749 lines
32 KiB
Python
749 lines
32 KiB
Python
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import unittest, struct
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import os
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from test import test_support
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import math
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from math import isinf, isnan, copysign, ldexp
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import operator
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INF = float("inf")
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NAN = float("nan")
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class GeneralFloatCases(unittest.TestCase):
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def test_float(self):
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self.assertEqual(float(3.14), 3.14)
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self.assertEqual(float(314), 314.0)
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self.assertEqual(float(314L), 314.0)
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self.assertEqual(float(" 3.14 "), 3.14)
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self.assertRaises(ValueError, float, " 0x3.1 ")
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self.assertRaises(ValueError, float, " -0x3.p-1 ")
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self.assertRaises(ValueError, float, " +0x3.p-1 ")
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self.assertRaises(ValueError, float, "++3.14")
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self.assertRaises(ValueError, float, "+-3.14")
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self.assertRaises(ValueError, float, "-+3.14")
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self.assertRaises(ValueError, float, "--3.14")
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if have_unicode:
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self.assertEqual(float(unicode(" 3.14 ")), 3.14)
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self.assertEqual(float(unicode(" \u0663.\u0661\u0664 ",'raw-unicode-escape')), 3.14)
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# Implementation limitation in PyFloat_FromString()
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self.assertRaises(ValueError, float, unicode("1"*10000))
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@test_support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE')
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def test_float_with_comma(self):
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# set locale to something that doesn't use '.' for the decimal point
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# float must not accept the locale specific decimal point but
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# it still has to accept the normal python syntac
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import locale
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if not locale.localeconv()['decimal_point'] == ',':
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return
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self.assertEqual(float(" 3.14 "), 3.14)
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self.assertEqual(float("+3.14 "), 3.14)
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self.assertEqual(float("-3.14 "), -3.14)
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self.assertEqual(float(".14 "), .14)
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self.assertEqual(float("3. "), 3.0)
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self.assertEqual(float("3.e3 "), 3000.0)
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self.assertEqual(float("3.2e3 "), 3200.0)
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self.assertEqual(float("2.5e-1 "), 0.25)
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self.assertEqual(float("5e-1"), 0.5)
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self.assertRaises(ValueError, float, " 3,14 ")
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self.assertRaises(ValueError, float, " +3,14 ")
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self.assertRaises(ValueError, float, " -3,14 ")
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self.assertRaises(ValueError, float, " 0x3.1 ")
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self.assertRaises(ValueError, float, " -0x3.p-1 ")
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self.assertRaises(ValueError, float, " +0x3.p-1 ")
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self.assertEqual(float(" 25.e-1 "), 2.5)
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self.assertEqual(fcmp(float(" .25e-1 "), .025), 0)
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def test_floatconversion(self):
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# Make sure that calls to __float__() work properly
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class Foo0:
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def __float__(self):
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return 42.
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class Foo1(object):
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def __float__(self):
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return 42.
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class Foo2(float):
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def __float__(self):
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return 42.
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class Foo3(float):
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def __new__(cls, value=0.):
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return float.__new__(cls, 2*value)
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def __float__(self):
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return self
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class Foo4(float):
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def __float__(self):
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return 42
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self.assertAlmostEqual(float(Foo0()), 42.)
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self.assertAlmostEqual(float(Foo1()), 42.)
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self.assertAlmostEqual(float(Foo2()), 42.)
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self.assertAlmostEqual(float(Foo3(21)), 42.)
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self.assertRaises(TypeError, float, Foo4(42))
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def test_floatasratio(self):
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for f, ratio in [
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(0.875, (7, 8)),
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(-0.875, (-7, 8)),
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(0.0, (0, 1)),
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(11.5, (23, 2)),
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]:
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self.assertEqual(f.as_integer_ratio(), ratio)
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for i in range(10000):
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f = random.random()
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f *= 10 ** random.randint(-100, 100)
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n, d = f.as_integer_ratio()
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self.assertEqual(float(n).__truediv__(d), f)
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R = fractions.Fraction
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self.assertEqual(R(0, 1),
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R(*float(0.0).as_integer_ratio()))
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self.assertEqual(R(5, 2),
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R(*float(2.5).as_integer_ratio()))
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self.assertEqual(R(1, 2),
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R(*float(0.5).as_integer_ratio()))
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self.assertEqual(R(4728779608739021, 2251799813685248),
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R(*float(2.1).as_integer_ratio()))
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self.assertEqual(R(-4728779608739021, 2251799813685248),
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R(*float(-2.1).as_integer_ratio()))
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self.assertEqual(R(-2100, 1),
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R(*float(-2100.0).as_integer_ratio()))
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self.assertRaises(OverflowError, float('inf').as_integer_ratio)
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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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class FormatFunctionsTestCase(unittest.TestCase):
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def setUp(self):
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self.save_formats = {'double':float.__getformat__('double'),
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'float':float.__getformat__('float')}
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def tearDown(self):
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float.__setformat__('double', self.save_formats['double'])
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float.__setformat__('float', self.save_formats['float'])
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def test_getformat(self):
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self.assert_(float.__getformat__('double') in
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['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
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self.assert_(float.__getformat__('float') in
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['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
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self.assertRaises(ValueError, float.__getformat__, 'chicken')
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self.assertRaises(TypeError, float.__getformat__, 1)
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def test_setformat(self):
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for t in 'double', 'float':
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float.__setformat__(t, 'unknown')
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if self.save_formats[t] == 'IEEE, big-endian':
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self.assertRaises(ValueError, float.__setformat__,
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t, 'IEEE, little-endian')
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elif self.save_formats[t] == 'IEEE, little-endian':
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self.assertRaises(ValueError, float.__setformat__,
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t, 'IEEE, big-endian')
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else:
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self.assertRaises(ValueError, float.__setformat__,
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t, 'IEEE, big-endian')
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self.assertRaises(ValueError, float.__setformat__,
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t, 'IEEE, little-endian')
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self.assertRaises(ValueError, float.__setformat__,
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t, 'chicken')
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self.assertRaises(ValueError, float.__setformat__,
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'chicken', 'unknown')
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BE_DOUBLE_INF = '\x7f\xf0\x00\x00\x00\x00\x00\x00'
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LE_DOUBLE_INF = ''.join(reversed(BE_DOUBLE_INF))
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BE_DOUBLE_NAN = '\x7f\xf8\x00\x00\x00\x00\x00\x00'
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LE_DOUBLE_NAN = ''.join(reversed(BE_DOUBLE_NAN))
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BE_FLOAT_INF = '\x7f\x80\x00\x00'
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LE_FLOAT_INF = ''.join(reversed(BE_FLOAT_INF))
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BE_FLOAT_NAN = '\x7f\xc0\x00\x00'
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LE_FLOAT_NAN = ''.join(reversed(BE_FLOAT_NAN))
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# on non-IEEE platforms, attempting to unpack a bit pattern
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# representing an infinity or a NaN should raise an exception.
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class UnknownFormatTestCase(unittest.TestCase):
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def setUp(self):
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self.save_formats = {'double':float.__getformat__('double'),
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'float':float.__getformat__('float')}
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float.__setformat__('double', 'unknown')
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float.__setformat__('float', 'unknown')
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def tearDown(self):
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float.__setformat__('double', self.save_formats['double'])
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float.__setformat__('float', self.save_formats['float'])
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def test_double_specials_dont_unpack(self):
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for fmt, data in [('>d', BE_DOUBLE_INF),
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('>d', BE_DOUBLE_NAN),
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('<d', LE_DOUBLE_INF),
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('<d', LE_DOUBLE_NAN)]:
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self.assertRaises(ValueError, struct.unpack, fmt, data)
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def test_float_specials_dont_unpack(self):
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for fmt, data in [('>f', BE_FLOAT_INF),
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('>f', BE_FLOAT_NAN),
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('<f', LE_FLOAT_INF),
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('<f', LE_FLOAT_NAN)]:
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self.assertRaises(ValueError, struct.unpack, fmt, data)
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# on an IEEE platform, all we guarantee is that bit patterns
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# representing infinities or NaNs do not raise an exception; all else
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# is accident (today).
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# let's also try to guarantee that -0.0 and 0.0 don't get confused.
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class IEEEFormatTestCase(unittest.TestCase):
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if float.__getformat__("double").startswith("IEEE"):
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def test_double_specials_do_unpack(self):
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for fmt, data in [('>d', BE_DOUBLE_INF),
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('>d', BE_DOUBLE_NAN),
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('<d', LE_DOUBLE_INF),
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('<d', LE_DOUBLE_NAN)]:
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struct.unpack(fmt, data)
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if float.__getformat__("float").startswith("IEEE"):
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def test_float_specials_do_unpack(self):
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for fmt, data in [('>f', BE_FLOAT_INF),
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('>f', BE_FLOAT_NAN),
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('<f', LE_FLOAT_INF),
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('<f', LE_FLOAT_NAN)]:
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struct.unpack(fmt, data)
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if float.__getformat__("double").startswith("IEEE"):
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def test_negative_zero(self):
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import math
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def pos_pos():
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return 0.0, math.atan2(0.0, -1)
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def pos_neg():
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return 0.0, math.atan2(-0.0, -1)
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def neg_pos():
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return -0.0, math.atan2(0.0, -1)
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def neg_neg():
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return -0.0, math.atan2(-0.0, -1)
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self.assertEquals(pos_pos(), neg_pos())
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self.assertEquals(pos_neg(), neg_neg())
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if float.__getformat__("double").startswith("IEEE"):
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def test_underflow_sign(self):
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import math
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# check that -1e-1000 gives -0.0, not 0.0
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self.assertEquals(math.atan2(-1e-1000, -1), math.atan2(-0.0, -1))
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self.assertEquals(math.atan2(float('-1e-1000'), -1),
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math.atan2(-0.0, -1))
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class ReprTestCase(unittest.TestCase):
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def test_repr(self):
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floats_file = open(os.path.join(os.path.split(__file__)[0],
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'floating_points.txt'))
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for line in floats_file:
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line = line.strip()
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if not line or line.startswith('#'):
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continue
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v = eval(line)
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self.assertEqual(v, eval(repr(v)))
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floats_file.close()
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# Beginning with Python 2.6 float has cross platform compatible
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# ways to create and represent inf and nan
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class InfNanTest(unittest.TestCase):
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def test_inf_from_str(self):
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self.assert_(isinf(float("inf")))
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self.assert_(isinf(float("+inf")))
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self.assert_(isinf(float("-inf")))
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self.assert_(isinf(float("infinity")))
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self.assert_(isinf(float("+infinity")))
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self.assert_(isinf(float("-infinity")))
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self.assertEqual(repr(float("inf")), "inf")
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self.assertEqual(repr(float("+inf")), "inf")
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self.assertEqual(repr(float("-inf")), "-inf")
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self.assertEqual(repr(float("infinity")), "inf")
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self.assertEqual(repr(float("+infinity")), "inf")
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self.assertEqual(repr(float("-infinity")), "-inf")
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self.assertEqual(repr(float("INF")), "inf")
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self.assertEqual(repr(float("+Inf")), "inf")
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self.assertEqual(repr(float("-iNF")), "-inf")
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self.assertEqual(repr(float("Infinity")), "inf")
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self.assertEqual(repr(float("+iNfInItY")), "inf")
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self.assertEqual(repr(float("-INFINITY")), "-inf")
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self.assertEqual(str(float("inf")), "inf")
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self.assertEqual(str(float("+inf")), "inf")
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self.assertEqual(str(float("-inf")), "-inf")
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self.assertEqual(str(float("infinity")), "inf")
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self.assertEqual(str(float("+infinity")), "inf")
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self.assertEqual(str(float("-infinity")), "-inf")
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self.assertRaises(ValueError, float, "info")
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self.assertRaises(ValueError, float, "+info")
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self.assertRaises(ValueError, float, "-info")
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self.assertRaises(ValueError, float, "in")
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self.assertRaises(ValueError, float, "+in")
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self.assertRaises(ValueError, float, "-in")
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self.assertRaises(ValueError, float, "infinit")
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self.assertRaises(ValueError, float, "+Infin")
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self.assertRaises(ValueError, float, "-INFI")
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self.assertRaises(ValueError, float, "infinitys")
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def test_inf_as_str(self):
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self.assertEqual(repr(1e300 * 1e300), "inf")
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self.assertEqual(repr(-1e300 * 1e300), "-inf")
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self.assertEqual(str(1e300 * 1e300), "inf")
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self.assertEqual(str(-1e300 * 1e300), "-inf")
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def test_nan_from_str(self):
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self.assert_(isnan(float("nan")))
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self.assert_(isnan(float("+nan")))
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self.assert_(isnan(float("-nan")))
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self.assertEqual(repr(float("nan")), "nan")
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self.assertEqual(repr(float("+nan")), "nan")
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self.assertEqual(repr(float("-nan")), "nan")
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self.assertEqual(repr(float("NAN")), "nan")
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self.assertEqual(repr(float("+NAn")), "nan")
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self.assertEqual(repr(float("-NaN")), "nan")
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self.assertEqual(str(float("nan")), "nan")
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self.assertEqual(str(float("+nan")), "nan")
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self.assertEqual(str(float("-nan")), "nan")
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self.assertRaises(ValueError, float, "nana")
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self.assertRaises(ValueError, float, "+nana")
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self.assertRaises(ValueError, float, "-nana")
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self.assertRaises(ValueError, float, "na")
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self.assertRaises(ValueError, float, "+na")
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self.assertRaises(ValueError, float, "-na")
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def test_nan_as_str(self):
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self.assertEqual(repr(1e300 * 1e300 * 0), "nan")
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self.assertEqual(repr(-1e300 * 1e300 * 0), "nan")
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self.assertEqual(str(1e300 * 1e300 * 0), "nan")
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self.assertEqual(str(-1e300 * 1e300 * 0), "nan")
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def notest_float_nan(self):
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self.assert_(NAN.is_nan())
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self.failIf(INF.is_nan())
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self.failIf((0.).is_nan())
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def notest_float_inf(self):
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self.assert_(INF.is_inf())
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self.failIf(NAN.is_inf())
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self.failIf((0.).is_inf())
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fromHex = float.fromhex
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toHex = float.hex
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class HexFloatTestCase(unittest.TestCase):
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MAX = fromHex('0x.fffffffffffff8p+1024') # max normal
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MIN = fromHex('0x1p-1022') # min normal
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TINY = fromHex('0x0.0000000000001p-1022') # min subnormal
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EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up
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def identical(self, x, y):
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# check that floats x and y are identical, or that both
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# are NaNs
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if isnan(x) or isnan(y):
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if isnan(x) == isnan(y):
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return
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elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)):
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return
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self.fail('%r not identical to %r' % (x, y))
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def test_ends(self):
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self.identical(self.MIN, ldexp(1.0, -1022))
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self.identical(self.TINY, ldexp(1.0, -1074))
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self.identical(self.EPS, ldexp(1.0, -52))
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self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970)))
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|
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def test_invalid_inputs(self):
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invalid_inputs = [
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'infi', # misspelt infinities and nans
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'-Infinit',
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'++inf',
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'-+Inf',
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'--nan',
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'+-NaN',
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'snan',
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'NaNs',
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'nna',
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'0xnan',
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'',
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' ',
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'x1.0p0',
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'0xX1.0p0',
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'+ 0x1.0p0', # internal whitespace
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'- 0x1.0p0',
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'0 x1.0p0',
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'0x 1.0p0',
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'0x1 2.0p0',
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'+0x1 .0p0',
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'0x1. 0p0',
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'-0x1.0 1p0',
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'-0x1.0 p0',
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'+0x1.0p +0',
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'0x1.0p -0',
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'0x1.0p 0',
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'+0x1.0p+ 0',
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'-0x1.0p- 0',
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'++0x1.0p-0', # double signs
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'--0x1.0p0',
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'+-0x1.0p+0',
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'-+0x1.0p0',
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'0x1.0p++0',
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'+0x1.0p+-0',
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'-0x1.0p-+0',
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'0x1.0p--0',
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'0x1.0.p0',
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'0x.p0', # no hex digits before or after point
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'0x1,p0', # wrong decimal point character
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'0x1pa',
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u'0x1p\uff10', # fullwidth Unicode digits
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u'\uff10x1p0',
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u'0x\uff11p0',
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u'0x1.\uff10p0',
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'0x1p0 \n 0x2p0',
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'0x1p0\0 0x1p0', # embedded null byte is not end of string
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]
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for x in invalid_inputs:
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try:
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result = fromHex(x)
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|
except ValueError:
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pass
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else:
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self.fail('Expected float.fromhex(%r) to raise ValueError; '
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'got %r instead' % (x, result))
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|
|
|
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def test_from_hex(self):
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MIN = self.MIN;
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MAX = self.MAX;
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TINY = self.TINY;
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EPS = self.EPS;
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|
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# two spellings of infinity, with optional signs; case-insensitive
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self.identical(fromHex('inf'), INF)
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self.identical(fromHex('+Inf'), INF)
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self.identical(fromHex('-INF'), -INF)
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self.identical(fromHex('iNf'), INF)
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self.identical(fromHex('Infinity'), INF)
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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(
|
|
FormatFunctionsTestCase,
|
|
UnknownFormatTestCase,
|
|
IEEEFormatTestCase,
|
|
ReprTestCase,
|
|
InfNanTest,
|
|
HexFloatTestCase,
|
|
)
|
|
|
|
if __name__ == '__main__':
|
|
test_main()
|