Remove support for nth root of negative numbers with odd powers.

Although nth roots of negative numbers are real for odd n, the
statistics module doesn't make use of this. Remove support for
negative roots from the private _nth_root function, which
simplifies the test suite.

Lib/statistics.py

@@ -335,10 +335,7 @@ class _nroot_NS:
         """Handle nth root of Reals, treated as a float."""
         assert isinstance(n, int) and n > 1
         if x < 0:
-            if n%2 == 0:
-                raise ValueError('domain error: even root of negative number')
-            else:
-                return -_nroot_NS.nroot(-x, n)
+            raise ValueError('domain error: root of negative number')
         elif x == 0:
             return math.copysign(0.0, x)
         elif x > 0:
@@ -433,6 +430,8 @@ class _nroot_NS:
             else:
                 # Preserve the input NAN.
                 return x
+        if x < 0:
+            raise ValueError('domain error: root of negative number')
         if x.is_infinite():
             return x
         # FIXME this hasn't had the extensive testing of the float

Lib/test/test_statistics.py

@@ -1095,13 +1095,6 @@ class Test_Nth_Root(NumericTestCase):
                 with self.subTest(n=n, inf=INF):
                     self.assertEqual(self.nroot(INF, n), INF)
 
-    def testNInf(self):
-        # Test that the root of -inf is -inf for odd n.
-        for NINF in (float('-inf'), decimal.Decimal('-inf')):
-            for n in range(3, 11, 2):
-                with self.subTest(n=n, inf=NINF):
-                    self.assertEqual(self.nroot(NINF, n), NINF)
-
     # FIXME: need to check Decimal zeroes too.
     def test_zero(self):
         # Test that the root of +0.0 is +0.0.
@@ -1157,13 +1150,15 @@ class Test_Nth_Root(NumericTestCase):
             with self.subTest(x=x):
                 self.assertRaises(TypeError, self.nroot, x, 3)
 
-    def testNegativeEvenPower(self):
-        # Test negative x with even n raises correctly.
+    def testNegativeError(self):
+        # Test negative x raises correctly.
         x = random.uniform(-20.0, -0.1)
         assert x < 0
-        for n in range(2, 9, 2):
+        for n in range(3, 7):
             with self.subTest(x=x, n=n):
                 self.assertRaises(ValueError, self.nroot, x, n)
+        # And Decimal.
+        self.assertRaises(ValueError, self.nroot, Decimal(-27), 3)
 
     # --- Test that nroot is never worse than calling math.pow() ---
 
@@ -1216,25 +1211,11 @@ class Test_Nth_Root(NumericTestCase):
                     x = i**n
                     self.assertEqual(self.nroot(x, n), i)
 
-    def testExactPowersNegatives(self):
-        # Test that small negative integer powers are calculated exactly.
-        for i in range(-1, -51, -1):
-            for n in range(3, 16, 2):
-                if (i, n) == (-35, 13):
-                    # See testExpectedFailure35p13
-                    continue
-                with self.subTest(i=i, n=n):
-                    x = i**n
-                    assert sign(x) == -1
-                    self.assertEqual(self.nroot(x, n), i)
-
     def testExpectedFailure35p13(self):
         # Test the expected failure 35**13 is almost exact.
         x = 35**13
         err = abs(self.nroot(x, 13) - 35)
         self.assertLessEqual(err, 0.000000001)
-        err = abs(self.nroot(-x, 13) + 35)
-        self.assertLessEqual(err, 0.000000001)
 
     def testOne(self):
         # Test that the root of 1.0 is 1.0.