diff -r 955547e57cff Lib/test/test_posixpath.py
--- a/Lib/test/test_posixpath.py	Sun Mar 13 19:32:21 2011 +0100
+++ b/Lib/test/test_posixpath.py	Mon Mar 14 14:48:58 2011 -0400
@@ -1,6 +1,7 @@
 import unittest
 from test import support, test_genericpath
 
+import posix
 import posixpath
 import os
 import sys
@@ -150,6 +151,7 @@
 
     def test_islink(self):
         self.assertIs(posixpath.islink(support.TESTFN + "1"), False)
+        self.assertIs(posixpath.lexists(support.TESTFN + "2"), False)
         f = open(support.TESTFN + "1", "wb")
         try:
             f.write(b"foo")
@@ -225,6 +227,40 @@
 
     def test_ismount(self):
         self.assertIs(posixpath.ismount("/"), True)
+        self.assertIs(posixpath.ismount(b"/"), True)
+
+        # Non-existent mountpoint.
+        self.assertIs(posixpath.ismount(ABSTFN), False)
+        try:
+            os.mkdir(ABSTFN)
+            self.assertIs(posixpath.ismount(ABSTFN), False)
+        finally:
+            safe_rmdir(ABSTFN)
+
+        # Symlinks are never mountpoints.
+        if support.can_symlink():
+            try:
+                os.symlink("/", ABSTFN)
+                self.assertIs(posixpath.ismount(ABSTFN), False)
+            finally:
+                os.unlink(ABSTFN)
+
+    def test_ismount_different_device(self):
+        # Simulate the path being on a different device from its parent by
+        # mocking out st_dev.
+        save_lstat = os.lstat
+        try:
+            def fake_lstat(path):
+                st_ino = 0
+                st_dev = 0
+                if path == ABSTFN:
+                    st_dev = 1
+                    st_ino = 1
+                return posix.stat_result((0,st_ino,st_dev,0,0,0,0,0,0,0))
+            os.lstat = fake_lstat
+            self.assertIs(posixpath.ismount(ABSTFN), True)
+        finally:
+            os.lstat = save_lstat
 
     def test_expanduser(self):
         self.assertEqual(posixpath.expanduser("foo"), "foo")
@@ -254,6 +290,10 @@
             with support.EnvironmentVarGuard() as env:
                 env['HOME'] = '/'
                 self.assertEqual(posixpath.expanduser("~"), "/")
+                # expanduser should fall back to using the password database
+                del env['HOME']
+                home = pwd.getpwuid(os.getuid()).pw_dir
+                self.assertEqual(posixpath.expanduser("~"), home)
 
     def test_normpath(self):
         self.assertEqual(posixpath.normpath(""), ".")
@@ -289,6 +329,16 @@
     @unittest.skipUnless(hasattr(os, "symlink"),
                          "Missing symlink implementation")
     @skip_if_ABSTFN_contains_backslash
+    def test_realpath_relative(self):
+        try:
+            os.symlink(posixpath.relpath(ABSTFN+"1"), ABSTFN)
+            self.assertEqual(realpath(ABSTFN), ABSTFN+"1")
+        finally:
+            support.unlink(ABSTFN)
+
+    @unittest.skipUnless(hasattr(os, "symlink"),
+                         "Missing symlink implementation")
+    @skip_if_ABSTFN_contains_backslash
     def test_realpath_symlink_loops(self):
         # Bug #930024, return the path unchanged if we get into an infinite
         # symlink loop.
@@ -443,6 +493,11 @@
         finally:
             os.getcwdb = real_getcwdb
 
+    def test_sameopenfile(self):
+        fname = support.TESTFN + "1"
+        with open(fname, "wb") as a, open(fname, "wb") as b:
+            self.assertTrue(posixpath.sameopenfile(a.fileno(), b.fileno()))
+
 
 class PosixCommonTest(test_genericpath.CommonTest):
     pathmodule = posixpath