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1595 lines (1409 loc) · 68.7 KB
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import fractions
import operator
import os
import random
import sys
import struct
import time
import unittest
from test import support
from test.support.testcase import FloatsAreIdenticalMixin
from test.support.numbers import (
VALID_UNDERSCORE_LITERALS,
INVALID_UNDERSCORE_LITERALS,
)
from math import isinf, isnan, copysign, ldexp
import math
try:
import _testcapi
except ImportError:
_testcapi = None
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, 'mathdata', 'formatfloat_testcases.txt')
class FloatSubclass(float):
pass
class OtherFloatSubclass(float):
pass
class MyIndex:
def __init__(self, value):
self.value = value
def __index__(self):
return self.value
class MyInt:
def __init__(self, value):
self.value = value
def __int__(self):
return self.value
class FloatLike:
def __init__(self, value):
self.value = value
def __float__(self):
return self.value
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.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.assertRaises(TypeError, float, {})
self.assertRaisesRegex(TypeError, "not 'dict'", float, {})
# Lone surrogate
self.assertRaises(ValueError, float, '\uD8F0')
# check that we don't accept alternate exponent markers
self.assertRaises(ValueError, float, "-1.7d29")
self.assertRaises(ValueError, float, "3D-14")
self.assertEqual(float(" \u0663.\u0661\u0664 "), 3.14)
self.assertEqual(float("\N{EM SPACE}3.14\N{EN SPACE}"), 3.14)
# extra long strings should not be a problem
float(b'.' + b'1'*1000)
float('.' + '1'*1000)
# Invalid unicode string
# See bpo-34087
self.assertRaises(ValueError, float, '\u3053\u3093\u306b\u3061\u306f')
def test_noargs(self):
self.assertEqual(float(), 0.0)
def test_underscores(self):
for lit in VALID_UNDERSCORE_LITERALS:
if not any(ch in lit for ch in 'jJxXoObB'):
self.assertEqual(float(lit), eval(lit))
self.assertEqual(float(lit), float(lit.replace('_', '')))
for lit in INVALID_UNDERSCORE_LITERALS:
if lit in ('0_7', '09_99'): # octals are not recognized here
continue
if not any(ch in lit for ch in 'jJxXoObB'):
self.assertRaises(ValueError, float, lit)
# Additional test cases; nan and inf are never valid as literals,
# only in the float() constructor, but we don't allow underscores
# in or around them.
self.assertRaises(ValueError, float, '_NaN')
self.assertRaises(ValueError, float, 'Na_N')
self.assertRaises(ValueError, float, 'IN_F')
self.assertRaises(ValueError, float, '-_INF')
self.assertRaises(ValueError, float, '-INF_')
# Check that we handle bytes values correctly.
self.assertRaises(ValueError, float, b'0_.\xff9')
def test_non_numeric_input_types(self):
# Test possible non-numeric types for the argument x, including
# subclasses of the explicitly documented accepted types.
class CustomStr(str): pass
class CustomBytes(bytes): pass
class CustomByteArray(bytearray): pass
factories = [
bytes,
bytearray,
lambda b: CustomStr(b.decode()),
CustomBytes,
CustomByteArray,
memoryview,
]
try:
from array import array
except ImportError:
pass
else:
factories.append(lambda b: array('B', b))
for f in factories:
x = f(b" 3.14 ")
with self.subTest(type(x)):
self.assertEqual(float(x), 3.14)
with self.assertRaisesRegex(ValueError, "could not convert"):
float(f(b'A' * 0x10))
def test_float_memoryview(self):
self.assertEqual(float(memoryview(b'12.3')[1:4]), 2.3)
self.assertEqual(float(memoryview(b'12.3\x00')[1:4]), 2.3)
self.assertEqual(float(memoryview(b'12.3 ')[1:4]), 2.3)
self.assertEqual(float(memoryview(b'12.3A')[1:4]), 2.3)
self.assertEqual(float(memoryview(b'12.34')[1:4]), 2.3)
def test_error_message(self):
def check(s):
with self.assertRaises(ValueError, msg='float(%r)' % (s,)) as cm:
float(s)
self.assertEqual(str(cm.exception),
'could not convert string to float: %r' % (s,))
check('\xbd')
check('123\xbd')
check(' 123 456 ')
check(b' 123 456 ')
# all whitespace (cf. https://github.com/python/cpython/issues/95605)
check('')
check(' ')
check('\t \n')
# non-ascii digits (error came from non-digit '!')
check('\u0663\u0661\u0664!')
# embedded NUL
check('123\x00')
check('123\x00 245')
check('123\x00245')
# byte string with embedded NUL
check(b'123\x00')
# non-UTF-8 byte string
check(b'123\xa0')
@support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE', '')
def test_float_with_comma(self):
# set locale to something that doesn't use '.' for the decimal point
# float must not accept the locale specific decimal point but
# it still has to accept the normal python syntax
import locale
if not locale.localeconv()['decimal_point'] == ',':
self.skipTest('decimal_point is not ","')
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.assertAlmostEqual(float(" .25e-1 "), .025)
def test_floatconversion(self):
# Make sure that calls to __float__() work properly
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.assertEqual(float(FloatLike(42.)), 42.)
self.assertEqual(float(Foo2()), 42.)
self.assertRaises(TypeError, float, Foo3(21))
self.assertRaises(TypeError, float, Foo4(42))
self.assertEqual(float(FooStr('8')), 9.)
self.assertRaises(TypeError, time.sleep, FloatLike(""))
# Issue #24731
f = FloatLike(OtherFloatSubclass(42.))
self.assertRaises(TypeError, float, f)
self.assertRaises(TypeError, FloatSubclass, f)
self.assertEqual(float(MyIndex(42)), 42.0)
self.assertRaises(OverflowError, float, MyIndex(2**2000))
self.assertRaises(TypeError, float, MyInt(42))
def test_keyword_args(self):
with self.assertRaisesRegex(TypeError, 'keyword argument'):
float(x='3.14')
def test_keywords_in_subclass(self):
class subclass(float):
pass
u = subclass(2.5)
self.assertIs(type(u), subclass)
self.assertEqual(float(u), 2.5)
with self.assertRaises(TypeError):
subclass(x=0)
class subclass_with_init(float):
def __init__(self, arg, newarg=None):
self.newarg = newarg
u = subclass_with_init(2.5, newarg=3)
self.assertIs(type(u), subclass_with_init)
self.assertEqual(float(u), 2.5)
self.assertEqual(u.newarg, 3)
class subclass_with_new(float):
def __new__(cls, arg, newarg=None):
self = super().__new__(cls, arg)
self.newarg = newarg
return self
u = subclass_with_new(2.5, newarg=3)
self.assertIs(type(u), subclass_with_new)
self.assertEqual(float(u), 2.5)
self.assertEqual(u.newarg, 3)
def assertEqualAndType(self, actual, expected_value, expected_type):
self.assertEqual(actual, expected_value)
self.assertIs(type(actual), expected_type)
def test_from_number(self, cls=float):
def eq(actual, expected):
self.assertEqual(actual, expected)
self.assertIs(type(actual), cls)
eq(cls.from_number(3.14), 3.14)
eq(cls.from_number(314), 314.0)
eq(cls.from_number(OtherFloatSubclass(3.14)), 3.14)
eq(cls.from_number(FloatLike(3.14)), 3.14)
eq(cls.from_number(MyIndex(314)), 314.0)
x = cls.from_number(NAN)
self.assertTrue(x != x)
self.assertIs(type(x), cls)
if cls is float:
self.assertIs(cls.from_number(NAN), NAN)
self.assertRaises(TypeError, cls.from_number, '3.14')
self.assertRaises(TypeError, cls.from_number, b'3.14')
self.assertRaises(TypeError, cls.from_number, 3.14j)
self.assertRaises(TypeError, cls.from_number, MyInt(314))
self.assertRaises(TypeError, cls.from_number, {})
self.assertRaises(TypeError, cls.from_number)
def test_from_number_subclass(self):
self.test_from_number(FloatSubclass)
def test_is_integer(self):
self.assertFalse((1.1).is_integer())
self.assertTrue((1.).is_integer())
self.assertFalse(float("nan").is_integer())
self.assertFalse(float("inf").is_integer())
def test_floatasratio(self):
for f, ratio in [
(0.875, (7, 8)),
(-0.875, (-7, 8)),
(0.0, (0, 1)),
(11.5, (23, 2)),
]:
self.assertEqual(f.as_integer_ratio(), ratio)
for i in range(10000):
f = random.random()
f *= 10 ** random.randint(-100, 100)
n, d = f.as_integer_ratio()
self.assertEqual(float(n).__truediv__(d), f)
R = fractions.Fraction
self.assertEqual(R(0, 1),
R(*float(0.0).as_integer_ratio()))
self.assertEqual(R(5, 2),
R(*float(2.5).as_integer_ratio()))
self.assertEqual(R(1, 2),
R(*float(0.5).as_integer_ratio()))
self.assertEqual(R(4728779608739021, 2251799813685248),
R(*float(2.1).as_integer_ratio()))
self.assertEqual(R(-4728779608739021, 2251799813685248),
R(*float(-2.1).as_integer_ratio()))
self.assertEqual(R(-2100, 1),
R(*float(-2100.0).as_integer_ratio()))
self.assertRaises(OverflowError, float('inf').as_integer_ratio)
self.assertRaises(OverflowError, float('-inf').as_integer_ratio)
self.assertRaises(ValueError, float('nan').as_integer_ratio)
def 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
# distinguishes -0.0 and 0.0.
self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))
def test_float_floor(self):
self.assertIsInstance(float(0.5).__floor__(), int)
self.assertEqual(float(0.5).__floor__(), 0)
self.assertEqual(float(1.0).__floor__(), 1)
self.assertEqual(float(1.5).__floor__(), 1)
self.assertEqual(float(-0.5).__floor__(), -1)
self.assertEqual(float(-1.0).__floor__(), -1)
self.assertEqual(float(-1.5).__floor__(), -2)
self.assertEqual(float(1.23e167).__floor__(), 1.23e167)
self.assertEqual(float(-1.23e167).__floor__(), -1.23e167)
self.assertRaises(ValueError, float("nan").__floor__)
self.assertRaises(OverflowError, float("inf").__floor__)
self.assertRaises(OverflowError, float("-inf").__floor__)
def test_float_ceil(self):
self.assertIsInstance(float(0.5).__ceil__(), int)
self.assertEqual(float(0.5).__ceil__(), 1)
self.assertEqual(float(1.0).__ceil__(), 1)
self.assertEqual(float(1.5).__ceil__(), 2)
self.assertEqual(float(-0.5).__ceil__(), 0)
self.assertEqual(float(-1.0).__ceil__(), -1)
self.assertEqual(float(-1.5).__ceil__(), -1)
self.assertEqual(float(1.23e167).__ceil__(), 1.23e167)
self.assertEqual(float(-1.23e167).__ceil__(), -1.23e167)
self.assertRaises(ValueError, float("nan").__ceil__)
self.assertRaises(OverflowError, float("inf").__ceil__)
self.assertRaises(OverflowError, float("-inf").__ceil__)
@support.requires_IEEE_754
def test_float_mod(self):
# Check behaviour of % operator for IEEE 754 special cases.
# In particular, check signs of zeros.
mod = operator.mod
self.assertEqualAndEqualSign(mod(-1.0, 1.0), 0.0)
self.assertEqualAndEqualSign(mod(-1e-100, 1.0), 1.0)
self.assertEqualAndEqualSign(mod(-0.0, 1.0), 0.0)
self.assertEqualAndEqualSign(mod(0.0, 1.0), 0.0)
self.assertEqualAndEqualSign(mod(1e-100, 1.0), 1e-100)
self.assertEqualAndEqualSign(mod(1.0, 1.0), 0.0)
self.assertEqualAndEqualSign(mod(-1.0, -1.0), -0.0)
self.assertEqualAndEqualSign(mod(-1e-100, -1.0), -1e-100)
self.assertEqualAndEqualSign(mod(-0.0, -1.0), -0.0)
self.assertEqualAndEqualSign(mod(0.0, -1.0), -0.0)
self.assertEqualAndEqualSign(mod(1e-100, -1.0), -1.0)
self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0)
@support.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)
def test_hash(self):
for x in range(-30, 30):
self.assertEqual(hash(float(x)), hash(x))
self.assertEqual(hash(float(sys.float_info.max)),
hash(int(sys.float_info.max)))
self.assertEqual(hash(float('inf')), sys.hash_info.inf)
self.assertEqual(hash(float('-inf')), -sys.hash_info.inf)
def test_hash_nan(self):
value = float('nan')
self.assertEqual(hash(value), object.__hash__(value))
class H:
def __hash__(self):
return 42
class F(float, H):
pass
value = F('nan')
self.assertEqual(hash(value), object.__hash__(value))
def test_issue_gh143006(self):
# When comparing negative non-integer float and int with the
# same number of bits in the integer part, __neg__() in the
# int subclass returning not an int caused an assertion error.
class EvilInt(int):
def __neg__(self):
return ""
i = -1 << 50
f = float(i) - 0.5
i = EvilInt(i)
self.assertFalse(f == i)
self.assertTrue(f != i)
self.assertTrue(f < i)
self.assertTrue(f <= i)
self.assertFalse(f > i)
self.assertFalse(f >= i)
@unittest.skipUnless(hasattr(float, "__getformat__"), "requires __getformat__")
class FormatFunctionsTestCase(unittest.TestCase):
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)
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 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):
@support.requires_IEEE_754
def test_double_specials_do_unpack(self):
for fmt, data in [('>d', BE_DOUBLE_INF),
('>d', BE_DOUBLE_NAN),
('<d', LE_DOUBLE_INF),
('<d', LE_DOUBLE_NAN)]:
struct.unpack(fmt, data)
@support.requires_IEEE_754
def test_float_specials_do_unpack(self):
for fmt, data in [('>f', BE_FLOAT_INF),
('>f', BE_FLOAT_NAN),
('<f', LE_FLOAT_INF),
('<f', LE_FLOAT_NAN)]:
struct.unpack(fmt, data)
@support.requires_IEEE_754
@unittest.skipIf(_testcapi is None, 'needs _testcapi')
def test_serialized_float_rounding(self):
FLT_MAX = _testcapi.FLT_MAX
self.assertEqual(struct.pack("<f", 3.40282356e38), struct.pack("<f", FLT_MAX))
self.assertEqual(struct.pack("<f", -3.40282356e38), struct.pack("<f", -FLT_MAX))
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")
# confirm format options expected to fail on floats, such as integer
# presentation types
for format_spec in 'sbcdoxX':
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')
# thousands separators
x = 123_456.123_456
self.assertEqual(format(x, '_f'), '123_456.123456')
self.assertEqual(format(x, ',f'), '123,456.123456')
self.assertEqual(format(x, '._f'), '123456.123_456')
self.assertEqual(format(x, '.,f'), '123456.123,456')
self.assertEqual(format(x, '_._f'), '123_456.123_456')
self.assertEqual(format(x, ',.,f'), '123,456.123,456')
self.assertEqual(format(x, '.10_f'), '123456.123_456_000_0')
self.assertEqual(format(x, '.10,f'), '123456.123,456,000,0')
self.assertEqual(format(x, '>21._f'), ' 123456.123_456')
self.assertEqual(format(x, '<21._f'), '123456.123_456 ')
self.assertEqual(format(x, '+.11_e'), '+1.234_561_234_56e+05')
self.assertEqual(format(x, '+.11,e'), '+1.234,561,234,56e+05')
self.assertEqual(format(x, '021_._f'), '0_000_123_456.123_456')
self.assertEqual(format(x, '020_._f'), '0_000_123_456.123_456')
self.assertEqual(format(x, '+021_._f'), '+0_000_123_456.123_456')
self.assertEqual(format(x, '21_._f'), ' 123_456.123_456')
self.assertEqual(format(x, '>021_._f'), '000000123_456.123_456')
self.assertEqual(format(x, '<021_._f'), '123_456.123_456000000')
self.assertEqual(format(x, '023_.10_f'), '0_123_456.123_456_000_0')
self.assertEqual(format(x, '022_.10_f'), '0_123_456.123_456_000_0')
self.assertEqual(format(x, '+023_.10_f'), '+0_123_456.123_456_000_0')
self.assertEqual(format(x, '023_.9_f'), '000_123_456.123_456_000')
self.assertEqual(format(x, '021_._e'), '0_000_001.234_561e+05')
self.assertEqual(format(x, '020_._e'), '0_000_001.234_561e+05')
self.assertEqual(format(x, '+021_._e'), '+0_000_001.234_561e+05')
self.assertEqual(format(x, '023_.10_e'), '0_001.234_561_234_6e+05')
self.assertEqual(format(x, '022_.10_e'), '0_001.234_561_234_6e+05')
self.assertEqual(format(x, '023_.9_e'), '000_001.234_561_235e+05')
self.assertRaises(ValueError, format, x, '._6f')
self.assertRaises(ValueError, format, x, '.,_f')
self.assertRaises(ValueError, format, x, '.6,_f')
self.assertRaises(ValueError, format, x, '.6_,f')
self.assertRaises(ValueError, format, x, '.6_n')
self.assertRaises(ValueError, format, x, '.6,n')
@support.requires_IEEE_754
@unittest.skipUnless(sys.float_repr_style == 'short',
"applies only when using short float repr style")
def test_format_testfile(self):
with open(format_testfile, encoding="utf-8") as testfile:
for line in testfile:
if line.startswith('--'):
continue
line = line.strip()
if not line:
continue
lhs, rhs = map(str.strip, line.split('->'))
fmt, arg = lhs.split()
f = float(arg)
self.assertEqual(fmt % f, rhs)
self.assertEqual(fmt % -f, '-' + rhs)
if fmt != '%r':
fmt2 = fmt[1:]
self.assertEqual(format(f, fmt2), rhs)
self.assertEqual(format(-f, fmt2), '-' + rhs)
def test_issue5864(self):
self.assertEqual(format(123.456, '.4'), '123.5')
self.assertEqual(format(1234.56, '.4'), '1.235e+03')
self.assertEqual(format(12345.6, '.4'), '1.235e+04')
def test_issue35560(self):
self.assertEqual(format(123.0, '00'), '123.0')
self.assertEqual(format(123.34, '00f'), '123.340000')
self.assertEqual(format(123.34, '00e'), '1.233400e+02')
self.assertEqual(format(123.34, '00g'), '123.34')
self.assertEqual(format(123.34, '00.10f'), '123.3400000000')
self.assertEqual(format(123.34, '00.10e'), '1.2334000000e+02')
self.assertEqual(format(123.34, '00.10g'), '123.34')
self.assertEqual(format(123.34, '01f'), '123.340000')
self.assertEqual(format(-123.0, '00'), '-123.0')
self.assertEqual(format(-123.34, '00f'), '-123.340000')
self.assertEqual(format(-123.34, '00e'), '-1.233400e+02')
self.assertEqual(format(-123.34, '00g'), '-123.34')
self.assertEqual(format(-123.34, '00.10f'), '-123.3400000000')
self.assertEqual(format(-123.34, '00.10f'), '-123.3400000000')
self.assertEqual(format(-123.34, '00.10e'), '-1.2334000000e+02')
self.assertEqual(format(-123.34, '00.10g'), '-123.34')
class ReprTestCase(unittest.TestCase):
def test_repr(self):
with open(os.path.join(os.path.split(__file__)[0],
'mathdata',
'floating_points.txt'), encoding="utf-8") as floats_file:
for line in floats_file:
line = line.strip()
if not line or line.startswith('#'):
continue
v = eval(line)
self.assertEqual(v, eval(repr(v)))
@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)))
# Since Python 3.2, repr and str are identical
self.assertEqual(repr(float(s)), str(float(s)))
self.assertEqual(repr(float(negs)), str(float(negs)))
@support.requires_IEEE_754
class RoundTestCase(unittest.TestCase, FloatsAreIdenticalMixin):
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)
def test_inf_nan_ndigits(self):
self.assertEqual(round(INF, 0), INF)
self.assertEqual(round(-INF, 0), -INF)
self.assertTrue(math.isnan(round(NAN, 0)))
def test_large_n(self):
for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]:
self.assertEqual(round(123.456, n), 123.456)
self.assertEqual(round(-123.456, n), -123.456)
self.assertEqual(round(1e300, n), 1e300)
self.assertEqual(round(1e-320, n), 1e-320)
self.assertEqual(round(1e150, 300), 1e150)
self.assertEqual(round(1e300, 307), 1e300)
self.assertEqual(round(-3.1415, 308), -3.1415)
self.assertEqual(round(1e150, 309), 1e150)
self.assertEqual(round(1.4e-315, 315), 1e-315)
def test_small_n(self):
for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]:
self.assertFloatsAreIdentical(round(123.456, n), 0.0)
self.assertFloatsAreIdentical(round(-123.456, n), -0.0)
self.assertFloatsAreIdentical(round(1e300, n), 0.0)
self.assertFloatsAreIdentical(round(1e-320, n), 0.0)
def test_overflow(self):
self.assertRaises(OverflowError, round, 1.6e308, -308)
self.assertRaises(OverflowError, round, -1.7e308, -308)
@unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
"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))