diff --git a/mercurial/localrepo.py b/mercurial/localrepo.py
--- a/mercurial/localrepo.py
+++ b/mercurial/localrepo.py
@@ -1135,7 +1135,7 @@ class revlogfilestorage(object):
     """File storage when using revlogs."""
 
     def file(self, path):
-        if path[0] == b'/':
+        if path.startswith(b'/'):
             path = path[1:]
 
         return filelog.filelog(self.svfs, path)
@@ -1146,7 +1146,7 @@ class revlognarrowfilestorage(object):
     """File storage when using revlogs and narrow files."""
 
     def file(self, path):
-        if path[0] == b'/':
+        if path.startswith(b'/'):
             path = path[1:]
 
         return filelog.narrowfilelog(self.svfs, path, self._storenarrowmatch)
diff --git a/mercurial/logcmdutil.py b/mercurial/logcmdutil.py
--- a/mercurial/logcmdutil.py
+++ b/mercurial/logcmdutil.py
@@ -845,7 +845,7 @@ def _makematcher(repo, revs, wopts):
         # slowpath; otherwise, we can turn off the slowpath
         if slowpath:
             for path in match.files():
-                if path == b'.' or path in repo.store:
+                if not path or path in repo.store:
                     break
             else:
                 slowpath = False
diff --git a/tests/test-log.t b/tests/test-log.t
--- a/tests/test-log.t
+++ b/tests/test-log.t
@@ -102,6 +102,41 @@ log on directory
   summary:     c
   
 
+log empty path (or repo root) of slow path shouldn't crash (issue6478)
+
+  $ hg log -ql1 '' inexistent
+  4:7e4639b4691b
+  $ hg log -ql1 . inexistent
+  4:7e4639b4691b
+  $ hg log -ql1 "`pwd`" inexistent
+  4:7e4639b4691b
+
+  $ hg log -ql1 '' e
+  4:7e4639b4691b
+  $ hg log -ql1 . e
+  4:7e4639b4691b
+  $ hg log -ql1 "`pwd`" e
+  4:7e4639b4691b
+
+log -f empty path (or repo root) shouldn't crash
+
+  $ hg log -qfl1 '' inexistent
+  abort: cannot follow file not in parent revision: "inexistent"
+  [255]
+  $ hg log -qfl1 . inexistent
+  abort: cannot follow file not in parent revision: "inexistent"
+  [255]
+  $ hg log -qfl1 "`pwd`" inexistent
+  abort: cannot follow file not in parent revision: "inexistent"
+  [255]
+
+  $ hg log -qfl1 '' e
+  4:7e4639b4691b
+  $ hg log -qfl1 . e
+  4:7e4639b4691b
+  $ hg log -qfl1 "`pwd`" e
+  4:7e4639b4691b
+
 -X, with explicit path
 
   $ hg log a -X a