gh-156695: Improve accuracy of complex powers with small negative integer exponents

Author: Aniketsy

Lib/test/test_complex.py

@@ -8,7 +8,7 @@
 )
 
 from random import random
-from math import isnan, copysign
+from math import isnan, copysign, ulp
 import operator
 
 INF = float("inf")
@@ -446,6 +446,20 @@ def test_pow_with_small_integer_exponents(self):
                     self.assertEqual(str(float_pow), str(int_pow))
                     self.assertEqual(str(complex_pow), str(int_pow))
 
+    @support.requires_IEEE_754
+    def test_pow_small_negative_integer_exponents(self):
+        z = complex(float.fromhex('0x1.47e9c711723f5p+81'),
+                    float.fromhex('0x1.38afd1168e49fp+85'))
+        expected = complex(float.fromhex('0x0.4000000000000p-1022'),
+                           float.fromhex('0x0.3ffffffffffffp-1022'))
+        for exponent in (-12, -12.0, complex(-12.0, 0.0)):
+            with self.subTest(exponent=exponent):
+                result = z ** exponent
+                self.assertLessEqual(abs(result.real - expected.real),
+                                     4 * ulp(expected.real))
+                self.assertLessEqual(abs(result.imag - expected.imag),
+                                     4 * ulp(expected.imag))
+
     def test_boolcontext(self):
         for i in range(100):
             self.assertTrue(complex(random() + 1e-6, random() + 1e-6))

Objects/complexobject.c

@@ -357,10 +357,10 @@ c_powu(Py_complex x, long n)
 static Py_complex
 c_powi(Py_complex x, long n)
 {
-    if (n > 0)
+    if (n >= 0)
         return c_powu(x,n);
     else
-        return _Py_c_quot(c_1, c_powu(x,-n));
+        return c_powu(_Py_c_quot(c_1, x), -n);
 
 }