diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index 0e07090..92285b2 100644
--- a/Lib/test/test_long.py
+++ b/Lib/test/test_long.py
@@ -15,7 +15,7 @@
         return self.format % self.args
 
 # SHIFT should match the value in longintrepr.h for best testing.
-SHIFT = 15
+SHIFT = sys.int_info.bits_per_digit
 BASE = 2 ** SHIFT
 MASK = BASE - 1
 KARATSUBA_CUTOFF = 70   # from longobject.c
@@ -120,6 +120,35 @@
                 y = self.getran(leny) or 1
                 self.check_division(x, y)
 
+        # specific numbers chosen to exercise corner cases of the
+        # current long division implementation
+
+        # 30-bit cases involving a quotient digit estimate of BASE+1
+        self.check_division(1231948412290879395966702881,
+                            1147341367131428698)
+        self.check_division(815427756481275430342312021515587883,
+                       707270836069027745)
+        self.check_division(627976073697012820849443363563599041,
+                       643588798496057020)
+        self.check_division(1115141373653752303710932756325578065,
+                       1038556335171453937726882627)
+        # 30-bit cases that require the post-subtraction correction step
+        self.check_division(922498905405436751940989320930368494,
+                       949985870686786135626943396)
+        self.check_division(768235853328091167204009652174031844,
+                       1091555541180371554426545266)
+
+        # 15-bit cases involving a quotient digit estimate of BASE+1
+        self.check_division(20172188947443, 615611397)
+        self.check_division(1020908530270155025, 950795710)
+        self.check_division(128589565723112408, 736393718)
+        self.check_division(609919780285761575, 18613274546784)
+        # 15-bit cases that require the post-subtraction correction step
+        self.check_division(710031681576388032, 26769404391308)
+        self.check_division(1933622614268221, 30212853348836)
+
+
+
     def test_karatsuba(self):
         digits = list(range(1, 5)) + list(range(KARATSUBA_CUTOFF,
                                                 KARATSUBA_CUTOFF + 10))
diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index 9f0c139..427b721 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -333,6 +333,9 @@
         self.assert_(isinstance(sys.executable, str))
         self.assertEqual(len(sys.float_info), 11)
         self.assertEqual(sys.float_info.radix, 2)
+        self.assertEqual(len(sys.int_info), 2)
+        self.assert_(sys.int_info.bits_per_digit % 5 == 0)
+        self.assert_(sys.int_info.sizeof_digit >= 1)
         self.assert_(isinstance(sys.hexversion, int))
         self.assert_(isinstance(sys.maxsize, int))
         self.assert_(isinstance(sys.maxunicode, int))
@@ -437,6 +440,7 @@
         if hasattr(sys, "gettotalrefcount"):
             self.header += '2P'
             self.vheader += '2P'
+        self.longdigit = sys.int_info.sizeof_digit
         import _testcapi
         self.gc_headsize = _testcapi.SIZEOF_PYGC_HEAD
         self.file = open(test.support.TESTFN, 'wb')
@@ -471,7 +475,7 @@
         size = self.calcsize
         gc_header_size = self.gc_headsize
         # bool objects are not gc tracked
-        self.assertEqual(sys.getsizeof(True), size(vh) + self.H)
+        self.assertEqual(sys.getsizeof(True), size(vh) + self.longdigit)
         # but lists are
         self.assertEqual(sys.getsizeof([]), size(vh + 'PP') + gc_header_size)
 
@@ -479,8 +483,8 @@
         h = self.header
         vh = self.vheader
         size = self.calcsize
-        self.assertEqual(sys.getsizeof(True), size(vh) + self.H)
-        self.assertEqual(sys.getsizeof(True, -1), size(vh) + self.H)
+        self.assertEqual(sys.getsizeof(True), size(vh) + self.longdigit)
+        self.assertEqual(sys.getsizeof(True, -1), size(vh) + self.longdigit)
 
     def test_objecttypes(self):
         # check all types defined in Objects/
@@ -489,7 +493,7 @@
         size = self.calcsize
         check = self.check_sizeof
         # bool
-        check(True, size(vh) + self.H)
+        check(True, size(vh) + self.longdigit)
         # buffer
         # XXX
         # builtin_function_or_method
@@ -607,11 +611,12 @@
         check(reversed([]), size(h + 'lP'))
         # long
         check(0, size(vh))
-        check(1, size(vh) + self.H)
-        check(-1, size(vh) + self.H)
-        check(32768, size(vh) + 2*self.H)
-        check(32768*32768-1, size(vh) + 2*self.H)
-        check(32768*32768, size(vh) + 3*self.H)
+        check(1, size(vh) + self.longdigit)
+        check(-1, size(vh) + self.longdigit)
+        PyLong_BASE = 2**sys.int_info.bits_per_digit
+        check(PyLong_BASE, size(vh) + 2*self.longdigit)
+        check(PyLong_BASE**2-1, size(vh) + 2*self.longdigit)
+        check(PyLong_BASE**2, size(vh) + 3*self.longdigit)
         # memory
         check(memoryview(b''), size(h + 'P PP2P2i7P'))
         # module