import unittest, struct import os import sys from test import support import math from math import isinf, isnan, copysign, ldexp import operator import random, fractions INF = float("inf") NAN = float("nan") #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(" 3.14 "), 3.14) self.assertEqual(float(b" 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") self.assertRaises(ValueError, float, ".nan") self.assertRaises(ValueError, float, "+.inf") self.assertRaises(ValueError, float, ".") self.assertRaises(ValueError, float, "-.") self.assertEqual(float(b" \u0663.\u0661\u0664 ".decode('raw-unicode-escape')), 3.14) @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(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 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(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) def test_float_containment(self): floats = (INF, -INF, 0.0, 1.0, NAN) for f in floats: self.assert_(f in [f], "'%r' not in []" % f) self.assert_(f in (f,), "'%r' not in ()" % f) self.assert_(f in {f}, "'%r' not in set()" % f) self.assert_(f in {f: None}, "'%r' not in {}" % f) self.assertEqual([f].count(f), 1, "[].count('%r') != 1" % f) self.assert_(f in floats, "'%r' not in container" % f) for f in floats: # nonidentical containers, same type, same contents self.assert_([f] == [f], "[%r] != [%r]" % (f, f)) self.assert_((f,) == (f,), "(%r,) != (%r,)" % (f, f)) self.assert_({f} == {f}, "{%r} != {%r}" % (f, f)) self.assert_({f : None} == {f: None}, "{%r : None} != " "{%r : None}" % (f, f)) # identical containers l, t, s, d = [f], (f,), {f}, {f: None} self.assert_(l == l, "[%r] not equal to itself" % f) self.assert_(t == t, "(%r,) not equal to itself" % f) self.assert_(s == s, "{%r} not equal to itself" % f) self.assert_(d == d, "{%r : None} not equal to itself" % f) 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 = b'\x7f\xf0\x00\x00\x00\x00\x00\x00' LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF)) BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00' LE_DOUBLE_NAN = bytes(reversed(BE_DOUBLE_NAN)) BE_FLOAT_INF = b'\x7f\x80\x00\x00' LE_FLOAT_INF = bytes(reversed(BE_FLOAT_INF)) BE_FLOAT_NAN = b'\x7f\xc0\x00\x00' LE_FLOAT_NAN = bytes(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), ('f', BE_FLOAT_INF), ('>f', BE_FLOAT_NAN), ('d', BE_DOUBLE_INF), ('>d', BE_DOUBLE_NAN), ('f', BE_FLOAT_INF), ('>f', BE_FLOAT_NAN), ('')) fmt, arg = lhs.split() self.assertEqual(fmt % float(arg), rhs) self.assertEqual(fmt % -float(arg), '-' + rhs) def test_issue5864(self): self.assertEquals(format(123.456, '.4'), '123.5') self.assertEquals(format(1234.56, '.4'), '1.235e+03') self.assertEquals(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))) class RoundTestCase(unittest.TestCase): @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), "test requires IEEE 754 doubles") def test_inf_nan(self): self.assertRaises(OverflowError, round, INF) self.assertRaises(OverflowError, round, -INF) self.assertRaises(ValueError, round, NAN) @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), "test requires IEEE 754 doubles") 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) @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), "test requires IEEE 754 doubles") 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) @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), "test requires IEEE 754 doubles") 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', "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) # round-half-even self.assertEqual(round(25.0, -1), 20.0) self.assertEqual(round(35.0, -1), 40.0) self.assertEqual(round(45.0, -1), 40.0) self.assertEqual(round(55.0, -1), 60.0) self.assertEqual(round(65.0, -1), 60.0) self.assertEqual(round(75.0, -1), 80.0) self.assertEqual(round(85.0, -1), 80.0) self.assertEqual(round(95.0, -1), 100.0) @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', "applies only when using short float repr style") def test_matches_float_format(self): # round should give the same results as float formatting for i in range(500): x = i/1000. self.assertEqual(float(format(x, '.0f')), round(x, 0)) self.assertEqual(float(format(x, '.1f')), round(x, 1)) self.assertEqual(float(format(x, '.2f')), round(x, 2)) self.assertEqual(float(format(x, '.3f')), round(x, 3)) for i in range(5, 5000, 10): x = i/1000. self.assertEqual(float(format(x, '.0f')), round(x, 0)) self.assertEqual(float(format(x, '.1f')), round(x, 1)) self.assertEqual(float(format(x, '.2f')), round(x, 2)) self.assertEqual(float(format(x, '.3f')), round(x, 3)) for i in range(500): x = random.random() self.assertEqual(float(format(x, '.0f')), round(x, 0)) self.assertEqual(float(format(x, '.1f')), round(x, 1)) self.assertEqual(float(format(x, '.2f')), round(x, 2)) self.assertEqual(float(format(x, '.3f')), round(x, 3)) # 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', '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', '0x1p\uff10', # fullwidth Unicode digits '\uff10x1p0', '0x\uff11p0', '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_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(' 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 range(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(): support.run_unittest( GeneralFloatCases, FormatFunctionsTestCase, UnknownFormatTestCase, IEEEFormatTestCase, FormatTestCase, ReprTestCase, RoundTestCase, InfNanTest, HexFloatTestCase, ) if __name__ == '__main__': test_main()