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Merged revisions 77139-77140 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk ........ r77139 | mark.dickinson | 2009-12-30 12:12:23 +0000 (Wed, 30 Dec 2009) | 3 lines Issue #7534: Fix handling of nans, infinities, and negative zero in ** operator, on IEEE 754 platforms. Thanks Marcos Donolo for original patch. ........ r77140 | mark.dickinson | 2009-12-30 12:22:49 +0000 (Wed, 30 Dec 2009) | 1 line Add Marcos Donolo for work on issue 7534 patch. ........
This commit is contained in:
Mark Dickinson
parent
faa6b7f421
commit
9ab44b509a
@ -72,7 +72,7 @@ False
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>>> NAN >= 0
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False
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All operations involving a NaN return a NaN except for the power of *0* and *1*.
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All operations involving a NaN return a NaN except for nan**0 and 1**nan.
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>>> 1 + NAN
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nan
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>>> 1 * NAN
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@ -81,8 +81,10 @@ nan
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nan
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>>> 1 ** NAN
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1.0
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>>> NAN ** 0
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1.0
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>>> 0 ** NAN
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0.0
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nan
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>>> (1.0 + FI.epsilon) * NAN
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nan
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@ -11,6 +11,11 @@ import random, fractions
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INF = float("inf")
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NAN = float("nan")
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# decorator for skipping tests on non-IEEE 754 platforms
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requires_IEEE_754 = unittest.skipUnless(
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float.__getformat__("double").startswith("IEEE"),
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"test requires IEEE 754 doubles")
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#locate file with float format test values
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test_dir = os.path.dirname(__file__) or os.curdir
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format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt')
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@ -161,6 +166,212 @@ class GeneralFloatCases(unittest.TestCase):
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self.assertTrue(s == s, "{%r} not equal to itself" % f)
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self.assertTrue(d == d, "{%r : None} not equal to itself" % f)
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def assertEqualAndEqualSign(self, a, b):
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# fail unless a == b and a and b have the same sign bit;
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# the only difference from assertEqual is that this test
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# distingishes -0.0 and 0.0.
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self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))
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@requires_IEEE_754
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def test_float_pow(self):
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# test builtin pow and ** operator for IEEE 754 special cases.
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# Special cases taken from section F.9.4.4 of the C99 specification
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for pow_op in pow, operator.pow:
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# x**NAN is NAN for any x except 1
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self.assertTrue(isnan(pow_op(-INF, NAN)))
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self.assertTrue(isnan(pow_op(-2.0, NAN)))
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self.assertTrue(isnan(pow_op(-1.0, NAN)))
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self.assertTrue(isnan(pow_op(-0.5, NAN)))
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self.assertTrue(isnan(pow_op(-0.0, NAN)))
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self.assertTrue(isnan(pow_op(0.0, NAN)))
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self.assertTrue(isnan(pow_op(0.5, NAN)))
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self.assertTrue(isnan(pow_op(2.0, NAN)))
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self.assertTrue(isnan(pow_op(INF, NAN)))
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self.assertTrue(isnan(pow_op(NAN, NAN)))
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# NAN**y is NAN for any y except +-0
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self.assertTrue(isnan(pow_op(NAN, -INF)))
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self.assertTrue(isnan(pow_op(NAN, -2.0)))
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self.assertTrue(isnan(pow_op(NAN, -1.0)))
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self.assertTrue(isnan(pow_op(NAN, -0.5)))
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self.assertTrue(isnan(pow_op(NAN, 0.5)))
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self.assertTrue(isnan(pow_op(NAN, 1.0)))
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self.assertTrue(isnan(pow_op(NAN, 2.0)))
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self.assertTrue(isnan(pow_op(NAN, INF)))
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# (+-0)**y raises ZeroDivisionError for y a negative odd integer
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self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0)
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self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0)
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# (+-0)**y raises ZeroDivisionError for y finite and negative
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# but not an odd integer
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self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0)
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self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5)
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self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0)
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self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5)
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# (+-0)**y is +-0 for y a positive odd integer
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self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0)
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self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0)
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# (+-0)**y is 0 for y finite and positive but not an odd integer
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self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0)
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self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0)
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self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0)
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self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0)
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# (-1)**+-inf is 1
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self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0)
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# 1**y is 1 for any y, even if y is an infinity or nan
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self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0)
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# x**+-0 is 1 for any x, even if x is a zero, infinity, or nan
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self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0)
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# x**y defers to complex pow for finite negative x and
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# non-integral y.
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self.assertEqual(type(pow_op(-2.0, -0.5)), complex)
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self.assertEqual(type(pow_op(-2.0, 0.5)), complex)
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self.assertEqual(type(pow_op(-1.0, -0.5)), complex)
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self.assertEqual(type(pow_op(-1.0, 0.5)), complex)
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self.assertEqual(type(pow_op(-0.5, -0.5)), complex)
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self.assertEqual(type(pow_op(-0.5, 0.5)), complex)
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# x**-INF is INF for abs(x) < 1
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self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF)
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self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF)
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self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF)
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self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF)
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# x**-INF is 0 for abs(x) > 1
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self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0)
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self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0)
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self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0)
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self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0)
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# x**INF is 0 for abs(x) < 1
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self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0)
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self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0)
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self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0)
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self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0)
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# x**INF is INF for abs(x) > 1
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self.assertEqualAndEqualSign(pow_op(-INF, INF), INF)
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self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF)
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self.assertEqualAndEqualSign(pow_op(2.0, INF), INF)
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self.assertEqualAndEqualSign(pow_op(INF, INF), INF)
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# (-INF)**y is -0.0 for y a negative odd integer
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self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0)
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# (-INF)**y is 0.0 for y negative but not an odd integer
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self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0)
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self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0)
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# (-INF)**y is -INF for y a positive odd integer
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self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF)
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# (-INF)**y is INF for y positive but not an odd integer
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self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF)
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self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF)
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# INF**y is INF for y positive
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self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF)
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self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF)
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self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF)
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# INF**y is 0.0 for y negative
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self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0)
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self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0)
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self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0)
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# basic checks not covered by the special cases above
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self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25)
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self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5)
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self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0)
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self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25)
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self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5)
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self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
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self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0)
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self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0)
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# 1 ** large and -1 ** large; some libms apparently
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# have problems with these
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self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0)
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self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0)
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self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0)
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# check sign for results that underflow to 0
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self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0)
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self.assertEqual(type(pow_op(-2.0, -2000.5)), complex)
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self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0)
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self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0)
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self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0)
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self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0)
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self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0)
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self.assertEqual(type(pow_op(-0.5, 2000.5)), complex)
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self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0)
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self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0)
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self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0)
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self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0)
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# check we don't raise an exception for subnormal results,
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# and validate signs. Tests currently disabled, since
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# they fail on systems where a subnormal result from pow
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# is flushed to zero (e.g. Debian/ia64.)
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#self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315)
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#self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315)
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#self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315)
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#self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315)
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#self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315)
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#self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315)
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#self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315)
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#self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315)
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class FormatFunctionsTestCase(unittest.TestCase):
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@ -186,6 +186,7 @@ Yves Dionne
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Daniel Dittmar
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Jaromir Dolecek
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Ismail Donmez
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Marcos Donolo
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Dima Dorfman
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Cesar Douady
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Dean Draayer
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@ -12,6 +12,10 @@ What's New in Python 3.2 Alpha 1?
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Core and Builtins
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-----------------
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- Issue #7534: Fix handling of IEEE specials (infinities, nans,
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negative zero) in ** operator. The behaviour now conforms to that
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described in C99 Annex F.
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- Issue #1811: improve accuracy and cross-platform consistency for
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true division of integers: the result of a/b is now correctly
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rounded for ints a and b (at least on IEEE 754 platforms), and in
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@ -671,10 +671,15 @@ float_floor_div(PyObject *v, PyObject *w)
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return r;
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}
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/* determine whether x is an odd integer or not; assumes that
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x is not an infinity or nan. */
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#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0)
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static PyObject *
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float_pow(PyObject *v, PyObject *w, PyObject *z)
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{
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double iv, iw, ix;
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int negate_result = 0;
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if ((PyObject *)z != Py_None) {
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PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
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@ -686,20 +691,56 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
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CONVERT_TO_DOUBLE(w, iw);
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/* Sort out special cases here instead of relying on pow() */
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if (iw == 0) { /* v**0 is 1, even 0**0 */
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if (iw == 0) { /* v**0 is 1, even 0**0 */
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return PyFloat_FromDouble(1.0);
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}
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if (iv == 0.0) { /* 0**w is error if w<0, else 1 */
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if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */
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return PyFloat_FromDouble(iv);
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}
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if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */
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return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw);
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}
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if (Py_IS_INFINITY(iw)) {
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/* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if
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* abs(v) > 1 (including case where v infinite)
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*
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* v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if
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* abs(v) > 1 (including case where v infinite)
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*/
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iv = fabs(iv);
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if (iv == 1.0)
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return PyFloat_FromDouble(1.0);
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else if ((iw > 0.0) == (iv > 1.0))
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return PyFloat_FromDouble(fabs(iw)); /* return inf */
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else
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return PyFloat_FromDouble(0.0);
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}
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if (Py_IS_INFINITY(iv)) {
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/* (+-inf)**w is: inf for w positive, 0 for w negative; in
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* both cases, we need to add the appropriate sign if w is
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* an odd integer.
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*/
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int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
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if (iw > 0.0)
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return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv));
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else
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return PyFloat_FromDouble(iw_is_odd ?
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copysign(0.0, iv) : 0.0);
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}
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if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero
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(already dealt with above), and an error
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if w is negative. */
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int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
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if (iw < 0.0) {
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PyErr_SetString(PyExc_ZeroDivisionError,
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"0.0 cannot be raised to a negative power");
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"0.0 cannot be raised to a "
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"negative power");
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return NULL;
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}
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return PyFloat_FromDouble(0.0);
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}
|
||||
if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
|
||||
return PyFloat_FromDouble(1.0);
|
||||
/* use correct sign if iw is odd */
|
||||
return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
|
||||
}
|
||||
|
||||
if (iv < 0.0) {
|
||||
/* Whether this is an error is a mess, and bumps into libm
|
||||
* bugs so we have to figure it out ourselves.
|
||||
@ -710,33 +751,41 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
|
||||
*/
|
||||
return PyComplex_Type.tp_as_number->nb_power(v, w, z);
|
||||
}
|
||||
/* iw is an exact integer, albeit perhaps a very large one.
|
||||
/* iw is an exact integer, albeit perhaps a very large
|
||||
* one. Replace iv by its absolute value and remember
|
||||
* to negate the pow result if iw is odd.
|
||||
*/
|
||||
iv = -iv;
|
||||
negate_result = DOUBLE_IS_ODD_INTEGER(iw);
|
||||
}
|
||||
|
||||
if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
|
||||
/* (-1) ** large_integer also ends up here. Here's an
|
||||
* extract from the comments for the previous
|
||||
* implementation explaining why this special case is
|
||||
* necessary:
|
||||
*
|
||||
* -1 raised to an exact integer should never be exceptional.
|
||||
* Alas, some libms (chiefly glibc as of early 2003) return
|
||||
* NaN and set EDOM on pow(-1, large_int) if the int doesn't
|
||||
* happen to be representable in a *C* integer. That's a
|
||||
* bug; we let that slide in math.pow() (which currently
|
||||
* reflects all platform accidents), but not for Python's **.
|
||||
*/
|
||||
if (iv == -1.0 && Py_IS_FINITE(iw)) {
|
||||
/* Return 1 if iw is even, -1 if iw is odd; there's
|
||||
* no guarantee that any C integral type is big
|
||||
* enough to hold iw, so we have to check this
|
||||
* indirectly.
|
||||
*/
|
||||
ix = floor(iw * 0.5) * 2.0;
|
||||
return PyFloat_FromDouble(ix == iw ? 1.0 : -1.0);
|
||||
}
|
||||
/* Else iv != -1.0, and overflow or underflow are possible.
|
||||
* Unless we're to write pow() ourselves, we have to trust
|
||||
* the platform to do this correctly.
|
||||
* bug.
|
||||
*/
|
||||
return PyFloat_FromDouble(negate_result ? -1.0 : 1.0);
|
||||
}
|
||||
|
||||
/* Now iv and iw are finite, iw is nonzero, and iv is
|
||||
* positive and not equal to 1.0. We finally allow
|
||||
* the platform pow to step in and do the rest.
|
||||
*/
|
||||
errno = 0;
|
||||
PyFPE_START_PROTECT("pow", return NULL)
|
||||
ix = pow(iv, iw);
|
||||
PyFPE_END_PROTECT(ix)
|
||||
Py_ADJUST_ERANGE1(ix);
|
||||
if (negate_result)
|
||||
ix = -ix;
|
||||
|
||||
if (errno != 0) {
|
||||
/* We don't expect any errno value other than ERANGE, but
|
||||
* the range of libm bugs appears unbounded.
|
||||
@ -748,6 +797,8 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
|
||||
return PyFloat_FromDouble(ix);
|
||||
}
|
||||
|
||||
#undef DOUBLE_IS_ODD_INTEGER
|
||||
|
||||
static PyObject *
|
||||
float_neg(PyFloatObject *v)
|
||||
{
|
||||
|
||||
Loading…
Reference in New Issue
Block a user