diff --git a/sphinx/ext/coverage.py b/sphinx/ext/coverage.py
index 4924d30b0..f41820e2a 100644
--- a/sphinx/ext/coverage.py
+++ b/sphinx/ext/coverage.py
@@ -173,8 +173,11 @@ class CoverageBuilder(Builder):
 
                         attrs = []
 
+                        for attr_name in dir(obj):
+                            attr = getattr(obj, attr_name)
                         for attr_name, attr in inspect.getmembers(
-                               obj, inspect.ismethod):
+                                obj, lambda x: inspect.ismethod(x) or \
+                                               inspect.isfunction(x)):
                             if attr_name[0] == '_':
                                 # starts with an underscore, ignore it
                                 continue
diff --git a/tests/path.py b/tests/path.py
index 28a8c22af..df96bce45 100644
--- a/tests/path.py
+++ b/tests/path.py
@@ -142,6 +142,33 @@ class path(str):
         finally:
             f.close()
 
+    def bytes(self):
+        """
+        Returns the bytes in the file.
+        """
+        f = open(self, mode='rb')
+        try:
+            return f.read()
+        finally:
+            f.close()
+
+    def write_bytes(self, bytes, append=False):
+        """
+        Writes the given `bytes` to the file.
+
+        :param append:
+            If ``True`` given `bytes` are added at the end of the file.
+        """
+        if append:
+            mode = 'ab'
+        else:
+            mode = 'wb'
+        f = open(self, mode=mode)
+        try:
+            f.write(bytes)
+        finally:
+            f.close()
+
     def exists(self):
         """
         Returns ``True`` if the path exist.
diff --git a/tests/test_coverage.py b/tests/test_coverage.py
index 1262ebf5b..cb8316358 100644
--- a/tests/test_coverage.py
+++ b/tests/test_coverage.py
@@ -33,7 +33,7 @@ def test_build(app):
     assert 'api.h' in c_undoc
     assert ' * Py_SphinxTest' in c_undoc
 
-    undoc_py, undoc_c = pickle.loads((app.outdir / 'undoc.pickle').text())
+    undoc_py, undoc_c = pickle.loads((app.outdir / 'undoc.pickle').bytes())
     assert len(undoc_c) == 1
     # the key is the full path to the header file, which isn't testable
     assert undoc_c.values()[0] == [('function', 'Py_SphinxTest')]