diff -r f494052eb476 Lib/test/test_long.py
--- a/Lib/test/test_long.py	Mon Feb 08 20:28:22 2016 +0200
+++ b/Lib/test/test_long.py	Mon Feb 08 17:36:33 2016 -0500
@@ -723,6 +723,20 @@
         for zero in ["huge / 0", "mhuge / 0"]:
             self.assertRaises(ZeroDivisionError, eval, zero, namespace)
 
+    def test_floordiv(self):
+        with self.assertRaises(ZeroDivisionError):
+            a = 1 // 0
+
+        self.assertEqual(2 // 3, 0)
+        self.assertEqual(2 // -3, -1)
+        self.assertEqual(-2 // 3, -1)
+        self.assertEqual(-2 // -3, 0)
+
+        self.assertEqual(-11 // -3, 3)
+        self.assertEqual(-11 // 3, -4)
+        self.assertEqual(11 // -3, -4)
+        self.assertEqual(11 // 3, 3)
+
     def check_truediv(self, a, b, skip_small=True):
         """Verify that the result of a/b is correctly rounded, by
         comparing it with a pure Python implementation of correctly
diff -r f494052eb476 Objects/longobject.c
--- a/Objects/longobject.c	Mon Feb 08 20:28:22 2016 +0200
+++ b/Objects/longobject.c	Mon Feb 08 17:36:33 2016 -0500
@@ -3573,6 +3573,26 @@
     PyLongObject *div;
 
     CHECK_BINOP(a, b);
+
+    if (Py_ABS(Py_SIZE(a)) == 1 && Py_ABS(Py_SIZE(b)) == 1) {
+        /* Fast path for single digit longs. */
+        sdigit left = ((PyLongObject*)a)->ob_digit[0];
+        sdigit right = ((PyLongObject*)b)->ob_digit[0];
+        sdigit div;
+
+        div = left / right;
+        if (Py_SIZE(a) != Py_SIZE(b)) {
+            /* either 'a' or 'b' is negative */
+            if (left != div * right) {
+                /* we want floor */
+                ++div;
+            }
+            div = -div;
+        }
+
+        return PyLong_FromLong(div);
+    }
+
     if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, NULL) < 0)
         div = NULL;
     return (PyObject *)div;