diff --git a/numpy/random/mtrand/mtrand.pyx b/numpy/random/mtrand/mtrand.pyx
index 9f901f14cc37..c0082a782d16 100644
--- a/numpy/random/mtrand/mtrand.pyx
+++ b/numpy/random/mtrand/mtrand.pyx
@@ -964,20 +964,31 @@ cdef class RandomState:
             high = low
             low = 0
 
+        # '_randint_type' is defined in
+        # 'generate_randint_helpers.py'
         key = np.dtype(dtype).name
-        if not key in _randint_type:
+        if key not in _randint_type:
             raise TypeError('Unsupported dtype "%s" for randint' % key)
+
         lowbnd, highbnd, randfunc = _randint_type[key]
 
-        if low < lowbnd:
+        # TODO: Do not cast these inputs to Python int
+        #
+        # This is a workaround until gh-8851 is resolved (bug in NumPy
+        # integer comparison and subtraction involving uint64 and non-
+        # uint64). Afterwards, remove these two lines.
+        ilow = int(low)
+        ihigh = int(high)
+
+        if ilow < lowbnd:
             raise ValueError("low is out of bounds for %s" % (key,))
-        if high > highbnd:
+        if ihigh > highbnd:
             raise ValueError("high is out of bounds for %s" % (key,))
-        if low >= high:
+        if ilow >= ihigh:
             raise ValueError("low >= high")
 
         with self.lock:
-            ret = randfunc(low, high - 1, size, self.state_address)
+            ret = randfunc(ilow, ihigh - 1, size, self.state_address)
 
             if size is None:
                 if dtype in (np.bool, np.int, np.long):
diff --git a/numpy/random/tests/test_random.py b/numpy/random/tests/test_random.py
index e10c442a5e65..0e739649496d 100644
--- a/numpy/random/tests/test_random.py
+++ b/numpy/random/tests/test_random.py
@@ -157,22 +157,42 @@ def test_rng_zero_and_extremes(self):
         for dt in self.itype:
             lbnd = 0 if dt is np.bool_ else np.iinfo(dt).min
             ubnd = 2 if dt is np.bool_ else np.iinfo(dt).max + 1
+
             tgt = ubnd - 1
             assert_equal(self.rfunc(tgt, tgt + 1, size=1000, dtype=dt), tgt)
+
             tgt = lbnd
             assert_equal(self.rfunc(tgt, tgt + 1, size=1000, dtype=dt), tgt)
+
             tgt = (lbnd + ubnd)//2
             assert_equal(self.rfunc(tgt, tgt + 1, size=1000, dtype=dt), tgt)
 
+    def test_full_range(self):
+        # Test for ticket #1690
+
+        for dt in self.itype:
+            lbnd = 0 if dt is np.bool_ else np.iinfo(dt).min
+            ubnd = 2 if dt is np.bool_ else np.iinfo(dt).max + 1
+
+            try:
+                self.rfunc(lbnd, ubnd, dtype=dt)
+            except Exception as e:
+                raise AssertionError("No error should have been raised, "
+                                     "but one was with the following "
+                                     "message:\n\n%s" % str(e))
+
     def test_in_bounds_fuzz(self):
         # Don't use fixed seed
         np.random.seed()
+
         for dt in self.itype[1:]:
             for ubnd in [4, 8, 16]:
                 vals = self.rfunc(2, ubnd, size=2**16, dtype=dt)
                 assert_(vals.max() < ubnd)
                 assert_(vals.min() >= 2)
-        vals = self.rfunc(0, 2, size=2**16, dtype=np.bool)
+
+        vals = self.rfunc(0, 2, size=2**16, dtype=np.bool_)
+
         assert_(vals.max() < 2)
         assert_(vals.min() >= 0)
 
@@ -209,6 +229,29 @@ def test_repeatability(self):
         res = hashlib.md5(val).hexdigest()
         assert_(tgt[np.dtype(np.bool).name] == res)
 
+    def test_int64_uint64_corner_case(self):
+        # When stored in Numpy arrays, `lbnd` is casted
+        # as np.int64, and `ubnd` is casted as np.uint64.
+        # Checking whether `lbnd` >= `ubnd` used to be
+        # done solely via direct comparison, which is incorrect
+        # because when Numpy tries to compare both numbers,
+        # it casts both to np.float64 because there is
+        # no integer superset of np.int64 and np.uint64. However,
+        # `ubnd` is too large to be represented in np.float64,
+        # causing it be round down to np.iinfo(np.int64).max,
+        # leading to a ValueError because `lbnd` now equals
+        # the new `ubnd`.
+
+        dt = np.int64
+        tgt = np.iinfo(np.int64).max
+        lbnd = np.int64(np.iinfo(np.int64).max)
+        ubnd = np.uint64(np.iinfo(np.int64).max + 1)
+
+        # None of these function calls should
+        # generate a ValueError now.
+        actual = np.random.randint(lbnd, ubnd, dtype=dt)
+        assert_equal(actual, tgt)
+
     def test_respect_dtype_singleton(self):
         # See gh-7203
         for dt in self.itype:
diff --git a/numpy/random/tests/test_regression.py b/numpy/random/tests/test_regression.py
index b50b6b2606c9..ce435b374df2 100644
--- a/numpy/random/tests/test_regression.py
+++ b/numpy/random/tests/test_regression.py
@@ -55,15 +55,6 @@ def test_permutation_longs(self):
         b = np.random.permutation(long(12))
         assert_array_equal(a, b)
 
-    def test_randint_range(self):
-        # Test for ticket #1690
-        lmax = np.iinfo('l').max
-        lmin = np.iinfo('l').min
-        try:
-            random.randint(lmin, lmax)
-        except:
-            raise AssertionError
-
     def test_shuffle_mixed_dimension(self):
         # Test for trac ticket #2074
         for t in [[1, 2, 3, None],