Add more tests.

Lib/test/test_complex.py

@@ -87,6 +87,10 @@ def assertClose(self, x, y, eps=1e-9):
         self.assertCloseAbs(x.real, y.real, eps)
         self.assertCloseAbs(x.imag, y.imag, eps)
 
+    def assertSameSign(self, x, y):
+        if copysign(1., x) != copysign(1., y):
+            self.fail(f'{x!r} and {y!r} have different signs')
+
     def check_div(self, x, y):
         """Compute complex z=x*y, and check that z/x==y and z/y==x."""
         z = x * y
@@ -456,16 +460,14 @@ def test_pow_with_small_integer_exponents(self):
                 self.assertComplexesAreIdentical(c**1, c)
                 self.assertComplexesAreIdentical(c**2, c*c)
                 self.assertComplexesAreIdentical(c**3, c*(c*c))
-                self.assertComplexesAreIdentical(c**4, (c*c)*(c*c))
-                self.assertComplexesAreIdentical(c**5, c*((c*c)*(c*c)))
-                self.assertComplexesAreIdentical(c**6, (c*c)*((c*c)*(c*c)))
-                self.assertComplexesAreIdentical(c**7, c*(c*c)*((c*c)*(c*c)))
-                self.assertComplexesAreIdentical(c**8, ((c*c)*(c*c))*((c*c)*(c*c)))
+                self.assertComplexesAreIdentical(c**3, (c*c)*c)
                 if not c:
                     continue
                 for n in range(1, 9):
                     with self.subTest(exponent=-n):
                         self.assertComplexesAreIdentical(c**-n, 1/(c**n))
+
+        # Special cases for complex division.
         for x in [+2, -2]:
             for y in [+0.0, -0.0]:
                 c = complex(x, y)
@@ -485,6 +487,25 @@ def test_pow_with_small_integer_exponents(self):
                     self.assertComplexesAreIdentical(c**-1, complex(+0.0*y, -1/x))
                     self.assertComplexesAreIdentical(c**-2, complex(-0.0, -y/x))
 
+        # Test that zeroes has the same sign as small non-zero values.
+        eps = 1e-8
+        pairs = [(complex(x, y), complex(x, copysign(0.0, y)))
+                 for x in [+1, -1] for y in [+eps, -eps]]
+        pairs += [(complex(y, x), complex(copysign(0.0, y), x))
+                  for x in [+1, -1] for y in [+eps, -eps]]
+        for c1, c2 in pairs:
+            for n in exponents:
+                with self.subTest(value=c1, exponent=n):
+                    r1 = c1**n
+                    r2 = c2**n
+                    self.assertClose(r1, r2)
+                    self.assertSameSign(r1.real, r2.real)
+                    self.assertSameSign(r1.imag, r2.imag)
+                    self.assertNotEqual(r1.real, 0.0)
+                    if n != 0:
+                        self.assertNotEqual(r1.imag, 0.0)
+                    self.assertTrue(r2.real == 0.0 or r2.imag == 0.0)
+
     def test_boolcontext(self):
         for i in range(100):
             self.assertTrue(complex(random() + 1e-6, random() + 1e-6))