chase: optimize the special case where no root dir specified

Now that we can recognize the root dir in chaseat() sanely, let's use it
top optimize the very common special case where we have no root dir to
consider, and directly call open_tree().

src/basic/chase.c

@@ -128,6 +128,7 @@ int chaseat(int dir_fd, const char *path, ChaseFlags flags, char **ret_path, int
         unsigned max_follow = CHASE_MAX; /* how many symlinks to follow before giving up and returning ELOOP */
         bool exists = true, append_trail_slash = false;
         struct stat st; /* stat obtained from fd */
+        bool need_absolute = false; /* allocate early to avoid compiler warnings around goto */
         const char *todo;
         int r;
 
@@ -220,6 +221,33 @@ int chaseat(int dir_fd, const char *path, ChaseFlags flags, char **ret_path, int
 
         _cleanup_close_ int _dir_fd = -EBADF;
         if (dir_fd == XAT_FDROOT) {
+
+                /* Shortcut the common case where no root dir is specified, and no special flags are given to
+                 * a regular open() */
+                if (!ret_path &&
+                    (flags & (CHASE_STEP|CHASE_NO_AUTOFS|CHASE_NONEXISTENT|CHASE_SAFE|CHASE_WARN|CHASE_PROHIBIT_SYMLINKS|CHASE_PARENT|CHASE_MKDIR_0755)) == 0) {
+                        _cleanup_free_ char *slash_path = NULL;
+
+                        if (!path_is_absolute(path)) {
+                                slash_path = strjoin("/", path);
+                                if (!slash_path)
+                                        return -ENOMEM;
+                        }
+
+                        /* We use open_tree() rather than regular open() here, because it gives us direct
+                         * control over automount behaviour, and otherwise is equivalent to open() with
+                         * O_PATH */
+                        fd = open_tree(-EBADF, slash_path ?: path, OPEN_TREE_CLOEXEC|(FLAGS_SET(flags, CHASE_TRIGGER_AUTOFS) ? 0 : AT_NO_AUTOMOUNT));
+                        if (fd < 0)
+                                return -errno;
+
+                        if (fstat(fd, &st) < 0)
+                                return -errno;
+
+                        exists = true;
+                        goto success;
+                }
+
                 _dir_fd = open("/", O_DIRECTORY|O_RDONLY|O_CLOEXEC);
                 if (_dir_fd < 0)
                         return -errno;
@@ -259,7 +287,7 @@ int chaseat(int dir_fd, const char *path, ChaseFlags flags, char **ret_path, int
         if (r < 0)
                 return r;
 
-        bool need_absolute = r;
+        need_absolute = r;
         if (need_absolute) {
                 done = strdup("/");
                 if (!done)
@@ -522,6 +550,7 @@ int chaseat(int dir_fd, const char *path, ChaseFlags flags, char **ret_path, int
                 close_and_replace(fd, child);
         }
 
+success:
         if (exists) {
                 if (FLAGS_SET(flags, CHASE_MUST_BE_DIRECTORY)) {
                         r = stat_verify_directory(&st);