diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index e648c0f..1a0e33d 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.long_info.bits_per_digit
 BASE = 2 ** SHIFT
 MASK = BASE - 1
 KARATSUBA_CUTOFF = 70   # from longobject.c
@@ -143,6 +143,35 @@
                 y = self.getran(leny) or 1L
                 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(1231948412290879395966702881L,
+                            1147341367131428698L)
+        self.check_division(815427756481275430342312021515587883L,
+                       707270836069027745L)
+        self.check_division(627976073697012820849443363563599041L,
+                       643588798496057020L)
+        self.check_division(1115141373653752303710932756325578065L,
+                       1038556335171453937726882627L)
+        # 30-bit cases that require the post-subtraction correction step
+        self.check_division(922498905405436751940989320930368494L,
+                       949985870686786135626943396L)
+        self.check_division(768235853328091167204009652174031844L,
+                       1091555541180371554426545266L)
+
+        # 15-bit cases involving a quotient digit estimate of BASE+1
+        self.check_division(20172188947443L, 615611397L)
+        self.check_division(1020908530270155025L, 950795710L)
+        self.check_division(128589565723112408L, 736393718L)
+        self.check_division(609919780285761575L, 18613274546784L)
+        # 15-bit cases that require the post-subtraction correction step
+        self.check_division(710031681576388032L, 26769404391308L)
+        self.check_division(1933622614268221L, 30212853348836L)
+
+
+
     def test_karatsuba(self):
         digits = range(1, 5) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 10)
         digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100])
diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index 128880d..a4554a6 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -332,6 +332,9 @@
         self.assert_(isinstance(sys.executable, basestring))
         self.assertEqual(len(sys.float_info), 11)
         self.assertEqual(sys.float_info.radix, 2)
+        self.assertEqual(len(sys.long_info), 2)
+        self.assert_(sys.long_info.bits_per_digit % 5 == 0)
+        self.assert_(sys.long_info.sizeof_digit >= 1)
         self.assert_(isinstance(sys.hexversion, int))
         self.assert_(isinstance(sys.maxint, int))
         if test.test_support.have_unicode:
@@ -417,6 +420,7 @@
         if hasattr(sys, "gettotalrefcount"):
             self.header += '2P'
             self.vheader += '2P'
+        self.longdigit = sys.long_info.sizeof_digit
         import _testcapi
         self.gc_headsize = _testcapi.SIZEOF_PYGC_HEAD
         self.file = open(test.test_support.TESTFN, 'wb')
@@ -594,11 +598,12 @@
         check(reversed([]), size(h + 'lP'))
         # long
         check(0L, size(vh))
-        check(1L, size(vh) + self.H)
-        check(-1L, size(vh) + self.H)
-        check(32768L, size(vh) + 2*self.H)
-        check(32768L*32768L-1, size(vh) + 2*self.H)
-        check(32768L*32768L, size(vh) + 3*self.H)
+        check(1L, size(vh) + self.longdigit)
+        check(-1L, size(vh) + self.longdigit)
+        PyLong_BASE = 2**sys.long_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)
         # module
         check(unittest, size(h + 'P'))
         # None