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Issue #7534: Fix handling of nans, infinities, and negative zero in **
operator, on IEEE 754 platforms. Thanks Marcos Donolo for original patch.
This commit is contained in:
Mark Dickinson
parent
569e61f351
commit
99d652ef66
4 changed files with 294 additions and 25 deletions
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@ -12,6 +12,11 @@ import sys
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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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@ -142,6 +147,213 @@ class GeneralFloatCases(unittest.TestCase):
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self.assertRaises(OverflowError, float('-inf').as_integer_ratio)
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self.assertRaises(ValueError, float('nan').as_integer_ratio)
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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 raises ValueError for finite negative x and non-integral y
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self.assertRaises(ValueError, pow_op, -2.0, -0.5)
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self.assertRaises(ValueError, pow_op, -2.0, 0.5)
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self.assertRaises(ValueError, pow_op, -1.0, -0.5)
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self.assertRaises(ValueError, pow_op, -1.0, 0.5)
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self.assertRaises(ValueError, pow_op, -0.5, -0.5)
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self.assertRaises(ValueError, pow_op, -0.5, 0.5)
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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.assertRaises(ValueError, pow_op, -2.0, -2000.5)
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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.assertRaises(ValueError, pow_op, -0.5, 2000.5)
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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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def setUp(self):
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