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Diffstat (limited to 'lib/python2.7/test/test_float.py')
| -rw-r--r-- | lib/python2.7/test/test_float.py | 1402 |
1 files changed, 1402 insertions, 0 deletions
diff --git a/lib/python2.7/test/test_float.py b/lib/python2.7/test/test_float.py new file mode 100644 index 0000000..4246371 --- /dev/null +++ b/lib/python2.7/test/test_float.py @@ -0,0 +1,1402 @@ + +import unittest, struct +import os +from test import test_support +import math +from math import isinf, isnan, copysign, ldexp +import operator +import random +import fractions +import sys + +INF = float("inf") +NAN = float("nan") + +have_getformat = hasattr(float, "__getformat__") +requires_getformat = unittest.skipUnless(have_getformat, + "requires __getformat__") +requires_setformat = unittest.skipUnless(hasattr(float, "__setformat__"), + "requires __setformat__") +# decorator for skipping tests on non-IEEE 754 platforms +requires_IEEE_754 = unittest.skipUnless(have_getformat and + 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') + +class GeneralFloatCases(unittest.TestCase): + + def test_float(self): + self.assertEqual(float(3.14), 3.14) + self.assertEqual(float(314), 314.0) + self.assertEqual(float(314L), 314.0) + self.assertEqual(float(" 3.14 "), 3.14) + self.assertRaises(ValueError, float, " 0x3.1 ") + self.assertRaises(ValueError, float, " -0x3.p-1 ") + self.assertRaises(ValueError, float, " +0x3.p-1 ") + self.assertRaises(ValueError, float, "++3.14") + self.assertRaises(ValueError, float, "+-3.14") + self.assertRaises(ValueError, float, "-+3.14") + self.assertRaises(ValueError, float, "--3.14") + # check that we don't accept alternate exponent markers + self.assertRaises(ValueError, float, "-1.7d29") + self.assertRaises(ValueError, float, "3D-14") + if test_support.have_unicode: + self.assertEqual(float(unicode(" 3.14 ")), 3.14) + self.assertEqual(float(unicode(" \u0663.\u0661\u0664 ",'raw-unicode-escape')), 3.14) + + # extra long strings should no longer be a problem + # (in 2.6, long unicode inputs to float raised ValueError) + float('.' + '1'*1000) + float(unicode('.' + '1'*1000)) + + def check_conversion_to_int(self, x): + """Check that int(x) has the correct value and type, for a float x.""" + n = int(x) + if x >= 0.0: + # x >= 0 and n = int(x) ==> n <= x < n + 1 + self.assertLessEqual(n, x) + self.assertLess(x, n + 1) + else: + # x < 0 and n = int(x) ==> n >= x > n - 1 + self.assertGreaterEqual(n, x) + self.assertGreater(x, n - 1) + + # Result should be an int if within range, else a long. + if -sys.maxint-1 <= n <= sys.maxint: + self.assertEqual(type(n), int) + else: + self.assertEqual(type(n), long) + + # Double check. + self.assertEqual(type(int(n)), type(n)) + + def test_conversion_to_int(self): + # Check that floats within the range of an int convert to type + # int, not long. (issue #11144.) + boundary = float(sys.maxint + 1) + epsilon = 2**-sys.float_info.mant_dig * boundary + + # These 2 floats are either side of the positive int/long boundary on + # both 32-bit and 64-bit systems. + self.check_conversion_to_int(boundary - epsilon) + self.check_conversion_to_int(boundary) + + # These floats are either side of the negative long/int boundary on + # 64-bit systems... + self.check_conversion_to_int(-boundary - 2*epsilon) + self.check_conversion_to_int(-boundary) + + # ... and these ones are either side of the negative long/int + # boundary on 32-bit systems. + self.check_conversion_to_int(-boundary - 1.0) + self.check_conversion_to_int(-boundary - 1.0 + 2*epsilon) + + @test_support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE') + def test_float_with_comma(self): + # set locale to something that doesn't use '.' for the decimal point + # float must not accept the locale specific decimal point but + # it still has to accept the normal python syntax + import locale + if not locale.localeconv()['decimal_point'] == ',': + return + + self.assertEqual(float(" 3.14 "), 3.14) + self.assertEqual(float("+3.14 "), 3.14) + self.assertEqual(float("-3.14 "), -3.14) + self.assertEqual(float(".14 "), .14) + self.assertEqual(float("3. "), 3.0) + self.assertEqual(float("3.e3 "), 3000.0) + self.assertEqual(float("3.2e3 "), 3200.0) + self.assertEqual(float("2.5e-1 "), 0.25) + self.assertEqual(float("5e-1"), 0.5) + self.assertRaises(ValueError, float, " 3,14 ") + self.assertRaises(ValueError, float, " +3,14 ") + self.assertRaises(ValueError, float, " -3,14 ") + self.assertRaises(ValueError, float, " 0x3.1 ") + self.assertRaises(ValueError, float, " -0x3.p-1 ") + self.assertRaises(ValueError, float, " +0x3.p-1 ") + self.assertEqual(float(" 25.e-1 "), 2.5) + self.assertEqual(test_support.fcmp(float(" .25e-1 "), .025), 0) + + def test_floatconversion(self): + # Make sure that calls to __float__() work properly + class Foo0: + def __float__(self): + return 42. + + class Foo1(object): + def __float__(self): + return 42. + + class Foo2(float): + def __float__(self): + return 42. + + class Foo3(float): + def __new__(cls, value=0.): + return float.__new__(cls, 2*value) + + def __float__(self): + return self + + class Foo4(float): + def __float__(self): + return 42 + + # Issue 5759: __float__ not called on str subclasses (though it is on + # unicode subclasses). + class FooStr(str): + def __float__(self): + return float(str(self)) + 1 + + class FooUnicode(unicode): + def __float__(self): + return float(unicode(self)) + 1 + + self.assertAlmostEqual(float(Foo0()), 42.) + self.assertAlmostEqual(float(Foo1()), 42.) + self.assertAlmostEqual(float(Foo2()), 42.) + self.assertAlmostEqual(float(Foo3(21)), 42.) + self.assertRaises(TypeError, float, Foo4(42)) + self.assertAlmostEqual(float(FooUnicode('8')), 9.) + self.assertAlmostEqual(float(FooStr('8')), 9.) + + def test_is_integer(self): + self.assertFalse((1.1).is_integer()) + self.assertTrue((1.).is_integer()) + self.assertFalse(float("nan").is_integer()) + self.assertFalse(float("inf").is_integer()) + + def test_floatasratio(self): + for f, ratio in [ + (0.875, (7, 8)), + (-0.875, (-7, 8)), + (0.0, (0, 1)), + (11.5, (23, 2)), + ]: + self.assertEqual(f.as_integer_ratio(), ratio) + + for i in range(10000): + f = random.random() + f *= 10 ** random.randint(-100, 100) + n, d = f.as_integer_ratio() + self.assertEqual(float(n).__truediv__(d), f) + + R = fractions.Fraction + self.assertEqual(R(0, 1), + R(*float(0.0).as_integer_ratio())) + self.assertEqual(R(5, 2), + R(*float(2.5).as_integer_ratio())) + self.assertEqual(R(1, 2), + R(*float(0.5).as_integer_ratio())) + self.assertEqual(R(4728779608739021, 2251799813685248), + R(*float(2.1).as_integer_ratio())) + self.assertEqual(R(-4728779608739021, 2251799813685248), + R(*float(-2.1).as_integer_ratio())) + self.assertEqual(R(-2100, 1), + R(*float(-2100.0).as_integer_ratio())) + + self.assertRaises(OverflowError, float('inf').as_integer_ratio) + 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 + # distinguishes -0.0 and 0.0. + self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b))) + + @requires_IEEE_754 + def test_float_mod(self): + # Check behaviour of % operator for IEEE 754 special cases. + # In particular, check signs of zeros. + mod = operator.mod + + self.assertEqualAndEqualSign(mod(-1.0, 1.0), 0.0) + self.assertEqualAndEqualSign(mod(-1e-100, 1.0), 1.0) + self.assertEqualAndEqualSign(mod(-0.0, 1.0), 0.0) + self.assertEqualAndEqualSign(mod(0.0, 1.0), 0.0) + self.assertEqualAndEqualSign(mod(1e-100, 1.0), 1e-100) + self.assertEqualAndEqualSign(mod(1.0, 1.0), 0.0) + + self.assertEqualAndEqualSign(mod(-1.0, -1.0), -0.0) + self.assertEqualAndEqualSign(mod(-1e-100, -1.0), -1e-100) + self.assertEqualAndEqualSign(mod(-0.0, -1.0), -0.0) + self.assertEqualAndEqualSign(mod(0.0, -1.0), -0.0) + self.assertEqualAndEqualSign(mod(1e-100, -1.0), -1.0) + self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0) + + @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) + + +@requires_setformat +class FormatFunctionsTestCase(unittest.TestCase): + + def setUp(self): + self.save_formats = {'double':float.__getformat__('double'), + 'float':float.__getformat__('float')} + + def tearDown(self): + float.__setformat__('double', self.save_formats['double']) + float.__setformat__('float', self.save_formats['float']) + + def test_getformat(self): + self.assertIn(float.__getformat__('double'), + ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) + self.assertIn(float.__getformat__('float'), + ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) + self.assertRaises(ValueError, float.__getformat__, 'chicken') + self.assertRaises(TypeError, float.__getformat__, 1) + + def test_setformat(self): + for t in 'double', 'float': + float.__setformat__(t, 'unknown') + if self.save_formats[t] == 'IEEE, big-endian': + self.assertRaises(ValueError, float.__setformat__, + t, 'IEEE, little-endian') + elif self.save_formats[t] == 'IEEE, little-endian': + self.assertRaises(ValueError, float.__setformat__, + t, 'IEEE, big-endian') + else: + self.assertRaises(ValueError, float.__setformat__, + t, 'IEEE, big-endian') + self.assertRaises(ValueError, float.__setformat__, + t, 'IEEE, little-endian') + self.assertRaises(ValueError, float.__setformat__, + t, 'chicken') + self.assertRaises(ValueError, float.__setformat__, + 'chicken', 'unknown') + +BE_DOUBLE_INF = '\x7f\xf0\x00\x00\x00\x00\x00\x00' +LE_DOUBLE_INF = ''.join(reversed(BE_DOUBLE_INF)) +BE_DOUBLE_NAN = '\x7f\xf8\x00\x00\x00\x00\x00\x00' +LE_DOUBLE_NAN = ''.join(reversed(BE_DOUBLE_NAN)) + +BE_FLOAT_INF = '\x7f\x80\x00\x00' +LE_FLOAT_INF = ''.join(reversed(BE_FLOAT_INF)) +BE_FLOAT_NAN = '\x7f\xc0\x00\x00' +LE_FLOAT_NAN = ''.join(reversed(BE_FLOAT_NAN)) + +# on non-IEEE platforms, attempting to unpack a bit pattern +# representing an infinity or a NaN should raise an exception. + +@requires_setformat +class UnknownFormatTestCase(unittest.TestCase): + def setUp(self): + self.save_formats = {'double':float.__getformat__('double'), + 'float':float.__getformat__('float')} + float.__setformat__('double', 'unknown') + float.__setformat__('float', 'unknown') + + def tearDown(self): + float.__setformat__('double', self.save_formats['double']) + float.__setformat__('float', self.save_formats['float']) + + def test_double_specials_dont_unpack(self): + for fmt, data in [('>d', BE_DOUBLE_INF), + ('>d', BE_DOUBLE_NAN), + ('<d', LE_DOUBLE_INF), + ('<d', LE_DOUBLE_NAN)]: + self.assertRaises(ValueError, struct.unpack, fmt, data) + + def test_float_specials_dont_unpack(self): + for fmt, data in [('>f', BE_FLOAT_INF), + ('>f', BE_FLOAT_NAN), + ('<f', LE_FLOAT_INF), + ('<f', LE_FLOAT_NAN)]: + self.assertRaises(ValueError, struct.unpack, fmt, data) + + +# on an IEEE platform, all we guarantee is that bit patterns +# representing infinities or NaNs do not raise an exception; all else +# is accident (today). +# let's also try to guarantee that -0.0 and 0.0 don't get confused. + +class IEEEFormatTestCase(unittest.TestCase): + + @requires_IEEE_754 + def test_double_specials_do_unpack(self): + for fmt, data in [('>d', BE_DOUBLE_INF), + ('>d', BE_DOUBLE_NAN), + ('<d', LE_DOUBLE_INF), + ('<d', LE_DOUBLE_NAN)]: + struct.unpack(fmt, data) + + @requires_IEEE_754 + def test_float_specials_do_unpack(self): + for fmt, data in [('>f', BE_FLOAT_INF), + ('>f', BE_FLOAT_NAN), + ('<f', LE_FLOAT_INF), + ('<f', LE_FLOAT_NAN)]: + struct.unpack(fmt, data) + + @requires_IEEE_754 + def test_negative_zero(self): + def pos_pos(): + return 0.0, math.atan2(0.0, -1) + def pos_neg(): + return 0.0, math.atan2(-0.0, -1) + def neg_pos(): + return -0.0, math.atan2(0.0, -1) + def neg_neg(): + return -0.0, math.atan2(-0.0, -1) + self.assertEqual(pos_pos(), neg_pos()) + self.assertEqual(pos_neg(), neg_neg()) + + @requires_IEEE_754 + def test_underflow_sign(self): + # check that -1e-1000 gives -0.0, not 0.0 + self.assertEqual(math.atan2(-1e-1000, -1), math.atan2(-0.0, -1)) + self.assertEqual(math.atan2(float('-1e-1000'), -1), + math.atan2(-0.0, -1)) + + def test_format(self): + # these should be rewritten to use both format(x, spec) and + # x.__format__(spec) + + self.assertEqual(format(0.0, 'f'), '0.000000') + + # the default is 'g', except for empty format spec + self.assertEqual(format(0.0, ''), '0.0') + self.assertEqual(format(0.01, ''), '0.01') + self.assertEqual(format(0.01, 'g'), '0.01') + + # empty presentation type should format in the same way as str + # (issue 5920) + x = 100/7. + self.assertEqual(format(x, ''), str(x)) + self.assertEqual(format(x, '-'), str(x)) + self.assertEqual(format(x, '>'), str(x)) + self.assertEqual(format(x, '2'), str(x)) + + self.assertEqual(format(1.0, 'f'), '1.000000') + + self.assertEqual(format(-1.0, 'f'), '-1.000000') + + self.assertEqual(format( 1.0, ' f'), ' 1.000000') + self.assertEqual(format(-1.0, ' f'), '-1.000000') + self.assertEqual(format( 1.0, '+f'), '+1.000000') + self.assertEqual(format(-1.0, '+f'), '-1.000000') + + # % formatting + self.assertEqual(format(-1.0, '%'), '-100.000000%') + + # conversion to string should fail + self.assertRaises(ValueError, format, 3.0, "s") + + # other format specifiers shouldn't work on floats, + # in particular int specifiers + for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + + [chr(x) for x in range(ord('A'), ord('Z')+1)]): + if not format_spec in 'eEfFgGn%': + self.assertRaises(ValueError, format, 0.0, format_spec) + self.assertRaises(ValueError, format, 1.0, format_spec) + self.assertRaises(ValueError, format, -1.0, format_spec) + self.assertRaises(ValueError, format, 1e100, format_spec) + self.assertRaises(ValueError, format, -1e100, format_spec) + self.assertRaises(ValueError, format, 1e-100, format_spec) + self.assertRaises(ValueError, format, -1e-100, format_spec) + + # issue 3382: 'f' and 'F' with inf's and nan's + self.assertEqual('{0:f}'.format(INF), 'inf') + self.assertEqual('{0:F}'.format(INF), 'INF') + self.assertEqual('{0:f}'.format(-INF), '-inf') + self.assertEqual('{0:F}'.format(-INF), '-INF') + self.assertEqual('{0:f}'.format(NAN), 'nan') + self.assertEqual('{0:F}'.format(NAN), 'NAN') + + @requires_IEEE_754 + def test_format_testfile(self): + with open(format_testfile) as testfile: + for line in open(format_testfile): + if line.startswith('--'): + continue + line = line.strip() + if not line: + continue + + lhs, rhs = map(str.strip, line.split('->')) + fmt, arg = lhs.split() + arg = float(arg) + self.assertEqual(fmt % arg, rhs) + if not math.isnan(arg) and copysign(1.0, arg) > 0.0: + self.assertEqual(fmt % -arg, '-' + rhs) + + def test_issue5864(self): + self.assertEqual(format(123.456, '.4'), '123.5') + self.assertEqual(format(1234.56, '.4'), '1.235e+03') + self.assertEqual(format(12345.6, '.4'), '1.235e+04') + +class ReprTestCase(unittest.TestCase): + def test_repr(self): + floats_file = open(os.path.join(os.path.split(__file__)[0], + 'floating_points.txt')) + for line in floats_file: + line = line.strip() + if not line or line.startswith('#'): + continue + v = eval(line) + self.assertEqual(v, eval(repr(v))) + floats_file.close() + + @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', + "applies only when using short float repr style") + def test_short_repr(self): + # test short float repr introduced in Python 3.1. One aspect + # of this repr is that we get some degree of str -> float -> + # str roundtripping. In particular, for any numeric string + # containing 15 or fewer significant digits, those exact same + # digits (modulo trailing zeros) should appear in the output. + # No more repr(0.03) -> "0.029999999999999999"! + + test_strings = [ + # output always includes *either* a decimal point and at + # least one digit after that point, or an exponent. + '0.0', + '1.0', + '0.01', + '0.02', + '0.03', + '0.04', + '0.05', + '1.23456789', + '10.0', + '100.0', + # values >= 1e16 get an exponent... + '1000000000000000.0', + '9999999999999990.0', + '1e+16', + '1e+17', + # ... and so do values < 1e-4 + '0.001', + '0.001001', + '0.00010000000000001', + '0.0001', + '9.999999999999e-05', + '1e-05', + # values designed to provoke failure if the FPU rounding + # precision isn't set correctly + '8.72293771110361e+25', + '7.47005307342313e+26', + '2.86438000439698e+28', + '8.89142905246179e+28', + '3.08578087079232e+35', + ] + + for s in test_strings: + negs = '-'+s + self.assertEqual(s, repr(float(s))) + self.assertEqual(negs, repr(float(negs))) + + +@requires_IEEE_754 +class RoundTestCase(unittest.TestCase): + def test_second_argument_type(self): + # any type with an __index__ method should be permitted as + # a second argument + self.assertAlmostEqual(round(12.34, True), 12.3) + + class MyIndex(object): + def __index__(self): return 4 + self.assertAlmostEqual(round(-0.123456, MyIndex()), -0.1235) + # but floats should be illegal + self.assertRaises(TypeError, round, 3.14159, 2.0) + + def test_inf_nan(self): + # rounding an infinity or nan returns the same number; + # (in py3k, rounding an infinity or nan raises an error, + # since the result can't be represented as a long). + self.assertEqual(round(INF), INF) + self.assertEqual(round(-INF), -INF) + self.assertTrue(math.isnan(round(NAN))) + for n in range(-5, 5): + self.assertEqual(round(INF, n), INF) + self.assertEqual(round(-INF, n), -INF) + self.assertTrue(math.isnan(round(NAN, n))) + + self.assertRaises(TypeError, round, INF, 0.0) + self.assertRaises(TypeError, round, -INF, 1.0) + self.assertRaises(TypeError, round, NAN, "ceci n'est pas un integer") + self.assertRaises(TypeError, round, -0.0, 1j) + + def test_large_n(self): + for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]: + self.assertEqual(round(123.456, n), 123.456) + self.assertEqual(round(-123.456, n), -123.456) + self.assertEqual(round(1e300, n), 1e300) + self.assertEqual(round(1e-320, n), 1e-320) + self.assertEqual(round(1e150, 300), 1e150) + self.assertEqual(round(1e300, 307), 1e300) + self.assertEqual(round(-3.1415, 308), -3.1415) + self.assertEqual(round(1e150, 309), 1e150) + self.assertEqual(round(1.4e-315, 315), 1e-315) + + def test_small_n(self): + for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]: + self.assertEqual(round(123.456, n), 0.0) + self.assertEqual(round(-123.456, n), -0.0) + self.assertEqual(round(1e300, n), 0.0) + self.assertEqual(round(1e-320, n), 0.0) + + def test_overflow(self): + self.assertRaises(OverflowError, round, 1.6e308, -308) + self.assertRaises(OverflowError, round, -1.7e308, -308) + + @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', + "test applies only when using short float repr style") + def test_previous_round_bugs(self): + # particular cases that have occurred in bug reports + self.assertEqual(round(562949953421312.5, 1), + 562949953421312.5) + self.assertEqual(round(56294995342131.5, 3), + 56294995342131.5) + + @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', + "test applies only when using short float repr style") + def test_halfway_cases(self): + # Halfway cases need special attention, since the current + # implementation has to deal with them specially. Note that + # 2.x rounds halfway values up (i.e., away from zero) while + # 3.x does round-half-to-even. + self.assertAlmostEqual(round(0.125, 2), 0.13) + self.assertAlmostEqual(round(0.375, 2), 0.38) + self.assertAlmostEqual(round(0.625, 2), 0.63) + self.assertAlmostEqual(round(0.875, 2), 0.88) + self.assertAlmostEqual(round(-0.125, 2), -0.13) + self.assertAlmostEqual(round(-0.375, 2), -0.38) + self.assertAlmostEqual(round(-0.625, 2), -0.63) + self.assertAlmostEqual(round(-0.875, 2), -0.88) + + self.assertAlmostEqual(round(0.25, 1), 0.3) + self.assertAlmostEqual(round(0.75, 1), 0.8) + self.assertAlmostEqual(round(-0.25, 1), -0.3) + self.assertAlmostEqual(round(-0.75, 1), -0.8) + + self.assertEqual(round(-6.5, 0), -7.0) + self.assertEqual(round(-5.5, 0), -6.0) + self.assertEqual(round(-1.5, 0), -2.0) + self.assertEqual(round(-0.5, 0), -1.0) + self.assertEqual(round(0.5, 0), 1.0) + self.assertEqual(round(1.5, 0), 2.0) + self.assertEqual(round(2.5, 0), 3.0) + self.assertEqual(round(3.5, 0), 4.0) + self.assertEqual(round(4.5, 0), 5.0) + self.assertEqual(round(5.5, 0), 6.0) + self.assertEqual(round(6.5, 0), 7.0) + + # same but without an explicit second argument; in 3.x these + # will give integers + self.assertEqual(round(-6.5), -7.0) + self.assertEqual(round(-5.5), -6.0) + self.assertEqual(round(-1.5), -2.0) + self.assertEqual(round(-0.5), -1.0) + self.assertEqual(round(0.5), 1.0) + self.assertEqual(round(1.5), 2.0) + self.assertEqual(round(2.5), 3.0) + self.assertEqual(round(3.5), 4.0) + self.assertEqual(round(4.5), 5.0) + self.assertEqual(round(5.5), 6.0) + self.assertEqual(round(6.5), 7.0) + + self.assertEqual(round(-25.0, -1), -30.0) + self.assertEqual(round(-15.0, -1), -20.0) + self.assertEqual(round(-5.0, -1), -10.0) + self.assertEqual(round(5.0, -1), 10.0) + self.assertEqual(round(15.0, -1), 20.0) + self.assertEqual(round(25.0, -1), 30.0) + self.assertEqual(round(35.0, -1), 40.0) + self.assertEqual(round(45.0, -1), 50.0) + self.assertEqual(round(55.0, -1), 60.0) + self.assertEqual(round(65.0, -1), 70.0) + self.assertEqual(round(75.0, -1), 80.0) + self.assertEqual(round(85.0, -1), 90.0) + self.assertEqual(round(95.0, -1), 100.0) + self.assertEqual(round(12325.0, -1), 12330.0) + + self.assertEqual(round(350.0, -2), 400.0) + self.assertEqual(round(450.0, -2), 500.0) + + self.assertAlmostEqual(round(0.5e21, -21), 1e21) + self.assertAlmostEqual(round(1.5e21, -21), 2e21) + self.assertAlmostEqual(round(2.5e21, -21), 3e21) + self.assertAlmostEqual(round(5.5e21, -21), 6e21) + self.assertAlmostEqual(round(8.5e21, -21), 9e21) + + self.assertAlmostEqual(round(-1.5e22, -22), -2e22) + self.assertAlmostEqual(round(-0.5e22, -22), -1e22) + self.assertAlmostEqual(round(0.5e22, -22), 1e22) + self.assertAlmostEqual(round(1.5e22, -22), 2e22) + + + @requires_IEEE_754 + def test_format_specials(self): + # Test formatting of nans and infs. + + def test(fmt, value, expected): + # Test with both % and format(). + self.assertEqual(fmt % value, expected, fmt) + if not '#' in fmt: + # Until issue 7094 is implemented, format() for floats doesn't + # support '#' formatting + fmt = fmt[1:] # strip off the % + self.assertEqual(format(value, fmt), expected, fmt) + + for fmt in ['%e', '%f', '%g', '%.0e', '%.6f', '%.20g', + '%#e', '%#f', '%#g', '%#.20e', '%#.15f', '%#.3g']: + pfmt = '%+' + fmt[1:] + sfmt = '% ' + fmt[1:] + test(fmt, INF, 'inf') + test(fmt, -INF, '-inf') + test(fmt, NAN, 'nan') + test(fmt, -NAN, 'nan') + # When asking for a sign, it's always provided. nans are + # always positive. + test(pfmt, INF, '+inf') + test(pfmt, -INF, '-inf') + test(pfmt, NAN, '+nan') + test(pfmt, -NAN, '+nan') + # When using ' ' for a sign code, only infs can be negative. + # Others have a space. + test(sfmt, INF, ' inf') + test(sfmt, -INF, '-inf') + test(sfmt, NAN, ' nan') + test(sfmt, -NAN, ' nan') + + +# Beginning with Python 2.6 float has cross platform compatible +# ways to create and represent inf and nan +class InfNanTest(unittest.TestCase): + def test_inf_from_str(self): + self.assertTrue(isinf(float("inf"))) + self.assertTrue(isinf(float("+inf"))) + self.assertTrue(isinf(float("-inf"))) + self.assertTrue(isinf(float("infinity"))) + self.assertTrue(isinf(float("+infinity"))) + self.assertTrue(isinf(float("-infinity"))) + + self.assertEqual(repr(float("inf")), "inf") + self.assertEqual(repr(float("+inf")), "inf") + self.assertEqual(repr(float("-inf")), "-inf") + self.assertEqual(repr(float("infinity")), "inf") + self.assertEqual(repr(float("+infinity")), "inf") + self.assertEqual(repr(float("-infinity")), "-inf") + + self.assertEqual(repr(float("INF")), "inf") + self.assertEqual(repr(float("+Inf")), "inf") + self.assertEqual(repr(float("-iNF")), "-inf") + self.assertEqual(repr(float("Infinity")), "inf") + self.assertEqual(repr(float("+iNfInItY")), "inf") + self.assertEqual(repr(float("-INFINITY")), "-inf") + + self.assertEqual(str(float("inf")), "inf") + self.assertEqual(str(float("+inf")), "inf") + self.assertEqual(str(float("-inf")), "-inf") + self.assertEqual(str(float("infinity")), "inf") + self.assertEqual(str(float("+infinity")), "inf") + self.assertEqual(str(float("-infinity")), "-inf") + + self.assertRaises(ValueError, float, "info") + self.assertRaises(ValueError, float, "+info") + self.assertRaises(ValueError, float, "-info") + self.assertRaises(ValueError, float, "in") + self.assertRaises(ValueError, float, "+in") + self.assertRaises(ValueError, float, "-in") + self.assertRaises(ValueError, float, "infinit") + self.assertRaises(ValueError, float, "+Infin") + self.assertRaises(ValueError, float, "-INFI") + self.assertRaises(ValueError, float, "infinitys") + + def test_inf_as_str(self): + self.assertEqual(repr(1e300 * 1e300), "inf") + self.assertEqual(repr(-1e300 * 1e300), "-inf") + + self.assertEqual(str(1e300 * 1e300), "inf") + self.assertEqual(str(-1e300 * 1e300), "-inf") + + def test_nan_from_str(self): + self.assertTrue(isnan(float("nan"))) + self.assertTrue(isnan(float("+nan"))) + self.assertTrue(isnan(float("-nan"))) + + self.assertEqual(repr(float("nan")), "nan") + self.assertEqual(repr(float("+nan")), "nan") + self.assertEqual(repr(float("-nan")), "nan") + + self.assertEqual(repr(float("NAN")), "nan") + self.assertEqual(repr(float("+NAn")), "nan") + self.assertEqual(repr(float("-NaN")), "nan") + + self.assertEqual(str(float("nan")), "nan") + self.assertEqual(str(float("+nan")), "nan") + self.assertEqual(str(float("-nan")), "nan") + + self.assertRaises(ValueError, float, "nana") + self.assertRaises(ValueError, float, "+nana") + self.assertRaises(ValueError, float, "-nana") + self.assertRaises(ValueError, float, "na") + self.assertRaises(ValueError, float, "+na") + self.assertRaises(ValueError, float, "-na") + + def test_nan_as_str(self): + self.assertEqual(repr(1e300 * 1e300 * 0), "nan") + self.assertEqual(repr(-1e300 * 1e300 * 0), "nan") + + self.assertEqual(str(1e300 * 1e300 * 0), "nan") + self.assertEqual(str(-1e300 * 1e300 * 0), "nan") + + def notest_float_nan(self): + self.assertTrue(NAN.is_nan()) + self.assertFalse(INF.is_nan()) + self.assertFalse((0.).is_nan()) + + def notest_float_inf(self): + self.assertTrue(INF.is_inf()) + self.assertFalse(NAN.is_inf()) + self.assertFalse((0.).is_inf()) + + def test_hash_inf(self): + # the actual values here should be regarded as an + # implementation detail, but they need to be + # identical to those used in the Decimal module. + self.assertEqual(hash(float('inf')), 314159) + self.assertEqual(hash(float('-inf')), -271828) + self.assertEqual(hash(float('nan')), 0) + + +fromHex = float.fromhex +toHex = float.hex +class HexFloatTestCase(unittest.TestCase): + MAX = fromHex('0x.fffffffffffff8p+1024') # max normal + MIN = fromHex('0x1p-1022') # min normal + TINY = fromHex('0x0.0000000000001p-1022') # min subnormal + EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up + + def identical(self, x, y): + # check that floats x and y are identical, or that both + # are NaNs + if isnan(x) or isnan(y): + if isnan(x) == isnan(y): + return + elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)): + return + self.fail('%r not identical to %r' % (x, y)) + + def test_ends(self): + self.identical(self.MIN, ldexp(1.0, -1022)) + self.identical(self.TINY, ldexp(1.0, -1074)) + self.identical(self.EPS, ldexp(1.0, -52)) + self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970))) + + def test_invalid_inputs(self): + invalid_inputs = [ + 'infi', # misspelt infinities and nans + '-Infinit', + '++inf', + '-+Inf', + '--nan', + '+-NaN', + 'snan', + 'NaNs', + 'nna', + 'an', + 'nf', + 'nfinity', + 'inity', + 'iinity', + '0xnan', + '', + ' ', + 'x1.0p0', + '0xX1.0p0', + '+ 0x1.0p0', # internal whitespace + '- 0x1.0p0', + '0 x1.0p0', + '0x 1.0p0', + '0x1 2.0p0', + '+0x1 .0p0', + '0x1. 0p0', + '-0x1.0 1p0', + '-0x1.0 p0', + '+0x1.0p +0', + '0x1.0p -0', + '0x1.0p 0', + '+0x1.0p+ 0', + '-0x1.0p- 0', + '++0x1.0p-0', # double signs + '--0x1.0p0', + '+-0x1.0p+0', + '-+0x1.0p0', + '0x1.0p++0', + '+0x1.0p+-0', + '-0x1.0p-+0', + '0x1.0p--0', + '0x1.0.p0', + '0x.p0', # no hex digits before or after point + '0x1,p0', # wrong decimal point character + '0x1pa', + u'0x1p\uff10', # fullwidth Unicode digits + u'\uff10x1p0', + u'0x\uff11p0', + u'0x1.\uff10p0', + '0x1p0 \n 0x2p0', + '0x1p0\0 0x1p0', # embedded null byte is not end of string + ] + for x in invalid_inputs: + try: + result = fromHex(x) + except ValueError: + pass + else: + self.fail('Expected float.fromhex(%r) to raise ValueError; ' + 'got %r instead' % (x, result)) + + + def test_whitespace(self): + value_pairs = [ + ('inf', INF), + ('-Infinity', -INF), + ('nan', NAN), + ('1.0', 1.0), + ('-0x.2', -0.125), + ('-0.0', -0.0) + ] + whitespace = [ + '', + ' ', + '\t', + '\n', + '\n \t', + '\f', + '\v', + '\r' + ] + for inp, expected in value_pairs: + for lead in whitespace: + for trail in whitespace: + got = fromHex(lead + inp + trail) + self.identical(got, expected) + + + def test_from_hex(self): + MIN = self.MIN; + MAX = self.MAX; + TINY = self.TINY; + EPS = self.EPS; + + # two spellings of infinity, with optional signs; case-insensitive + self.identical(fromHex('inf'), INF) + self.identical(fromHex('+Inf'), INF) + self.identical(fromHex('-INF'), -INF) + self.identical(fromHex('iNf'), INF) + self.identical(fromHex('Infinity'), INF) + self.identical(fromHex('+INFINITY'), INF) + self.identical(fromHex('-infinity'), -INF) + self.identical(fromHex('-iNFiNitY'), -INF) + + # nans with optional sign; case insensitive + self.identical(fromHex('nan'), NAN) + self.identical(fromHex('+NaN'), NAN) + self.identical(fromHex('-NaN'), NAN) + self.identical(fromHex('-nAN'), NAN) + + # variations in input format + self.identical(fromHex('1'), 1.0) + self.identical(fromHex('+1'), 1.0) + self.identical(fromHex('1.'), 1.0) + self.identical(fromHex('1.0'), 1.0) + self.identical(fromHex('1.0p0'), 1.0) + self.identical(fromHex('01'), 1.0) + self.identical(fromHex('01.'), 1.0) + self.identical(fromHex('0x1'), 1.0) + self.identical(fromHex('0x1.'), 1.0) + self.identical(fromHex('0x1.0'), 1.0) + self.identical(fromHex('+0x1.0'), 1.0) + self.identical(fromHex('0x1p0'), 1.0) + self.identical(fromHex('0X1p0'), 1.0) + self.identical(fromHex('0X1P0'), 1.0) + self.identical(fromHex('0x1P0'), 1.0) + self.identical(fromHex('0x1.p0'), 1.0) + self.identical(fromHex('0x1.0p0'), 1.0) + self.identical(fromHex('0x.1p4'), 1.0) + self.identical(fromHex('0x.1p04'), 1.0) + self.identical(fromHex('0x.1p004'), 1.0) + self.identical(fromHex('0x1p+0'), 1.0) + self.identical(fromHex('0x1P-0'), 1.0) + self.identical(fromHex('+0x1p0'), 1.0) + self.identical(fromHex('0x01p0'), 1.0) + self.identical(fromHex('0x1p00'), 1.0) + self.identical(fromHex(u'0x1p0'), 1.0) + self.identical(fromHex(' 0x1p0 '), 1.0) + self.identical(fromHex('\n 0x1p0'), 1.0) + self.identical(fromHex('0x1p0 \t'), 1.0) + self.identical(fromHex('0xap0'), 10.0) + self.identical(fromHex('0xAp0'), 10.0) + self.identical(fromHex('0xaP0'), 10.0) + self.identical(fromHex('0xAP0'), 10.0) + self.identical(fromHex('0xbep0'), 190.0) + self.identical(fromHex('0xBep0'), 190.0) + self.identical(fromHex('0xbEp0'), 190.0) + self.identical(fromHex('0XBE0P-4'), 190.0) + self.identical(fromHex('0xBEp0'), 190.0) + self.identical(fromHex('0xB.Ep4'), 190.0) + self.identical(fromHex('0x.BEp8'), 190.0) + self.identical(fromHex('0x.0BEp12'), 190.0) + + # moving the point around + pi = fromHex('0x1.921fb54442d18p1') + self.identical(fromHex('0x.006487ed5110b46p11'), pi) + self.identical(fromHex('0x.00c90fdaa22168cp10'), pi) + self.identical(fromHex('0x.01921fb54442d18p9'), pi) + self.identical(fromHex('0x.03243f6a8885a3p8'), pi) + self.identical(fromHex('0x.06487ed5110b46p7'), pi) + self.identical(fromHex('0x.0c90fdaa22168cp6'), pi) + self.identical(fromHex('0x.1921fb54442d18p5'), pi) + self.identical(fromHex('0x.3243f6a8885a3p4'), pi) + self.identical(fromHex('0x.6487ed5110b46p3'), pi) + self.identical(fromHex('0x.c90fdaa22168cp2'), pi) + self.identical(fromHex('0x1.921fb54442d18p1'), pi) + self.identical(fromHex('0x3.243f6a8885a3p0'), pi) + self.identical(fromHex('0x6.487ed5110b46p-1'), pi) + self.identical(fromHex('0xc.90fdaa22168cp-2'), pi) + self.identical(fromHex('0x19.21fb54442d18p-3'), pi) + self.identical(fromHex('0x32.43f6a8885a3p-4'), pi) + self.identical(fromHex('0x64.87ed5110b46p-5'), pi) + self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi) + self.identical(fromHex('0x192.1fb54442d18p-7'), pi) + self.identical(fromHex('0x324.3f6a8885a3p-8'), pi) + self.identical(fromHex('0x648.7ed5110b46p-9'), pi) + self.identical(fromHex('0xc90.fdaa22168cp-10'), pi) + self.identical(fromHex('0x1921.fb54442d18p-11'), pi) + # ... + self.identical(fromHex('0x1921fb54442d1.8p-47'), pi) + self.identical(fromHex('0x3243f6a8885a3p-48'), pi) + self.identical(fromHex('0x6487ed5110b46p-49'), pi) + self.identical(fromHex('0xc90fdaa22168cp-50'), pi) + self.identical(fromHex('0x1921fb54442d18p-51'), pi) + self.identical(fromHex('0x3243f6a8885a30p-52'), pi) + self.identical(fromHex('0x6487ed5110b460p-53'), pi) + self.identical(fromHex('0xc90fdaa22168c0p-54'), pi) + self.identical(fromHex('0x1921fb54442d180p-55'), pi) + + + # results that should overflow... + self.assertRaises(OverflowError, fromHex, '-0x1p1024') + self.assertRaises(OverflowError, fromHex, '0x1p+1025') + self.assertRaises(OverflowError, fromHex, '+0X1p1030') + self.assertRaises(OverflowError, fromHex, '-0x1p+1100') + self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789') + self.assertRaises(OverflowError, fromHex, '+0X.8p+1025') + self.assertRaises(OverflowError, fromHex, '+0x0.8p1025') + self.assertRaises(OverflowError, fromHex, '-0x0.4p1026') + self.assertRaises(OverflowError, fromHex, '0X2p+1023') + self.assertRaises(OverflowError, fromHex, '0x2.p1023') + self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023') + self.assertRaises(OverflowError, fromHex, '+0X4p+1022') + self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023') + self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023') + self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023') + self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022') + self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970') + self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960') + self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960') + + # ...and those that round to +-max float + self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX) + self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX) + self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX) + + # zeros + self.identical(fromHex('0x0p0'), 0.0) + self.identical(fromHex('0x0p1000'), 0.0) + self.identical(fromHex('-0x0p1023'), -0.0) + self.identical(fromHex('0X0p1024'), 0.0) + self.identical(fromHex('-0x0p1025'), -0.0) + self.identical(fromHex('0X0p2000'), 0.0) + self.identical(fromHex('0x0p123456789123456789'), 0.0) + self.identical(fromHex('-0X0p-0'), -0.0) + self.identical(fromHex('-0X0p-1000'), -0.0) + self.identical(fromHex('0x0p-1023'), 0.0) + self.identical(fromHex('-0X0p-1024'), -0.0) + self.identical(fromHex('-0x0p-1025'), -0.0) + self.identical(fromHex('-0x0p-1072'), -0.0) + self.identical(fromHex('0X0p-1073'), 0.0) + self.identical(fromHex('-0x0p-1074'), -0.0) + self.identical(fromHex('0x0p-1075'), 0.0) + self.identical(fromHex('0X0p-1076'), 0.0) + self.identical(fromHex('-0X0p-2000'), -0.0) + self.identical(fromHex('-0x0p-123456789123456789'), -0.0) + + # values that should underflow to 0 + self.identical(fromHex('0X1p-1075'), 0.0) + self.identical(fromHex('-0X1p-1075'), -0.0) + self.identical(fromHex('-0x1p-123456789123456789'), -0.0) + self.identical(fromHex('0x1.00000000000000001p-1075'), TINY) + self.identical(fromHex('-0x1.1p-1075'), -TINY) + self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY) + + # check round-half-even is working correctly near 0 ... + self.identical(fromHex('0x1p-1076'), 0.0) + self.identical(fromHex('0X2p-1076'), 0.0) + self.identical(fromHex('0X3p-1076'), TINY) + self.identical(fromHex('0x4p-1076'), TINY) + self.identical(fromHex('0X5p-1076'), TINY) + self.identical(fromHex('0X6p-1076'), 2*TINY) + self.identical(fromHex('0x7p-1076'), 2*TINY) + self.identical(fromHex('0X8p-1076'), 2*TINY) + self.identical(fromHex('0X9p-1076'), 2*TINY) + self.identical(fromHex('0xap-1076'), 2*TINY) + self.identical(fromHex('0Xbp-1076'), 3*TINY) + self.identical(fromHex('0xcp-1076'), 3*TINY) + self.identical(fromHex('0Xdp-1076'), 3*TINY) + self.identical(fromHex('0Xep-1076'), 4*TINY) + self.identical(fromHex('0xfp-1076'), 4*TINY) + self.identical(fromHex('0x10p-1076'), 4*TINY) + self.identical(fromHex('-0x1p-1076'), -0.0) + self.identical(fromHex('-0X2p-1076'), -0.0) + self.identical(fromHex('-0x3p-1076'), -TINY) + self.identical(fromHex('-0X4p-1076'), -TINY) + self.identical(fromHex('-0x5p-1076'), -TINY) + self.identical(fromHex('-0x6p-1076'), -2*TINY) + self.identical(fromHex('-0X7p-1076'), -2*TINY) + self.identical(fromHex('-0X8p-1076'), -2*TINY) + self.identical(fromHex('-0X9p-1076'), -2*TINY) + self.identical(fromHex('-0Xap-1076'), -2*TINY) + self.identical(fromHex('-0xbp-1076'), -3*TINY) + self.identical(fromHex('-0xcp-1076'), -3*TINY) + self.identical(fromHex('-0Xdp-1076'), -3*TINY) + self.identical(fromHex('-0xep-1076'), -4*TINY) + self.identical(fromHex('-0Xfp-1076'), -4*TINY) + self.identical(fromHex('-0X10p-1076'), -4*TINY) + + # ... and near MIN ... + self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY) + self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY) + self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY) + self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY) + self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY) + self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY) + self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY) + self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY) + self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY) + self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN) + self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN) + self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN) + self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN) + self.identical(fromHex('0x1.00000000000000p-1022'), MIN) + self.identical(fromHex('0x1.00000000000002p-1022'), MIN) + self.identical(fromHex('0x1.00000000000004p-1022'), MIN) + self.identical(fromHex('0x1.00000000000006p-1022'), MIN) + self.identical(fromHex('0x1.00000000000008p-1022'), MIN) + self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY) + self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY) + self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY) + self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY) + self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY) + self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY) + self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY) + self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY) + + # ... and near 1.0. + self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS) + self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS) + self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS) + self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS) + self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS) + self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2) + self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2) + self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2) + self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2) + self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2) + self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2) + self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2) + self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0) + self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0) + self.identical(fromHex('0X0.fffffffffffffep0'), 1.0) + self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0) + self.identical(fromHex('0X1.00000000000000p0'), 1.0) + self.identical(fromHex('0X1.00000000000001p0'), 1.0) + self.identical(fromHex('0x1.00000000000002p0'), 1.0) + self.identical(fromHex('0X1.00000000000003p0'), 1.0) + self.identical(fromHex('0x1.00000000000004p0'), 1.0) + self.identical(fromHex('0X1.00000000000005p0'), 1.0) + self.identical(fromHex('0X1.00000000000006p0'), 1.0) + self.identical(fromHex('0X1.00000000000007p0'), 1.0) + self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'), + 1.0) + self.identical(fromHex('0x1.00000000000008p0'), 1.0) + self.identical(fromHex('0x1.00000000000008000000000000000001p0'), + 1+EPS) + self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS) + self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS) + self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS) + self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS) + self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS) + self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS) + self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS) + self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS) + self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS) + self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS) + self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS) + self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS) + self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS) + self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS) + self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS) + self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'), + 1.0+EPS) + self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS) + self.identical(fromHex('0X1.00000000000018000000000000000001p0'), + 1.0+2*EPS) + self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS) + self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS) + self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS) + self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS) + self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS) + self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS) + self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS) + self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS) + + def test_roundtrip(self): + def roundtrip(x): + return fromHex(toHex(x)) + + for x in [NAN, INF, self.MAX, self.MIN, self.MIN-self.TINY, self.TINY, 0.0]: + self.identical(x, roundtrip(x)) + self.identical(-x, roundtrip(-x)) + + # fromHex(toHex(x)) should exactly recover x, for any non-NaN float x. + import random + for i in xrange(10000): + e = random.randrange(-1200, 1200) + m = random.random() + s = random.choice([1.0, -1.0]) + try: + x = s*ldexp(m, e) + except OverflowError: + pass + else: + self.identical(x, fromHex(toHex(x))) + + +def test_main(): + test_support.run_unittest( + GeneralFloatCases, + FormatFunctionsTestCase, + UnknownFormatTestCase, + IEEEFormatTestCase, + ReprTestCase, + RoundTestCase, + InfNanTest, + HexFloatTestCase, + ) + +if __name__ == '__main__': + test_main() |