bpo-40282: Allow random.getrandbits(0) (GH-19539)

diff --git a/Lib/random.py b/Lib/random.py
index 82345fa..3243938 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -261,6 +261,8 @@
     def _randbelow_with_getrandbits(self, n):
         "Return a random int in the range [0,n).  Raises ValueError if n==0."
 
+        if not n:
+            raise ValueError("Boundary cannot be zero")
         getrandbits = self.getrandbits
         k = n.bit_length()  # don't use (n-1) here because n can be 1
         r = getrandbits(k)          # 0 <= r < 2**k
@@ -733,8 +735,8 @@
 
     def getrandbits(self, k):
         """getrandbits(k) -> x.  Generates an int with k random bits."""
-        if k <= 0:
-            raise ValueError('number of bits must be greater than zero')
+        if k < 0:
+            raise ValueError('number of bits must be non-negative')
         numbytes = (k + 7) // 8                       # bits / 8 and rounded up
         x = int.from_bytes(_urandom(numbytes), 'big')
         return x >> (numbytes * 8 - k)                # trim excess bits
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index f709e52..efac36a 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -263,6 +263,31 @@
             self.assertEqual(x1, x2)
             self.assertEqual(y1, y2)
 
+    def test_getrandbits(self):
+        # Verify ranges
+        for k in range(1, 1000):
+            self.assertTrue(0 <= self.gen.getrandbits(k) < 2**k)
+        self.assertEqual(self.gen.getrandbits(0), 0)
+
+        # Verify all bits active
+        getbits = self.gen.getrandbits
+        for span in [1, 2, 3, 4, 31, 32, 32, 52, 53, 54, 119, 127, 128, 129]:
+            all_bits = 2**span-1
+            cum = 0
+            cpl_cum = 0
+            for i in range(100):
+                v = getbits(span)
+                cum |= v
+                cpl_cum |= all_bits ^ v
+            self.assertEqual(cum, all_bits)
+            self.assertEqual(cpl_cum, all_bits)
+
+        # Verify argument checking
+        self.assertRaises(TypeError, self.gen.getrandbits)
+        self.assertRaises(TypeError, self.gen.getrandbits, 1, 2)
+        self.assertRaises(ValueError, self.gen.getrandbits, -1)
+        self.assertRaises(TypeError, self.gen.getrandbits, 10.1)
+
     def test_pickling(self):
         for proto in range(pickle.HIGHEST_PROTOCOL + 1):
             state = pickle.dumps(self.gen, proto)
@@ -390,26 +415,6 @@
         raises(0, 42, 0)
         raises(0, 42, 3.14159)
 
-    def test_genrandbits(self):
-        # Verify ranges
-        for k in range(1, 1000):
-            self.assertTrue(0 <= self.gen.getrandbits(k) < 2**k)
-
-        # Verify all bits active
-        getbits = self.gen.getrandbits
-        for span in [1, 2, 3, 4, 31, 32, 32, 52, 53, 54, 119, 127, 128, 129]:
-            cum = 0
-            for i in range(100):
-                cum |= getbits(span)
-            self.assertEqual(cum, 2**span-1)
-
-        # Verify argument checking
-        self.assertRaises(TypeError, self.gen.getrandbits)
-        self.assertRaises(TypeError, self.gen.getrandbits, 1, 2)
-        self.assertRaises(ValueError, self.gen.getrandbits, 0)
-        self.assertRaises(ValueError, self.gen.getrandbits, -1)
-        self.assertRaises(TypeError, self.gen.getrandbits, 10.1)
-
     def test_randbelow_logic(self, _log=log, int=int):
         # check bitcount transition points:  2**i and 2**(i+1)-1
         # show that: k = int(1.001 + _log(n, 2))
@@ -629,34 +634,18 @@
             self.assertEqual(set(range(start,stop)),
                 set([self.gen.randrange(start,stop) for i in range(100)]))
 
-    def test_genrandbits(self):
+    def test_getrandbits(self):
+        super().test_getrandbits()
+
         # Verify cross-platform repeatability
         self.gen.seed(1234567)
         self.assertEqual(self.gen.getrandbits(100),
                          97904845777343510404718956115)
-        # Verify ranges
-        for k in range(1, 1000):
-            self.assertTrue(0 <= self.gen.getrandbits(k) < 2**k)
-
-        # Verify all bits active
-        getbits = self.gen.getrandbits
-        for span in [1, 2, 3, 4, 31, 32, 32, 52, 53, 54, 119, 127, 128, 129]:
-            cum = 0
-            for i in range(100):
-                cum |= getbits(span)
-            self.assertEqual(cum, 2**span-1)
-
-        # Verify argument checking
-        self.assertRaises(TypeError, self.gen.getrandbits)
-        self.assertRaises(TypeError, self.gen.getrandbits, 'a')
-        self.assertRaises(TypeError, self.gen.getrandbits, 1, 2)
-        self.assertRaises(ValueError, self.gen.getrandbits, 0)
-        self.assertRaises(ValueError, self.gen.getrandbits, -1)
 
     def test_randrange_uses_getrandbits(self):
         # Verify use of getrandbits by randrange
         # Use same seed as in the cross-platform repeatability test
-        # in test_genrandbits above.
+        # in test_getrandbits above.
         self.gen.seed(1234567)
         # If randrange uses getrandbits, it should pick getrandbits(100)
         # when called with a 100-bits stop argument.