| |
| import unittest, struct |
| import os |
| from test import test_support |
| import math |
| from math import isinf, isnan, copysign, ldexp |
| import operator |
| import random, fractions |
| |
| INF = float("inf") |
| NAN = float("nan") |
| |
| 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") |
| 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) |
| # Implementation limitation in PyFloat_FromString() |
| self.assertRaises(ValueError, float, unicode("1"*10000)) |
| |
| @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 syntac |
| 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_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) |
| |
| 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.assert_(float.__getformat__('double') in |
| ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) |
| self.assert_(float.__getformat__('float') in |
| ['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. |
| |
| 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): |
| if float.__getformat__("double").startswith("IEEE"): |
| 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) |
| |
| if float.__getformat__("float").startswith("IEEE"): |
| 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) |
| |
| if float.__getformat__("double").startswith("IEEE"): |
| def test_negative_zero(self): |
| import math |
| 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.assertEquals(pos_pos(), neg_pos()) |
| self.assertEquals(pos_neg(), neg_neg()) |
| |
| if float.__getformat__("double").startswith("IEEE"): |
| def test_underflow_sign(self): |
| import math |
| # check that -1e-1000 gives -0.0, not 0.0 |
| self.assertEquals(math.atan2(-1e-1000, -1), math.atan2(-0.0, -1)) |
| self.assertEquals(math.atan2(float('-1e-1000'), -1), |
| math.atan2(-0.0, -1)) |
| |
| 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() |
| |
| # 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.assert_(isinf(float("inf"))) |
| self.assert_(isinf(float("+inf"))) |
| self.assert_(isinf(float("-inf"))) |
| self.assert_(isinf(float("infinity"))) |
| self.assert_(isinf(float("+infinity"))) |
| self.assert_(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.assert_(isnan(float("nan"))) |
| self.assert_(isnan(float("+nan"))) |
| self.assert_(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.assert_(NAN.is_nan()) |
| self.failIf(INF.is_nan()) |
| self.failIf((0.).is_nan()) |
| |
| def notest_float_inf(self): |
| self.assert_(INF.is_inf()) |
| self.failIf(NAN.is_inf()) |
| self.failIf((0.).is_inf()) |
| |
| 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, |
| InfNanTest, |
| HexFloatTestCase, |
| ) |
| |
| if __name__ == '__main__': |
| test_main() |
