mirrors/cpython
0
0
Fork 0
mirror of https://github.com/python/cpython.git synced 2024-11-25 19:03:49 +08:00
Code Issues Packages Projects Releases Wiki Activity
b3a8984488
cpython/Lib/test/test_float.py
Mark Dickinson 6ded1d5687 Merged revisions 82117 via svnmerge from 
svn+ssh://pythondev@svn.python.org/python/trunk

........
  r82117 | mark.dickinson | 2010-06-20 19:50:19 +0100 (Sun, 20 Jun 2010) | 1 line

  Merge test_strtod and test_float string-to-float conversion tests.
........
2010-06-20 20:01:04 +00:00

1284 lines
57 KiB
Python
Raw Blame History

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")
# decorator for skipping tests on non-IEEE 754 platforms
requires_IEEE_754 = unittest.skipUnless(
float.__getformat__("double").startswith("IEEE"),
"test requires IEEE 754 doubles")
#locate file with float format test values
test_dir = os.path.dirname(__file__) or os.curdir
format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt')
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, "-.")
# check that we don't accept alternate exponent markers
self.assertRaises(ValueError, float, "-1.7d29")
self.assertRaises(ValueError, float, "3D-14")
self.assertEqual(float(b" \u0663.\u0661\u0664 ".decode('raw-unicode-escape')), 3.14)
# extra long strings should not be a problem
float(b'.' + b'1'*1000)
float('.' + '1'*1000)
@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.assertIn(f, [f])
self.assertIn(f, (f,))
self.assertIn(f, {f})
self.assertIn(f, {f: None})
self.assertEqual([f].count(f), 1, "[].count('%r') != 1" % f)
self.assertIn(f, floats)
for f in floats:
# nonidentical containers, same type, same contents
self.assertTrue([f] == [f], "[%r] != [%r]" % (f, f))
self.assertTrue((f,) == (f,), "(%r,) != (%r,)" % (f, f))
self.assertTrue({f} == {f}, "{%r} != {%r}" % (f, f))
self.assertTrue({f : None} == {f: None}, "{%r : None} != "
"{%r : None}" % (f, f))
# identical containers
l, t, s, d = [f], (f,), {f}, {f: None}
self.assertTrue(l == l, "[%r] not equal to itself" % f)
self.assertTrue(t == t, "(%r,) not equal to itself" % f)
self.assertTrue(s == s, "{%r} not equal to itself" % f)
self.assertTrue(d == d, "{%r : None} not equal to itself" % f)
def assertEqualAndEqualSign(self, a, b):
# fail unless a == b and a and b have the same sign bit;
# the only difference from assertEqual is that this test
# distingishes -0.0 and 0.0.
self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))
@requires_IEEE_754
def test_float_pow(self):
# test builtin pow and ** operator for IEEE 754 special cases.
# Special cases taken from section F.9.4.4 of the C99 specification
for pow_op in pow, operator.pow:
# x**NAN is NAN for any x except 1
self.assertTrue(isnan(pow_op(-INF, NAN)))
self.assertTrue(isnan(pow_op(-2.0, NAN)))
self.assertTrue(isnan(pow_op(-1.0, NAN)))
self.assertTrue(isnan(pow_op(-0.5, NAN)))
self.assertTrue(isnan(pow_op(-0.0, NAN)))
self.assertTrue(isnan(pow_op(0.0, NAN)))
self.assertTrue(isnan(pow_op(0.5, NAN)))
self.assertTrue(isnan(pow_op(2.0, NAN)))
self.assertTrue(isnan(pow_op(INF, NAN)))
self.assertTrue(isnan(pow_op(NAN, NAN)))
# NAN**y is NAN for any y except +-0
self.assertTrue(isnan(pow_op(NAN, -INF)))
self.assertTrue(isnan(pow_op(NAN, -2.0)))
self.assertTrue(isnan(pow_op(NAN, -1.0)))
self.assertTrue(isnan(pow_op(NAN, -0.5)))
self.assertTrue(isnan(pow_op(NAN, 0.5)))
self.assertTrue(isnan(pow_op(NAN, 1.0)))
self.assertTrue(isnan(pow_op(NAN, 2.0)))
self.assertTrue(isnan(pow_op(NAN, INF)))
# (+-0)**y raises ZeroDivisionError for y a negative odd integer
self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0)
self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0)
# (+-0)**y raises ZeroDivisionError for y finite and negative
# but not an odd integer
self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0)
self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5)
self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0)
self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5)
# (+-0)**y is +-0 for y a positive odd integer
self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0)
self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0)
# (+-0)**y is 0 for y finite and positive but not an odd integer
self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0)
self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0)
self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0)
self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0)
# (-1)**+-inf is 1
self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0)
# 1**y is 1 for any y, even if y is an infinity or nan
self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0)
# x**+-0 is 1 for any x, even if x is a zero, infinity, or nan
self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0)
# x**y defers to complex pow for finite negative x and
# non-integral y.
self.assertEqual(type(pow_op(-2.0, -0.5)), complex)
self.assertEqual(type(pow_op(-2.0, 0.5)), complex)
self.assertEqual(type(pow_op(-1.0, -0.5)), complex)
self.assertEqual(type(pow_op(-1.0, 0.5)), complex)
self.assertEqual(type(pow_op(-0.5, -0.5)), complex)
self.assertEqual(type(pow_op(-0.5, 0.5)), complex)
# x**-INF is INF for abs(x) < 1
self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF)
self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF)
self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF)
self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF)
# x**-INF is 0 for abs(x) > 1
self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0)
self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0)
self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0)
self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0)
# x**INF is 0 for abs(x) < 1
self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0)
self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0)
self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0)
self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0)
# x**INF is INF for abs(x) > 1
self.assertEqualAndEqualSign(pow_op(-INF, INF), INF)
self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF)
self.assertEqualAndEqualSign(pow_op(2.0, INF), INF)
self.assertEqualAndEqualSign(pow_op(INF, INF), INF)
# (-INF)**y is -0.0 for y a negative odd integer
self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0)
# (-INF)**y is 0.0 for y negative but not an odd integer
self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0)
self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0)
# (-INF)**y is -INF for y a positive odd integer
self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF)
# (-INF)**y is INF for y positive but not an odd integer
self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF)
self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF)
# INF**y is INF for y positive
self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF)
self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF)
self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF)
# INF**y is 0.0 for y negative
self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0)
self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0)
self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0)
# basic checks not covered by the special cases above
self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25)
self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5)
self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0)
self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0)
self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0)
self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25)
self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5)
self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0)
self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0)
# 1 ** large and -1 ** large; some libms apparently
# have problems with these
self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0)
self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0)
self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0)
# check sign for results that underflow to 0
self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0)
self.assertEqual(type(pow_op(-2.0, -2000.5)), complex)
self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0)
self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0)
self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0)
self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0)
self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0)
self.assertEqual(type(pow_op(-0.5, 2000.5)), complex)
self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0)
self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0)
self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0)
self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0)
# check we don't raise an exception for subnormal results,
# and validate signs. Tests currently disabled, since
# they fail on systems where a subnormal result from pow
# is flushed to zero (e.g. Debian/ia64.)
#self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315)
#self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315)
#self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315)
#self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315)
#self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315)
#self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315)
#self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315)
#self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315)
class FormatFunctionsTestCase(unittest.TestCase):
def setUp(self):
self.save_formats = {'double':float.__getformat__('double'),
'float':float.__getformat__('float')}
def tearDown(self):
float.__setformat__('double', self.save_formats['double'])
float.__setformat__('float', self.save_formats['float'])
def test_getformat(self):
self.assertIn(float.__getformat__('double'),
['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
self.assertIn(float.__getformat__('float'),
['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
self.assertRaises(ValueError, float.__getformat__, 'chicken')
self.assertRaises(TypeError, float.__getformat__, 1)
def test_setformat(self):
for t in 'double', 'float':
float.__setformat__(t, 'unknown')
if self.save_formats[t] == 'IEEE, big-endian':
self.assertRaises(ValueError, float.__setformat__,
t, 'IEEE, little-endian')
elif self.save_formats[t] == 'IEEE, little-endian':
self.assertRaises(ValueError, float.__setformat__,
t, 'IEEE, big-endian')
else:
self.assertRaises(ValueError, float.__setformat__,
t, 'IEEE, big-endian')
self.assertRaises(ValueError, float.__setformat__,
t, 'IEEE, little-endian')
self.assertRaises(ValueError, float.__setformat__,
t, 'chicken')
self.assertRaises(ValueError, float.__setformat__,
'chicken', 'unknown')
BE_DOUBLE_INF = 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),
('<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):
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())
class FormatTestCase(unittest.TestCase):
def test_format(self):
# these should be rewritten to use both format(x, spec) and
# x.__format__(spec)
self.assertEqual(format(0.0, 'f'), '0.000000')
# the default is 'g', except for empty format spec
self.assertEqual(format(0.0, ''), '0.0')
self.assertEqual(format(0.01, ''), '0.01')
self.assertEqual(format(0.01, 'g'), '0.01')
# empty presentation type should format in the same way as str
# (issue 5920)
x = 100/7.
self.assertEqual(format(x, ''), str(x))
self.assertEqual(format(x, '-'), str(x))
self.assertEqual(format(x, '>'), str(x))
self.assertEqual(format(x, '2'), str(x))
self.assertEqual(format(1.0, 'f'), '1.000000')
self.assertEqual(format(-1.0, 'f'), '-1.000000')
self.assertEqual(format( 1.0, ' f'), ' 1.000000')
self.assertEqual(format(-1.0, ' f'), '-1.000000')
self.assertEqual(format( 1.0, '+f'), '+1.000000')
self.assertEqual(format(-1.0, '+f'), '-1.000000')
# % formatting
self.assertEqual(format(-1.0, '%'), '-100.000000%')
# conversion to string should fail
self.assertRaises(ValueError, format, 3.0, "s")
# other format specifiers shouldn't work on floats,
# in particular int specifiers
for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] +
[chr(x) for x in range(ord('A'), ord('Z')+1)]):
if not format_spec in 'eEfFgGn%':
self.assertRaises(ValueError, format, 0.0, format_spec)
self.assertRaises(ValueError, format, 1.0, format_spec)
self.assertRaises(ValueError, format, -1.0, format_spec)
self.assertRaises(ValueError, format, 1e100, format_spec)
self.assertRaises(ValueError, format, -1e100, format_spec)
self.assertRaises(ValueError, format, 1e-100, format_spec)
self.assertRaises(ValueError, format, -1e-100, format_spec)
# issue 3382
self.assertEqual(format(NAN, 'f'), 'nan')
self.assertEqual(format(NAN, 'F'), 'NAN')
self.assertEqual(format(INF, 'f'), 'inf')
self.assertEqual(format(INF, 'F'), 'INF')
@unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
"test requires IEEE 754 doubles")
def test_format_testfile(self):
for line in open(format_testfile):
if line.startswith('--'):
continue
line = line.strip()
if not line:
continue
lhs, rhs = map(str.strip, line.split('->'))
fmt, arg = lhs.split()
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)
self.assertRaises(TypeError, round, INF, 0.0)
self.assertRaises(TypeError, round, -INF, 1.0)
self.assertRaises(TypeError, round, NAN, "ceci n'est pas un integer")
self.assertRaises(TypeError, round, -0.0, 1j)
@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))
@unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
"test requires IEEE 754 doubles")
def test_format_specials(self):
# Test formatting of nans and infs.
def test(fmt, value, expected):
# Test with both % and format().
self.assertEqual(fmt % value, expected, fmt)
if not '#' in fmt:
# Until issue 7094 is implemented, format() for floats doesn't
# support '#' formatting
fmt = fmt[1:] # strip off the %
self.assertEqual(format(value, fmt), expected, fmt)
for fmt in ['%e', '%f', '%g', '%.0e', '%.6f', '%.20g',
'%#e', '%#f', '%#g', '%#.20e', '%#.15f', '%#.3g']:
pfmt = '%+' + fmt[1:]
sfmt = '% ' + fmt[1:]
test(fmt, INF, 'inf')
test(fmt, -INF, '-inf')
test(fmt, NAN, 'nan')
test(fmt, -NAN, 'nan')
# When asking for a sign, it's always provided. nans are
# always positive.
test(pfmt, INF, '+inf')
test(pfmt, -INF, '-inf')
test(pfmt, NAN, '+nan')
test(pfmt, -NAN, '+nan')
# When using ' ' for a sign code, only infs can be negative.
# Others have a space.
test(sfmt, INF, ' inf')
test(sfmt, -INF, '-inf')
test(sfmt, NAN, ' nan')
test(sfmt, -NAN, ' nan')
# Beginning with Python 2.6 float has cross platform compatible
# ways to create and represent inf and nan
class InfNanTest(unittest.TestCase):
def test_inf_from_str(self):
self.assertTrue(isinf(float("inf")))
self.assertTrue(isinf(float("+inf")))
self.assertTrue(isinf(float("-inf")))
self.assertTrue(isinf(float("infinity")))
self.assertTrue(isinf(float("+infinity")))
self.assertTrue(isinf(float("-infinity")))
self.assertEqual(repr(float("inf")), "inf")
self.assertEqual(repr(float("+inf")), "inf")
self.assertEqual(repr(float("-inf")), "-inf")
self.assertEqual(repr(float("infinity")), "inf")
self.assertEqual(repr(float("+infinity")), "inf")
self.assertEqual(repr(float("-infinity")), "-inf")
self.assertEqual(repr(float("INF")), "inf")
self.assertEqual(repr(float("+Inf")), "inf")
self.assertEqual(repr(float("-iNF")), "-inf")
self.assertEqual(repr(float("Infinity")), "inf")
self.assertEqual(repr(float("+iNfInItY")), "inf")
self.assertEqual(repr(float("-INFINITY")), "-inf")
self.assertEqual(str(float("inf")), "inf")
self.assertEqual(str(float("+inf")), "inf")
self.assertEqual(str(float("-inf")), "-inf")
self.assertEqual(str(float("infinity")), "inf")
self.assertEqual(str(float("+infinity")), "inf")
self.assertEqual(str(float("-infinity")), "-inf")
self.assertRaises(ValueError, float, "info")
self.assertRaises(ValueError, float, "+info")
self.assertRaises(ValueError, float, "-info")
self.assertRaises(ValueError, float, "in")
self.assertRaises(ValueError, float, "+in")
self.assertRaises(ValueError, float, "-in")
self.assertRaises(ValueError, float, "infinit")
self.assertRaises(ValueError, float, "+Infin")
self.assertRaises(ValueError, float, "-INFI")
self.assertRaises(ValueError, float, "infinitys")
self.assertRaises(ValueError, float, "++Inf")
self.assertRaises(ValueError, float, "-+inf")
self.assertRaises(ValueError, float, "+-infinity")
self.assertRaises(ValueError, float, "--Infinity")
def test_inf_as_str(self):
self.assertEqual(repr(1e300 * 1e300), "inf")
self.assertEqual(repr(-1e300 * 1e300), "-inf")
self.assertEqual(str(1e300 * 1e300), "inf")
self.assertEqual(str(-1e300 * 1e300), "-inf")
def test_nan_from_str(self):
self.assertTrue(isnan(float("nan")))
self.assertTrue(isnan(float("+nan")))
self.assertTrue(isnan(float("-nan")))
self.assertEqual(repr(float("nan")), "nan")
self.assertEqual(repr(float("+nan")), "nan")
self.assertEqual(repr(float("-nan")), "nan")
self.assertEqual(repr(float("NAN")), "nan")
self.assertEqual(repr(float("+NAn")), "nan")
self.assertEqual(repr(float("-NaN")), "nan")
self.assertEqual(str(float("nan")), "nan")
self.assertEqual(str(float("+nan")), "nan")
self.assertEqual(str(float("-nan")), "nan")
self.assertRaises(ValueError, float, "nana")
self.assertRaises(ValueError, float, "+nana")
self.assertRaises(ValueError, float, "-nana")
self.assertRaises(ValueError, float, "na")
self.assertRaises(ValueError, float, "+na")
self.assertRaises(ValueError, float, "-na")
self.assertRaises(ValueError, float, "++nan")
self.assertRaises(ValueError, float, "-+NAN")
self.assertRaises(ValueError, float, "+-NaN")
self.assertRaises(ValueError, float, "--nAn")
def test_nan_as_str(self):
self.assertEqual(repr(1e300 * 1e300 * 0), "nan")
self.assertEqual(repr(-1e300 * 1e300 * 0), "nan")
self.assertEqual(str(1e300 * 1e300 * 0), "nan")
self.assertEqual(str(-1e300 * 1e300 * 0), "nan")
def notest_float_nan(self):
self.assertTrue(NAN.is_nan())
self.assertFalse(INF.is_nan())
self.assertFalse((0.).is_nan())
def notest_float_inf(self):
self.assertTrue(INF.is_inf())
self.assertFalse(NAN.is_inf())
self.assertFalse((0.).is_inf())
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',
'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_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(' 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()
Reference in New Issue View Git Blame Copy Permalink