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	Tue Feb 09 17:07:11 2016 -0500
@@ -689,6 +689,14 @@
         self.assertRaises(OverflowError, int, float('-inf'))
         self.assertRaises(ValueError, int, float('nan'))
 
+    def test_mod_division(self):
+        with self.assertRaises(ZeroDivisionError):
+            _ = 1 % 0
+        self.assertEqual(13 % 10, 3)
+        self.assertEqual(-13 % 10, 7)
+        self.assertEqual(13 % -10, -7)
+        self.assertEqual(-13 % -10, -3)
+
     def test_true_division(self):
         huge = 1 << 40000
         mhuge = -huge
@@ -723,6 +731,20 @@
         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	Tue Feb 09 17:07:11 2016 -0500
@@ -3502,6 +3502,48 @@
     return (PyObject *)z;
 }
 
+/* Fast modulo division for single-digit longs. */
+static PyObject *
+fast_mod(PyLongObject *a, PyLongObject *b)
+{
+    sdigit left = a->ob_digit[0];
+    sdigit right = b->ob_digit[0];
+    sdigit mod;
+
+    assert(Py_ABS(Py_SIZE(a)) == 1);
+    assert(Py_ABS(Py_SIZE(b)) == 1);
+
+    if (Py_SIZE(a) == Py_SIZE(b)) {
+        mod = left % right;
+    } else {
+        /* Either 'a' or 'b' is negative. */
+        mod = right - 1 - (left - 1) % right;
+    }
+
+    return PyLong_FromLong(mod);
+}
+
+/* Fast modulo division for single-digit longs. */
+static PyObject *
+fast_floor_div(PyLongObject *a, PyLongObject *b)
+{
+    sdigit left = a->ob_digit[0];
+    sdigit right = b->ob_digit[0];
+    sdigit div;
+
+    assert(Py_ABS(Py_SIZE(a)) == 1);
+    assert(Py_ABS(Py_SIZE(b)) == 1);
+
+    if (Py_SIZE(a) == Py_SIZE(b)) {
+        div = left / right;
+    } else {
+        /* Either 'a' or 'b' is negative. */
+        div = -1 - (left - 1) / right;
+    }
+
+    return PyLong_FromLong(div);
+}
+
 /* The / and % operators are now defined in terms of divmod().
    The expression a mod b has the value a - b*floor(a/b).
    The long_divrem function gives the remainder after division of
@@ -3529,6 +3571,24 @@
 {
     PyLongObject *div, *mod;
 
+    if (Py_ABS(Py_SIZE(v)) == 1 && Py_ABS(Py_SIZE(w)) == 1) {
+        /* Fast path for signle-digit longs */
+        if (pdiv != NULL) {
+            div = (PyLongObject *)fast_floor_div(v, w);
+            if (div == NULL) {
+                return -1;
+            }
+            *pdiv = div;
+        }
+        if (pmod != NULL) {
+            mod = (PyLongObject *)fast_mod(v, w);
+            if (mod == NULL) {
+                return -1;
+            }
+            *pmod = mod;
+        }
+        return 0;
+    }
     if (long_divrem(v, w, &div, &mod) < 0)
         return -1;
     if ((Py_SIZE(mod) < 0 && Py_SIZE(w) > 0) ||
@@ -3573,6 +3633,11 @@
     PyLongObject *div;
 
     CHECK_BINOP(a, b);
+
+    if (Py_ABS(Py_SIZE(a)) == 1 && Py_ABS(Py_SIZE(b)) == 1) {
+        return fast_floor_div((PyLongObject*)a, (PyLongObject*)b);
+    }
+
     if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, NULL) < 0)
         div = NULL;
     return (PyObject *)div;
@@ -3848,6 +3913,10 @@
 
     CHECK_BINOP(a, b);
 
+    if (Py_ABS(Py_SIZE(a)) == 1 && Py_ABS(Py_SIZE(b)) == 1) {
+        return fast_mod((PyLongObject*)a, (PyLongObject*)b);
+    }
+
     if (l_divmod((PyLongObject*)a, (PyLongObject*)b, NULL, &mod) < 0)
         mod = NULL;
     return (PyObject *)mod;