bpo-33089: Multidimensional math.hypot() (GH-8474)

1 files changed, 66 insertions, 10 deletions

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 44785d3..4843899 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -16,6 +16,7 @@ NAN = float('nan')
 INF = float('inf')
 NINF = float('-inf')
 FLOAT_MAX = sys.float_info.max
+FLOAT_MIN = sys.float_info.min
 
 # detect evidence of double-rounding: fsum is not always correctly
 # rounded on machines that suffer from double rounding.
@@ -720,16 +721,71 @@ class MathTests(unittest.TestCase):
         self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12)
 
     def testHypot(self):
-        self.assertRaises(TypeError, math.hypot)
-        self.ftest('hypot(0,0)', math.hypot(0,0), 0)
-        self.ftest('hypot(3,4)', math.hypot(3,4), 5)
-        self.assertEqual(math.hypot(NAN, INF), INF)
-        self.assertEqual(math.hypot(INF, NAN), INF)
-        self.assertEqual(math.hypot(NAN, NINF), INF)
-        self.assertEqual(math.hypot(NINF, NAN), INF)
-        self.assertRaises(OverflowError, math.hypot, FLOAT_MAX, FLOAT_MAX)
-        self.assertTrue(math.isnan(math.hypot(1.0, NAN)))
-        self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))
+        from decimal import Decimal
+        from fractions import Fraction
+
+        hypot = math.hypot
+
+        # Test different numbers of arguments (from zero to five)
+        # against a straightforward pure python implementation
+        args = math.e, math.pi, math.sqrt(2.0), math.gamma(3.5), math.sin(2.1)
+        for i in range(len(args)+1):
+            self.assertAlmostEqual(
+                hypot(*args[:i]),
+                math.sqrt(sum(s**2 for s in args[:i]))
+            )
+
+        # Test allowable types (those with __float__)
+        self.assertEqual(hypot(12.0, 5.0), 13.0)
+        self.assertEqual(hypot(12, 5), 13)
+        self.assertEqual(hypot(Decimal(12), Decimal(5)), 13)
+        self.assertEqual(hypot(Fraction(12, 32), Fraction(5, 32)), Fraction(13, 32))
+        self.assertEqual(hypot(bool(1), bool(0), bool(1), bool(1)), math.sqrt(3))
+
+        # Test corner cases
+        self.assertEqual(hypot(0.0, 0.0), 0.0)     # Max input is zero
+        self.assertEqual(hypot(-10.5), 10.5)       # Negative input
+        self.assertEqual(hypot(), 0.0)             # Negative input
+        self.assertEqual(1.0,
+            math.copysign(1.0, hypot(-0.0))        # Convert negative zero to positive zero
+        )
+
+        # Test handling of bad arguments
+        with self.assertRaises(TypeError):         # Reject keyword args
+            hypot(x=1)
+        with self.assertRaises(TypeError):         # Reject values without __float__
+            hypot(1.1, 'string', 2.2)
+
+        # Any infinity gives positive infinity.
+        self.assertEqual(hypot(INF), INF)
+        self.assertEqual(hypot(0, INF), INF)
+        self.assertEqual(hypot(10, INF), INF)
+        self.assertEqual(hypot(-10, INF), INF)
+        self.assertEqual(hypot(NAN, INF), INF)
+        self.assertEqual(hypot(INF, NAN), INF)
+        self.assertEqual(hypot(NINF, NAN), INF)
+        self.assertEqual(hypot(NAN, NINF), INF)
+        self.assertEqual(hypot(-INF, INF), INF)
+        self.assertEqual(hypot(-INF, -INF), INF)
+        self.assertEqual(hypot(10, -INF), INF)
+
+        # If no infinity, any NaN gives a Nan.
+        self.assertTrue(math.isnan(hypot(NAN)))
+        self.assertTrue(math.isnan(hypot(0, NAN)))
+        self.assertTrue(math.isnan(hypot(NAN, 10)))
+        self.assertTrue(math.isnan(hypot(10, NAN)))
+        self.assertTrue(math.isnan(hypot(NAN, NAN)))
+        self.assertTrue(math.isnan(hypot(NAN)))
+
+        # Verify scaling for extremely large values
+        fourthmax = FLOAT_MAX / 4.0
+        for n in range(32):
+            self.assertEqual(hypot(*([fourthmax]*n)), fourthmax * math.sqrt(n))
+
+        # Verify scaling for extremely small values
+        for exp in range(32):
+            scale = FLOAT_MIN / 2.0 ** exp
+            self.assertEqual(math.hypot(4*scale, 3*scale), 5*scale)
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)