Index: Lib/test/test_sys.py
===================================================================
--- Lib/test/test_sys.py	(revision 64296)
+++ Lib/test/test_sys.py	(working copy)
@@ -538,8 +538,8 @@
         self.check_sizeof([], h + l + p + l)
         self.check_sizeof([1, 2, 3], h + l + p + l + 3*l)
         # unicode
-        import math
-        usize = math.log(sys.maxunicode + 1, 2) / 8
+        import _testcapi
+        usize = _testcapi.Py_UNICODE_SIZEOF
         samples = [u'', u'1'*100]
         # we need to test for both sizes, because we don't know if the string
         # has been cached
Index: Modules/_testcapimodule.c
===================================================================
--- Modules/_testcapimodule.c	(revision 64296)
+++ Modules/_testcapimodule.c	(working copy)
@@ -967,6 +967,7 @@
 	PyModule_AddObject(m, "ULLONG_MAX", PyLong_FromUnsignedLongLong(PY_ULLONG_MAX));
 	PyModule_AddObject(m, "PY_SSIZE_T_MAX", PyInt_FromSsize_t(PY_SSIZE_T_MAX));
 	PyModule_AddObject(m, "PY_SSIZE_T_MIN", PyInt_FromSsize_t(PY_SSIZE_T_MIN));
+	PyModule_AddObject(m, "Py_UNICODE_SIZEOF", PyInt_FromSsize_t(sizeof(Py_UNICODE)));
 
 	TestError = PyErr_NewException("_testcapi.error", NULL, NULL);
 	Py_INCREF(TestError);