("destination '%s' is not a directory"), dest_path[0]);

-------------8<-------------8<-------------8<-------------8<-------------8<-------------

It doesn't make for the prettiest condition (so your current approach might
be better in terms of readability) but, to me, it creates a clearer
distinction between the "if" and "else if" blocks (which handle the case
where 'dest_path[0]' is a directory), and the "else" block (which handles
the case where 'dest_path[0]' is a file).

+		} else if (argc != 1) {
 			die(_("destination '%s' is not a directory"), dest_path[0]);
-		destination = dest_path;
+		} else {
+			destination = dest_path;
+		}
+	}
+	if (dst_w_slash != dest_path[0]) {
+		free((char *)dst_w_slash);
+		dst_w_slash = NULL;

Looks good.

 	}
 
 	/* Checking */