diff -r 01943b2114a6 Lib/test/test_itertools.py
--- a/Lib/test/test_itertools.py	Thu Sep 08 15:04:38 2016 +0200
+++ b/Lib/test/test_itertools.py	Thu Sep 08 20:55:35 2016 +0300
@@ -516,6 +516,14 @@ class TestBasicOps(unittest.TestCase):
                          list(range(-maxsize-5, -maxsize+5)))
         self.assertEqual(list(islice(count(10, maxsize+5), 3)),
                          list(range(10, 10+3*(maxsize+5), maxsize+5)))
+        self.assertEqual(take(3, count(3.25)), [3.25, 4.25, 5.25])
+        self.assertEqual(take(3, count(3.25-4j)), [3.25-4j, 4.25-4j, 5.25-4j])
+        self.assertEqual(take(3, count(Decimal('1.1'))),
+                         [Decimal('1.1'), Decimal('2.1'), Decimal('3.1')])
+        self.assertEqual(take(3, count(Fraction(2, 3))),
+                         [Fraction(2, 3), Fraction(5, 3), Fraction(8, 3)])
+        BIGINT = 1<<1000
+        self.assertEqual(take(3, count(BIGINT)), [BIGINT, BIGINT+1, BIGINT+2])
         c = count(3)
         self.assertEqual(repr(c), 'count(3)')
         next(c)
@@ -523,8 +531,10 @@ class TestBasicOps(unittest.TestCase):
         c = count(-9)
         self.assertEqual(repr(c), 'count(-9)')
         next(c)
+        self.assertEqual(next(c), -8)
         self.assertEqual(repr(count(10.25)), 'count(10.25)')
-        self.assertEqual(next(c), -8)
+        self.assertEqual(repr(count(10.0)), 'count(10.0)')
+        self.assertEqual(type(next(count(10.0))), float)
         for i in (-sys.maxsize-5, -sys.maxsize+5 ,-10, -1, 0, 10, sys.maxsize-5, sys.maxsize+5):
             # Test repr
             r1 = repr(count(i))
@@ -548,16 +558,20 @@ class TestBasicOps(unittest.TestCase):
                          [('a', 2), ('b', 5), ('c', 8)])
         self.assertEqual(lzip('abc',count(step=-1)),
                          [('a', 0), ('b', -1), ('c', -2)])
+        self.assertRaises(TypeError, count, 'a', 'b')
         self.assertEqual(lzip('abc',count(2,0)), [('a', 2), ('b', 2), ('c', 2)])
         self.assertEqual(lzip('abc',count(2,1)), [('a', 2), ('b', 3), ('c', 4)])
         self.assertEqual(lzip('abc',count(2,3)), [('a', 2), ('b', 5), ('c', 8)])
         self.assertEqual(take(20, count(maxsize-15, 3)), take(20, range(maxsize-15, maxsize+100, 3)))
         self.assertEqual(take(20, count(-maxsize-15, 3)), take(20, range(-maxsize-15,-maxsize+100, 3)))
+        self.assertEqual(take(3, count(2, 1.25)), [2, 3.25, 4.5])
         self.assertEqual(take(3, count(2, 3.25-4j)), [2, 5.25-4j, 8.5-8j])
         self.assertEqual(take(3, count(Decimal('1.1'), Decimal('.1'))),
                          [Decimal('1.1'), Decimal('1.2'), Decimal('1.3')])
         self.assertEqual(take(3, count(Fraction(2,3), Fraction(1,7))),
                          [Fraction(2,3), Fraction(17,21), Fraction(20,21)])
+        BIGINT = 1<<1000
+        self.assertEqual(take(3, count(step=BIGINT)), [0, BIGINT, 2*BIGINT])
         self.assertEqual(repr(take(3, count(10, 2.5))), repr([10, 12.5, 15.0]))
         c = count(3, 5)
         self.assertEqual(repr(c), 'count(3, 5)')
@@ -575,6 +589,10 @@ class TestBasicOps(unittest.TestCase):
         self.assertEqual(repr(count(10.5, 1.25)), 'count(10.5, 1.25)')
         self.assertEqual(repr(count(10.5, 1)), 'count(10.5)')           # suppress step=1 when it's an int
         self.assertEqual(repr(count(10.5, 1.00)), 'count(10.5, 1.0)')   # do show float values lilke 1.0
+        self.assertEqual(repr(count(10, 1.00)), 'count(10, 1.0)')
+        c = count(10, 1.0)
+        self.assertEqual(type(next(c)), int)
+        self.assertEqual(type(next(c)), float)
         for i in (-sys.maxsize-5, -sys.maxsize+5 ,-10, -1, 0, 10, sys.maxsize-5, sys.maxsize+5):
             for j in  (-sys.maxsize-5, -sys.maxsize+5 ,-10, -1, 0, 1, 10, sys.maxsize-5, sys.maxsize+5):
                 # Test repr
diff -r 01943b2114a6 Modules/itertoolsmodule.c
--- a/Modules/itertoolsmodule.c	Thu Sep 08 15:04:38 2016 +0200
+++ b/Modules/itertoolsmodule.c	Thu Sep 08 20:55:35 2016 +0300
@@ -3907,7 +3907,7 @@ static PyObject *
 count_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
     countobject *lz;
-    int slow_mode = 0;
+    int slow_mode;
     Py_ssize_t cnt = 0;
     PyObject *long_cnt = NULL;
     PyObject *long_step = NULL;
@@ -3924,16 +3924,26 @@ count_new(PyTypeObject *type, PyObject *
                     return NULL;
     }
 
+    slow_mode = !(long_cnt == NULL || PyLong_Check(long_cnt)) ||
+                !(long_step == NULL || PyLong_Check(long_step));
+
+    /* If not specified, step defaults to 1 */
     if (long_cnt != NULL) {
-        cnt = PyLong_AsSsize_t(long_cnt);
-        if ((cnt == -1 && PyErr_Occurred()) || !PyLong_Check(long_cnt)) {
-            PyErr_Clear();
-            slow_mode = 1;
+        if (!slow_mode) {
+            assert(PyLong_Check(long_cnt));
+            cnt = PyLong_AsSsize_t(long_cnt);
+            if (cnt == -1 && PyErr_Occurred()) {
+                PyErr_Clear();
+                slow_mode = 1;
+            }
         }
         Py_INCREF(long_cnt);
     } else {
         cnt = 0;
         long_cnt = PyLong_FromLong(0);
+        if (long_cnt == NULL) {
+            return NULL;
+        }
     }
 
     /* If not specified, step defaults to 1 */
@@ -3949,11 +3959,14 @@ count_new(PyTypeObject *type, PyObject *
     assert(long_cnt != NULL && long_step != NULL);
 
     /* Fast mode only works when the step is 1 */
-    step = PyLong_AsLong(long_step);
-    if (step != 1) {
-        slow_mode = 1;
-        if (step == -1 && PyErr_Occurred())
-            PyErr_Clear();
+    if (!slow_mode) {
+        assert(PyLong_Check(long_step));
+        step = PyLong_AsLong(long_step);
+        if (step != 1) {
+            slow_mode = 1;
+            if (step == -1 && PyErr_Occurred())
+                PyErr_Clear();
+        }
     }
 
     if (slow_mode)