diff --git a/Include/pymath.h b/Include/pymath.h
index 6cf69f98acf933..87a49d18ac22ed 100644
--- a/Include/pymath.h
+++ b/Include/pymath.h
@@ -221,10 +221,14 @@ PyAPI_FUNC(void) _Py_set_387controlword(unsigned short);
 #define _Py_IntegralTypeMax(type) ((_Py_IntegralTypeSigned(type)) ? (((((type)1 << (sizeof(type)*CHAR_BIT - 2)) - 1) << 1) + 1) : ~(type)0)
 /* Return the minimum value of integral type *type*. */
 #define _Py_IntegralTypeMin(type) ((_Py_IntegralTypeSigned(type)) ? -_Py_IntegralTypeMax(type) - 1 : 0)
+
 /* Check whether *v* is in the range of integral type *type*. This is most
- * useful if *v* is floating-point, since demoting a floating-point *v* to an
- * integral type that cannot represent *v*'s integral part is undefined
- * behavior. */
-#define _Py_InIntegralTypeRange(type, v) (_Py_IntegralTypeMin(type) <= v && v <= _Py_IntegralTypeMax(type))
+ * useful if *v* is floating-point, since demoting a floating-point *v* to
+ * an integral type that cannot represent *v*'s integral part is undefined
+ * behavior. If however sizeof(*v*) == sizeof(*type*) and *v* is a
+ * floating-point, maximal value of *type* cannot be represented exactly,
+ * thus the check, to be true needs to use strict less than (<).
+ */
+#define _Py_InIntegralTypeRange(type, v) (_Py_IntegralTypeMin(type) <= v && v < _Py_IntegralTypeMax(type))
 
 #endif /* Py_PYMATH_H */
diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
index 7354b969907b16..03208597fd482c 100644
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -160,6 +160,7 @@ def test_conversions(self):
     def test_sleep(self):
         self.assertRaises(ValueError, time.sleep, -2)
         self.assertRaises(ValueError, time.sleep, -1)
+        self.assertRaises(OverflowError, time.sleep, 2**63 / SEC_TO_NS)
         time.sleep(1.2)
 
     def test_strftime(self):
diff --git a/Misc/ACKS b/Misc/ACKS
index 8c8d954a312cb4..86eef013ff9e0b 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -1830,3 +1830,4 @@ Jelle Zijlstra
 Gennadiy Zlobin
 Doug Zongker
 Peter Åstrand
+Michał Radwański
diff --git a/Misc/NEWS.d/next/Core and Builtins/2018-08-18-01-39-06.bpo-34423.8rsQIk.rst b/Misc/NEWS.d/next/Core and Builtins/2018-08-18-01-39-06.bpo-34423.8rsQIk.rst
new file mode 100644
index 00000000000000..b33096dca81456
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2018-08-18-01-39-06.bpo-34423.8rsQIk.rst	
@@ -0,0 +1,2 @@
+``time.sleep(2**63 / 10**9)`` no longer eludes range checks and doesn't
+overflow.