Index: Lib/test/test_float.py =================================================================== --- Lib/test/test_float.py (revision 76881) +++ Lib/test/test_float.py (working copy) @@ -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 +147,182 @@ 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(-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))) + self.assertTrue(isnan(pow_op(NAN, NAN))) + + # (+-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) + + class FormatFunctionsTestCase(unittest.TestCase): def setUp(self): Index: Lib/test/ieee754.txt =================================================================== --- Lib/test/ieee754.txt (revision 76881) +++ Lib/test/ieee754.txt (working copy) @@ -72,7 +72,7 @@ >>> NAN >= 0 False -All operations involving a NaN return a NaN except for the power of *0* and *1*. +All operations involving a NaN return a NaN except for nan**0 and 1**nan. >>> 1 + NAN nan >>> 1 * NAN @@ -81,8 +81,10 @@ nan >>> 1 ** NAN 1.0 +>>> NAN ** 0 +1.0 >>> 0 ** NAN -0.0 +nan >>> (1.0 + FI.epsilon) * NAN nan