Extend _sqrtprod() to cover the full range of inputs. Add tests. (GH-107855)

Lib/test/test_statistics.py

@@ -28,6 +28,12 @@ import statistics
 
 # === Helper functions and class ===
 
+# Test copied from Lib/test/test_math.py
+# detect evidence of double-rounding: fsum is not always correctly
+# rounded on machines that suffer from double rounding.
+x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer
+HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)
+
 def sign(x):
     """Return -1.0 for negatives, including -0.0, otherwise +1.0."""
     return math.copysign(1, x)
@@ -2564,6 +2570,79 @@ class TestCorrelationAndCovariance(unittest.TestCase):
         self.assertAlmostEqual(statistics.correlation(x, y), 1)
         self.assertAlmostEqual(statistics.covariance(x, y), 0.1)
 
+    def test_sqrtprod_helper_function_fundamentals(self):
+        # Verify that results are close to sqrt(x * y)
+        for i in range(100):
+            x = random.expovariate()
+            y = random.expovariate()
+            expected = math.sqrt(x * y)
+            actual = statistics._sqrtprod(x, y)
+            with self.subTest(x=x, y=y, expected=expected, actual=actual):
+                self.assertAlmostEqual(expected, actual)
+
+        x, y, target = 0.8035720646477457, 0.7957468097636939, 0.7996498651651661
+        self.assertEqual(statistics._sqrtprod(x, y), target)
+        self.assertNotEqual(math.sqrt(x * y), target)
+
+        # Test that range extremes avoid underflow and overflow
+        smallest = sys.float_info.min * sys.float_info.epsilon
+        self.assertEqual(statistics._sqrtprod(smallest, smallest), smallest)
+        biggest = sys.float_info.max
+        self.assertEqual(statistics._sqrtprod(biggest, biggest), biggest)
+
+        # Check special values and the sign of the result
+        special_values = [0.0, -0.0, 1.0, -1.0, 4.0, -4.0,
+                          math.nan, -math.nan, math.inf, -math.inf]
+        for x, y in itertools.product(special_values, repeat=2):
+            try:
+                expected = math.sqrt(x * y)
+            except ValueError:
+                expected = 'ValueError'
+            try:
+                actual = statistics._sqrtprod(x, y)
+            except ValueError:
+                actual = 'ValueError'
+            with self.subTest(x=x, y=y, expected=expected, actual=actual):
+                if isinstance(expected, str) and expected == 'ValueError':
+                    self.assertEqual(actual, 'ValueError')
+                    continue
+                self.assertIsInstance(actual, float)
+                if math.isnan(expected):
+                    self.assertTrue(math.isnan(actual))
+                    continue
+                self.assertEqual(actual, expected)
+                self.assertEqual(sign(actual), sign(expected))
+
+    @requires_IEEE_754
+    @unittest.skipIf(HAVE_DOUBLE_ROUNDING,
+                     "accuracy not guaranteed on machines with double rounding")
+    @support.cpython_only    # Allow for a weaker sumprod() implmentation
+    def test_sqrtprod_helper_function_improved_accuracy(self):
+        # Test a known example where accuracy is improved
+        x, y, target = 0.8035720646477457, 0.7957468097636939, 0.7996498651651661
+        self.assertEqual(statistics._sqrtprod(x, y), target)
+        self.assertNotEqual(math.sqrt(x * y), target)
+
+        def reference_value(x: float, y: float) -> float:
+            x = decimal.Decimal(x)
+            y = decimal.Decimal(y)
+            with decimal.localcontext() as ctx:
+                ctx.prec = 200
+                return float((x * y).sqrt())
+
+        # Verify that the new function with improved accuracy
+        # agrees with a reference value more often than old version.
+        new_agreements = 0
+        old_agreements = 0
+        for i in range(10_000):
+            x = random.expovariate()
+            y = random.expovariate()
+            new = statistics._sqrtprod(x, y)
+            old = math.sqrt(x * y)
+            ref = reference_value(x, y)
+            new_agreements += (new == ref)
+            old_agreements += (old == ref)
+        self.assertGreater(new_agreements, old_agreements)
 
     def test_correlation_spearman(self):
         # https://statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide-2.php