Issue #7534: Fix handling of nans, infinities, and negative zero in **
operator, on IEEE 754 platforms. Thanks Marcos Donolo for original patch.
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index 564f24f..ddaf7bd 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -12,6 +12,11 @@
INF = float("inf")
NAN = float("nan")
+# decorator for skipping tests on non-IEEE 754 platforms
+requires_IEEE_754 = unittest.skipUnless(
+ float.__getformat__("double").startswith("IEEE"),
+ "test requires IEEE 754 doubles")
+
#locate file with float format test values
test_dir = os.path.dirname(__file__) or os.curdir
format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt')
@@ -142,6 +147,213 @@
self.assertRaises(OverflowError, float('-inf').as_integer_ratio)
self.assertRaises(ValueError, float('nan').as_integer_ratio)
+ def assertEqualAndEqualSign(self, a, b):
+ # fail unless a == b and a and b have the same sign bit;
+ # the only difference from assertEqual is that this test
+ # distingishes -0.0 and 0.0.
+ self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))
+
+ @requires_IEEE_754
+ def test_float_pow(self):
+ # test builtin pow and ** operator for IEEE 754 special cases.
+ # Special cases taken from section F.9.4.4 of the C99 specification
+
+ for pow_op in pow, operator.pow:
+ # x**NAN is NAN for any x except 1
+ self.assertTrue(isnan(pow_op(-INF, NAN)))
+ self.assertTrue(isnan(pow_op(-2.0, NAN)))
+ self.assertTrue(isnan(pow_op(-1.0, NAN)))
+ self.assertTrue(isnan(pow_op(-0.5, NAN)))
+ self.assertTrue(isnan(pow_op(-0.0, NAN)))
+ self.assertTrue(isnan(pow_op(0.0, NAN)))
+ self.assertTrue(isnan(pow_op(0.5, NAN)))
+ self.assertTrue(isnan(pow_op(2.0, NAN)))
+ self.assertTrue(isnan(pow_op(INF, NAN)))
+ self.assertTrue(isnan(pow_op(NAN, NAN)))
+
+ # NAN**y is NAN for any y except +-0
+ self.assertTrue(isnan(pow_op(NAN, -INF)))
+ self.assertTrue(isnan(pow_op(NAN, -2.0)))
+ self.assertTrue(isnan(pow_op(NAN, -1.0)))
+ self.assertTrue(isnan(pow_op(NAN, -0.5)))
+ self.assertTrue(isnan(pow_op(NAN, 0.5)))
+ self.assertTrue(isnan(pow_op(NAN, 1.0)))
+ self.assertTrue(isnan(pow_op(NAN, 2.0)))
+ self.assertTrue(isnan(pow_op(NAN, INF)))
+
+ # (+-0)**y raises ZeroDivisionError for y a negative odd integer
+ self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0)
+ self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0)
+
+ # (+-0)**y raises ZeroDivisionError for y finite and negative
+ # but not an odd integer
+ self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0)
+ self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5)
+ self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0)
+ self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5)
+
+ # (+-0)**y is +-0 for y a positive odd integer
+ self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0)
+ self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0)
+
+ # (+-0)**y is 0 for y finite and positive but not an odd integer
+ self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0)
+ self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0)
+ self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0)
+ self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0)
+
+ # (-1)**+-inf is 1
+ self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0)
+
+ # 1**y is 1 for any y, even if y is an infinity or nan
+ self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0)
+
+ # x**+-0 is 1 for any x, even if x is a zero, infinity, or nan
+ self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0)
+
+ # x**y raises ValueError for finite negative x and non-integral y
+ self.assertRaises(ValueError, pow_op, -2.0, -0.5)
+ self.assertRaises(ValueError, pow_op, -2.0, 0.5)
+ self.assertRaises(ValueError, pow_op, -1.0, -0.5)
+ self.assertRaises(ValueError, pow_op, -1.0, 0.5)
+ self.assertRaises(ValueError, pow_op, -0.5, -0.5)
+ self.assertRaises(ValueError, pow_op, -0.5, 0.5)
+
+ # x**-INF is INF for abs(x) < 1
+ self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF)
+ self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF)
+ self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF)
+ self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF)
+
+ # x**-INF is 0 for abs(x) > 1
+ self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0)
+ self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0)
+ self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0)
+
+ # x**INF is 0 for abs(x) < 1
+ self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0)
+ self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0)
+ self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0)
+ self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0)
+
+ # x**INF is INF for abs(x) > 1
+ self.assertEqualAndEqualSign(pow_op(-INF, INF), INF)
+ self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF)
+ self.assertEqualAndEqualSign(pow_op(2.0, INF), INF)
+ self.assertEqualAndEqualSign(pow_op(INF, INF), INF)
+
+ # (-INF)**y is -0.0 for y a negative odd integer
+ self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0)
+
+ # (-INF)**y is 0.0 for y negative but not an odd integer
+ self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0)
+ self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0)
+
+ # (-INF)**y is -INF for y a positive odd integer
+ self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF)
+
+ # (-INF)**y is INF for y positive but not an odd integer
+ self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF)
+ self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF)
+
+ # INF**y is INF for y positive
+ self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF)
+ self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF)
+ self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF)
+
+ # INF**y is 0.0 for y negative
+ self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0)
+ self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0)
+ self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0)
+
+ # basic checks not covered by the special cases above
+ self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25)
+ self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5)
+ self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0)
+ self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25)
+ self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5)
+ self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0)
+
+ # 1 ** large and -1 ** large; some libms apparently
+ # have problems with these
+ self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0)
+ self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0)
+ self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0)
+
+ # check sign for results that underflow to 0
+ self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0)
+ self.assertRaises(ValueError, pow_op, -2.0, -2000.5)
+ self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0)
+ self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0)
+ self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0)
+ self.assertRaises(ValueError, pow_op, -0.5, 2000.5)
+ self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0)
+ self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0)
+ self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0)
+ self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0)
+
+ # check we don't raise an exception for subnormal results,
+ # and validate signs. Tests currently disabled, since
+ # they fail on systems where a subnormal result from pow
+ # is flushed to zero (e.g. Debian/ia64.)
+ #self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315)
+ #self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315)
+ #self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315)
+ #self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315)
+ #self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315)
+ #self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315)
+ #self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315)
+ #self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315)
+
+
class FormatFunctionsTestCase(unittest.TestCase):
def setUp(self):