diff --git a/Lib/test/support.py b/Lib/test/support.py
index 9a4e1b1..9fb3ee0 100644
--- a/Lib/test/support.py
+++ b/Lib/test/support.py
@@ -198,6 +198,36 @@
         # is exited) but there is a .pyo file.
         unlink(os.path.join(dirname, modname + '.pyo'))
 
+# On some platforms, should not run gui test even if it is allowed
+# in `use_resources'.
+if sys.platform.startswith('win'):
+    import ctypes
+    import ctypes.wintypes
+    def _is_gui_available():
+        UOI_FLAGS = 1
+        WSF_VISIBLE = 0x0001
+        class USEROBJECTFLAGS(ctypes.Structure):
+            _fields_ = [("fInherit", ctypes.wintypes.BOOL),
+                        ("fReserved", ctypes.wintypes.BOOL),
+                        ("dwFlags", ctypes.wintypes.DWORD)]
+        dll = ctypes.windll.user32
+        h = dll.GetProcessWindowStation()
+        if not h:
+            raise ctypes.WinError()
+        uof = USEROBJECTFLAGS()
+        needed = ctypes.wintypes.DWORD()
+        res = dll.GetUserObjectInformationW(h,
+            UOI_FLAGS,
+            ctypes.byref(uof),
+            ctypes.sizeof(uof),
+            ctypes.byref(needed))
+        if not res:
+            raise ctypes.WinError()
+        return bool(uof.dwFlags & WSF_VISIBLE)
+else:
+    def _is_gui_available():
+        return True
+
 def is_resource_enabled(resource):
     """Test whether a resource is enabled.  Known resources are set by
     regrtest.py."""
@@ -208,6 +238,8 @@
 
     If the caller's module is __main__ then automatically return True.  The
     possibility of False being returned occurs when regrtest.py is executing."""
+    if resource == 'gui' and not _is_gui_available():
+        raise unittest.SkipTest("Cannot use the 'gui' resource")
     # see if the caller's module is __main__ - if so, treat as if
     # the resource was set
     if sys._getframe(1).f_globals.get("__name__") == "__main__":
@@ -869,6 +901,8 @@
     return obj
 
 def requires_resource(resource):
+    if resource == 'gui' and not _is_gui_available():
+        return unittest.skip("resource 'gui' is not available")
     if is_resource_enabled(resource):
         return _id
     else:
diff --git a/Lib/test/test_mmap.py b/Lib/test/test_mmap.py
index 62569b9..d6addff 100644
--- a/Lib/test/test_mmap.py
+++ b/Lib/test/test_mmap.py
@@ -1,6 +1,6 @@
-from test.support import TESTFN, run_unittest, import_module
+from test.support import TESTFN, run_unittest, import_module, unlink, requires
 import unittest
-import os, re, itertools, socket
+import os, re, itertools, socket, sys
 
 # Skip test if we can't import mmap.
 mmap = import_module('mmap')
@@ -636,8 +636,63 @@
             finally:
                 s.close()
 
+
+class LargeMmapTests(unittest.TestCase):
+
+    def setUp(self):
+        unlink(TESTFN)
+
+    def tearDown(self):
+        unlink(TESTFN)
+
+    def _working_largefile(self):
+        # Only run if the current filesystem supports large files.
+        f = open(TESTFN, 'wb', buffering=0)
+        try:
+            f.seek(0x80000001)
+            f.write(b'x')
+            f.flush()
+        except (IOError, OverflowError):
+            raise unittest.SkipTest("filesystem does not have largefile support")
+        finally:
+            f.close()
+            unlink(TESTFN)
+
+    def test_large_offset(self):
+        if sys.platform[:3] == 'win' or sys.platform == 'darwin':
+            requires('largefile',
+                'test requires %s bytes and a long time to run' % str(0x180000000))
+        self._working_largefile()
+        with open(TESTFN, 'wb') as f:
+            f.seek(0x14FFFFFFF)
+            f.write(b" ")
+
+        with open(TESTFN, 'rb') as f:
+            m = mmap.mmap(f.fileno(), 0, offset=0x140000000, access=mmap.ACCESS_READ)
+            try:
+                self.assertEqual(m[0xFFFFFFF], 32)
+            finally:
+                m.close()
+
+    def test_large_filesize(self):
+        if sys.platform[:3] == 'win' or sys.platform == 'darwin':
+            requires('largefile',
+                'test requires %s bytes and a long time to run' % str(0x180000000))
+        self._working_largefile()
+        with open(TESTFN, 'wb') as f:
+            f.seek(0x17FFFFFFF)
+            f.write(b" ")
+
+        with open(TESTFN, 'rb') as f:
+            m = mmap.mmap(f.fileno(), 0x10000, access=mmap.ACCESS_READ)
+            try:
+                self.assertEqual(m.size(), 0x180000000)
+            finally:
+                m.close()
+
+
 def test_main():
-    run_unittest(MmapTests)
+    run_unittest(MmapTests, LargeMmapTests)
 
 if __name__ == '__main__':
     test_main()
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 4b16efb..b27049c 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -2,10 +2,16 @@
 from test import support
 import binascii
 import random
-from test.support import precisionbigmemtest, _1G
+import sys
+from test.support import precisionbigmemtest, _1G, _4G
 
 zlib = support.import_module('zlib')
 
+try:
+    import mmap
+except ImportError:
+    mmap = None
+
 
 class ChecksumTestCase(unittest.TestCase):
     # checksum test cases
@@ -57,6 +63,28 @@
         self.assertEqual(binascii.crc32(b'spam'), zlib.crc32(b'spam'))
 
 
+# Issue #10276 - check that inputs >=4GB are handled correctly.
+class ChecksumBigBufferTestCase(unittest.TestCase):
+
+    def setUp(self):
+        with open(support.TESTFN, "wb+") as f:
+            f.seek(_4G)
+            f.write(b"asdf")
+        with open(support.TESTFN, "rb") as f:
+            self.mapping = mmap.mmap(f.fileno(), 0, access=mmap.ACCESS_READ)
+
+    def tearDown(self):
+        self.mapping.close()
+        support.unlink(support.TESTFN)
+
+    @unittest.skipUnless(mmap, "mmap() is not available.")
+    @unittest.skipUnless(sys.maxsize > _4G, "Can't run on a 32-bit system.")
+    @unittest.skipUnless(support.is_resource_enabled("largefile"),
+                         "May use lots of disk space.")
+    def test_big_buffer(self):
+        self.assertEqual(zlib.crc32(self.mapping), 3058686908)
+        self.assertEqual(zlib.adler32(self.mapping), 82837919)
+
 
 class ExceptionTestCase(unittest.TestCase):
     # make sure we generate some expected errors
@@ -567,6 +595,7 @@
 def test_main():
     support.run_unittest(
         ChecksumTestCase,
+        ChecksumBigBufferTestCase,
         ExceptionTestCase,
         CompressTestCase,
         CompressObjectTestCase