def testRound(self):
if sys.version_info[0] >= 3:
self.assertTypedEquals(F(-200), round(F(-150), -2))
self.assertTypedEquals(F(-200), round(F(-250), -2))
self.assertTypedEquals(F(30), round(F(26), -1))
self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1))
self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1))
def testInitFromDecimal(self):
self.assertEqual((11, 10), _components(F(Decimal('1.1'))))
self.assertEqual((7, 200), _components(F(Decimal('3.5e-2'))))
self.assertEqual((0, 1), _components(F(Decimal('.000e20'))))
# bug 16469: error types should be consistent with decimal -> int
self.assertRaises(ValueError, F, Decimal('nan'))
self.assertRaises(ValueError, F, Decimal('snan'))
self.assertRaises(OverflowError, F, Decimal('inf'))
self.assertRaises(OverflowError, F, Decimal('-inf'))
def testInitFromFloat(self):
self.assertEqual((5, 2), _components(F(2.5)))
self.assertEqual((0, 1), _components(F(-0.0)))
self.assertEqual((3602879701896397, 36028797018963968),
_components(F(0.1)))
# bug 16469: error types should be consistent with float -> int
self.assertRaises(ValueError, F, float('nan'))
self.assertRaises(OverflowError, F, float('inf'))
self.assertRaises(OverflowError, F, float('-inf'))
def testApproximatePi(self):
# Algorithm borrowed from
# http://docs.python.org/lib/decimal-recipes.html
three = F(3)
lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
while abs(s - lasts) > F(1, 10**9):
lasts = s
n, na = n + na, na + 8
d, da = d + da, da + 32
t = (t * n) / d
s += t
self.assertAlmostEqual(math.pi, s)
def testMixedEqual(self):
self.assertTrue(0.5 == F(1, 2))
self.assertFalse(0.6 == F(1, 2))
self.assertTrue(F(1, 2) == 0.5)
self.assertFalse(F(1, 2) == 0.4)
# self.assertTrue(2 == F(4, 2))
self.assertFalse(2 == F(3, 2))
# self.assertTrue(F(4, 2) == 2)
self.assertFalse(F(5, 2) == 2)
self.assertFalse(F(5, 2) == float('nan'))
self.assertFalse(float('nan') == F(3, 7))
self.assertFalse(F(5, 2) == float('inf'))
self.assertFalse(float('-inf') == F(2, 5))
def testApproximateCos1(self):
# Algorithm borrowed from
# http://docs.python.org/lib/decimal-recipes.html
x = F(1)
i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
while abs(s - lasts) > F(1, 10**9):
lasts = s
i += 2
fact *= i * (i - 1)
num *= x * x
sign *= -1
s += num / fact * sign
self.assertAlmostEqual(math.cos(1), s)
def testHash_compare(self):
self.assertEqual(hash(fractions.Fraction(3, 2)), hash(F(3, 2)))
self.assertEqual(hash(fractions.Fraction(1, 2)), hash(F(1, 2)))
self.assertEqual(hash(fractions.Fraction(0, 2)), hash(F(0, 2)))
self.assertEqual(hash(fractions.Fraction(0, 1)), hash(F(0, 1)))
self.assertEqual(hash(fractions.Fraction(10, 1)), hash(F(10, 1)))
self.assertEqual(hash(fractions.Fraction(-1, 1)), hash(F(-1, 1)))
self.assertEqual(hash(fractions.Fraction(-1, 10)), hash(F(-1, 10)))
if sys.version_info >= (2, 7):
self.assertEqual(hash(fractions.Fraction(1.2)), hash(F(1.2)))
self.assertEqual(hash(fractions.Fraction(1.5)), hash(F(1.5)))
def test_copy_deepcopy_pickle(self):
r = F(13, 7)
dr = DummyFraction(13, 7)
self.assertEqual(id(r), id(copy(r)))
self.assertEqual(id(r), id(deepcopy(r)))
self.assertNotEqual(id(dr), id(copy(dr)))
self.assertNotEqual(id(dr), id(deepcopy(dr)))
self.assertTypedEquals(dr, copy(dr))
self.assertTypedEquals(dr, deepcopy(dr))
def test_pi_digits(self):
pi = (
"3.141592653589793238462643383279502884197169399375105820974944592307816406286"
"208998628034825342117067982148086513282306647093844609550582231725359408128481"
"117450284102701938521105559644622948954930381964428810975665933446128475648233"
"786783165271201909145648566923460348610454326648213393607260249141273724587006"
)
for i in range(2, len(pi)):
s = pi[:i]
ff = fractions.Fraction(s)
qf = F(s)
self.assertEqual(ff, qf)
self.assertEqual(ff.numerator, qf.numerator)
self.assertEqual(ff.denominator, qf.denominator)
def testBigFloatComparisons(self):
# Because 10**23 can't be represented exactly as a float:
self.assertFalse(F(10**23) == float(10**23))
# The first test demonstrates why these are important.
self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
def testHash(self):
if sys.version_info >= (3, 2):
hmod = sys.hash_info.modulus
hinf = sys.hash_info.inf
self.assertEqual(hash(2.5), hash(F(5, 2)))
self.assertEqual(hash(10**50), hash(F(10**50)))
self.assertNotEqual(hash(float(10**23)), hash(F(10**23)))
self.assertEqual(hinf, hash(F(1, hmod)))
# Check that __hash__ produces the same value as hash(), for
# consistency with int and Decimal. (See issue #10356.)
self.assertEqual(hash(F(-1)), F(-1).__hash__())
def testComparisons(self):
self.assertTrue(F(1, 2) < F(2, 3))
self.assertFalse(F(1, 2) < F(1, 2))
self.assertTrue(F(1, 2) <= F(2, 3))
self.assertTrue(F(1, 2) <= F(1, 2))
self.assertFalse(F(2, 3) <= F(1, 2))
self.assertTrue(F(1, 2) == F(1, 2))
self.assertFalse(F(1, 2) == F(1, 3))
self.assertFalse(F(1, 2) != F(1, 2))
self.assertTrue(F(1, 2) != F(1, 3))
def testFromString(self):
self.assertEqual((5, 1), _components(F("5")))
self.assertEqual((3, 2), _components(F("3/2")))
self.assertEqual((3, 2), _components(F(" \n +3/2")))
self.assertEqual((-3, 2), _components(F("-3/2 ")))
self.assertEqual((13, 2), _components(F(" 013/02 \n ")))
self.assertEqual((16, 5), _components(F(" 3.2 ")))
self.assertEqual((-16, 5), _components(F(" -3.2 ")))
self.assertEqual((-3, 1), _components(F(" -3. ")))
self.assertEqual((3, 5), _components(F(" .6 ")))
self.assertEqual((-1, 8), _components(F(" -.125 ")))
self.assertEqual((-5, 4), _components(F(" -.125e1 ")))
self.assertEqual((-1, 80), _components(F(" -.125e-1 ")))
self.assertEqual((1, 3125), _components(F("32.e-5")))
self.assertEqual((1000000, 1), _components(F("1E+06")))
self.assertEqual((-12300, 1), _components(F("-1.23e4")))
self.assertEqual((-1, 800), _components(F("-.125e-2")))
self.assertEqual((0, 1), _components(F(" .0e+0\t")))
self.assertEqual((0, 1), _components(F("-0.000e0")))
self.assertEqual((0, 1), _components(F("-.000e0")))
self.assertEqual((123456789, 10000), _components(F(u"۱۲۳۴۵.۶۷۸۹")))
self.assertEqual((123456789, 1000), _components(F(u"۱۲۳۴۵۶۷۸۹E-۳")))
self.assertEqual((123456789, 1), _components(F(u"۱۲۳۴۵۶۷۸۹")))
# Long decimal parts
self.assertEqual((3235321053991263, 50000000000000000000),
_components(F("0.00006470642107982526")))
for i in range(130):
self.assertEqual((3, 10**(i + 1)),
_components(F("0." + "0" * i + "3")))
# Errors in fractions but not quicktions:
self.assertEqual((3, 2), _components(F("3 / 2")))
self.assertEqual((3, 2), _components(F("3 / +2")))
self.assertEqual((-3, 2), _components(F("3 / -2")))
# Errors in both:
self.assertRaisesMessage(ZeroDivisionError, "Fraction(3, 0)", F, "3/0")
self.assertRaisesMessage(ValueError,
"Invalid literal for Fraction: '3/'", F, "3/")
self.assertRaisesMessage(ValueError,
"Invalid literal for Fraction: '/2'", F, "/2")
# self.assertRaisesMessage(
# ValueError, "Invalid literal for Fraction: '3 /2'",
# F, "3 /2")
# self.assertRaisesMessage(
# # Denominators don't need a sign.
# ValueError, "Invalid literal for Fraction: '3/+2'",
# F, "3/+2")
self.assertRaisesMessage(
# Imitate float's parsing.
ValueError,
"Invalid literal for Fraction: '+ 3/2'",
F,
"+ 3/2")
self.assertRaisesMessage(
# Avoid treating '.' as a regex special character.
ValueError,
"Invalid literal for Fraction: '3a2'",
F,
"3a2")
self.assertRaisesMessage(
# Don't accept combinations of decimals and rationals.
ValueError,
"Invalid literal for Fraction: '3/7.2'",
F,
"3/7.2")
self.assertRaisesMessage(
# Don't accept combinations of decimals and rationals.
ValueError,
"Invalid literal for Fraction: '3.2/7'",
F,
"3.2/7")
self.assertRaisesMessage(
# Allow 3. and .3, but not .
ValueError,
"Invalid literal for Fraction: '.'",
F,
".")
def testConversions(self):
self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
self.assertTypedEquals(1, math.trunc(F(11, 10)))
if sys.version_info[0] >= 3:
self.assertTypedEquals(-2, math.floor(F(-11, 10)))
self.assertTypedEquals(-1, math.ceil(F(-11, 10)))
self.assertTypedEquals(-1, math.ceil(F(-10, 10)))
self.assertTypedEquals(-1, int(F(-11, 10)))
if sys.version_info[0] >= 3:
self.assertTypedEquals(0, round(F(-1, 10)))
self.assertTypedEquals(0, round(F(-5, 10)))
self.assertTypedEquals(-2, round(F(-15, 10)))
self.assertTypedEquals(-1, round(F(-7, 10)))
self.assertEqual(False, bool(F(0, 1)))
self.assertEqual(True, bool(F(3, 2)))
self.assertTypedEquals(0.1, float(F(1, 10)))
# Check that __float__ isn't implemented by converting the
# numerator and denominator to float before dividing.
self.assertRaises(OverflowError, float, int('2' * 400 + '7'))
self.assertAlmostEqual(
2.0 / 3, float(F(int('2' * 400 + '7'), int('3' * 400 + '1'))))
self.assertTypedEquals(0.1 + 0j, complex(F(1, 10)))
def testArithmetic(self):
self.assertEqual(F(1, 2), F(1, 10) + F(2, 5))
self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5))
self.assertEqual(F(1, 25), F(1, 10) * F(2, 5))
self.assertEqual(F(1, 4), F(1, 10) / F(2, 5))
self.assertTypedEquals(2, F(9, 10) // F(2, 5))
self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
self.assertEqual(F(5, 6), F(7, 3) % F(3, 2))
self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2))
self.assertEqual((F(1), F(5, 6)), divmod(F(7, 3), F(3, 2)))
self.assertEqual((F(-2), F(2, 3)), divmod(F(-7, 3), F(3, 2)))
self.assertEqual(F(8, 27), F(2, 3)**F(3))
self.assertEqual(F(27, 8), F(2, 3)**F(-3))
self.assertTypedEquals(2.0, F(4)**F(1, 2))
self.assertEqual(F(1, 1), +F(1, 1))
try:
z = pow(F(-1), F(1, 2))
except ValueError:
self.assertEqual(2, sys.version_info[0])
else:
self.assertAlmostEqual(z.real, 0)
self.assertEqual(z.imag, 1)
# Regression test for #27539.
p = F(-1, 2)**0
self.assertEqual(p, F(1, 1))
self.assertEqual(p.numerator, 1)
self.assertEqual(p.denominator, 1)
p = F(-1, 2)**-1
self.assertEqual(p, F(-2, 1))
self.assertEqual(p.numerator, -2)
self.assertEqual(p.denominator, 1)
p = F(-1, 2)**-2
self.assertEqual(p, F(4, 1))
self.assertEqual(p.numerator, 4)
self.assertEqual(p.denominator, 1)
def testLargeArithmetic(self):
self.assertTypedEquals(
F(10101010100808080808080808101010101010000000000000000,
1010101010101010101010101011111111101010101010101010101010101),
F(10**35 + 1, 10**27 + 1) % F(10**27 + 1, 10**35 - 1))
self.assertTypedEquals(F(7, 1901475900342344102245054808064),
F(-2**100, 3) % F(5, 2**100))
self.assertTypedTupleEquals(
(
9999999999999999 << 90 >> 90, # Py2 requires long ...
F(
10101010100808080808080808101010101010000000000000000,
1010101010101010101010101011111111101010101010101010101010101
)),
divmod(F(10**35 + 1, 10**27 + 1), F(10**27 + 1, 10**35 - 1)))
self.assertTypedEquals(-2**200 // 15, F(-2**100, 3) // F(5, 2**100))
self.assertTypedEquals(
1 << 90 >> 90, # Py2 requires long ...
F(5, 2**100) // F(3, 2**100))
self.assertTypedEquals((1, F(2, 2**100)),
divmod(F(5, 2**100), F(3, 2**100)))
self.assertTypedTupleEquals(
(-2**200 // 15, F(7, 1901475900342344102245054808064)),
divmod(F(-2**100, 3), F(5, 2**100)))
def testMixedLessEqual(self):
self.assertTrue(0.5 <= F(1, 2))
self.assertFalse(0.6 <= F(1, 2))
self.assertTrue(F(1, 2) <= 0.5)
self.assertFalse(F(1, 2) <= 0.4)
self.assertTrue(2 <= F(4, 2))
self.assertFalse(2 <= F(3, 2))
self.assertTrue(F(4, 2) <= 2)
self.assertFalse(F(5, 2) <= 2)
self.assertFalse(float('inf') <= F(1, 2))
self.assertTrue(float('-inf') <= F(0, 10))
self.assertFalse(float('nan') <= F(-3, 7))
self.assertTrue(F(1, 2) <= float('inf'))
self.assertFalse(F(17, 12) <= float('-inf'))
self.assertFalse(F(144, -89) <= float('nan'))
def testMixedArithmetic(self):
self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
self.assertTypedEquals(1.1, F(1, 10) + 1.0)
self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
self.assertTypedEquals(1.1, 1.0 + F(1, 10))
self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
self.assertTypedEquals(0.9, 1.0 - F(1, 10))
self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
self.assertTypedEquals(0.1, F(1, 10) * 1.0)
self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
self.assertTypedEquals(0.1, 1.0 * F(1, 10))
self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
self.assertTypedEquals(0.1, F(1, 10) / 1.0)
self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
self.assertTypedEquals(10.0, 1.0 / F(1, 10))
self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
self.assertTypedEquals(0, F(1, 10) // 1)
self.assertTypedEquals(0.0, F(1, 10) // 1.0)
self.assertTypedEquals(10, 1 // F(1, 10))
self.assertTypedEquals(10**23, 10**22 // F(1, 10))
self.assertTypedEquals(1.0 // 0.1, 1.0 // F(1, 10))
self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
self.assertTypedEquals(0.1, F(1, 10) % 1.0)
self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
# self.assertTypedEquals(0.0, 1.0 % F(1, 10))
self.assertTypedEquals(1.0 % 0.1, 1.0 % F(1, 10))
if sys.version_info >= (3, 5):
self.assertTypedEquals(0.1, F(1, 10) % float('inf'))
self.assertTypedEquals(float('-inf'), F(1, 10) % float('-inf'))
self.assertTypedEquals(float('inf'), F(-1, 10) % float('inf'))
self.assertTypedEquals(-0.1, F(-1, 10) % float('-inf'))
self.assertTypedTupleEquals((0, F(1, 10)), divmod(F(1, 10), 1))
self.assertTypedTupleEquals(divmod(0.1, 1.0), divmod(F(1, 10), 1.0))
self.assertTypedTupleEquals((10, F(0)), divmod(1, F(1, 10)))
self.assertTypedTupleEquals(divmod(1.0, 0.1), divmod(1.0, F(1, 10)))
if sys.version_info >= (3, 5):
self.assertTypedTupleEquals(divmod(0.1, float('inf')),
divmod(F(1, 10), float('inf')))
self.assertTypedTupleEquals(divmod(0.1, float('-inf')),
divmod(F(1, 10), float('-inf')))
self.assertTypedTupleEquals(divmod(-0.1, float('inf')),
divmod(F(-1, 10), float('inf')))
self.assertTypedTupleEquals(divmod(-0.1, float('-inf')),
divmod(F(-1, 10), float('-inf')))
# ** has more interesting conversion rules.
self.assertTypedEquals(F(100, 1), F(1, 10)**-2)
self.assertTypedEquals(F(100, 1), F(10, 1)**2)
self.assertTypedEquals(0.1, F(1, 10)**1.0)
self.assertTypedEquals(0.1 + 0j, F(1, 10)**(1.0 + 0j))
self.assertTypedEquals(4, 2**F(2, 1))
try:
z = pow(-1, F(1, 2))
except ValueError:
self.assertEqual(2, sys.version_info[0])
else:
self.assertAlmostEqual(0, z.real)
self.assertEqual(1, z.imag)
self.assertTypedEquals(F(1, 4), 2**F(-2, 1))
self.assertTypedEquals(2.0, 4**F(1, 2))
self.assertTypedEquals(0.25, 2.0**F(-2, 1))
self.assertTypedEquals(1.0 + 0j, (1.0 + 0j)**F(1, 10))
self.assertRaises(ZeroDivisionError, operator.pow, F(0, 1), -2)
def test_slots(self):
# Issue 4998
r = F(13, 7)
self.assertRaises(AttributeError, setattr, r, 'a', 10)
def testMixingWithDecimal(self):
# Decimal refuses mixed arithmetic (but not mixed comparisons)
self.assertRaises(TypeError, operator.add, F(3, 11),
Decimal('3.1415926'))
self.assertRaises(TypeError, operator.add, Decimal('3.1415926'),
F(3, 11))
def testMixedLess(self):
self.assertTrue(2 < F(5, 2))
self.assertFalse(2 < F(4, 2))
self.assertTrue(F(5, 2) < 3)
self.assertFalse(F(4, 2) < 2)
self.assertTrue(F(1, 2) < 0.6)
self.assertFalse(F(1, 2) < 0.4)
self.assertTrue(0.4 < F(1, 2))
self.assertFalse(0.5 < F(1, 2))
self.assertFalse(float('inf') < F(1, 2))
self.assertTrue(float('-inf') < F(0, 10))
self.assertFalse(float('nan') < F(-3, 7))
self.assertTrue(F(1, 2) < float('inf'))
self.assertFalse(F(17, 12) < float('-inf'))
self.assertFalse(F(144, -89) < float('nan'))
def testInit(self):
self.assertEqual((0, 1), _components(F()))
self.assertEqual((7, 1), _components(F(7)))
self.assertEqual((7, 3), _components(F(F(7, 3))))
self.assertEqual((-1, 1), _components(F(-1, 1)))
self.assertEqual((-1, 1), _components(F(1, -1)))
self.assertEqual((1, 1), _components(F(-2, -2)))
self.assertEqual((1, 2), _components(F(5, 10)))
self.assertEqual((7, 15), _components(F(7, 15)))
self.assertEqual((10**23, 1), _components(F(10**23)))
self.assertEqual((3, 77), _components(F(F(3, 7), 11)))
self.assertEqual((-9, 5), _components(F(2, F(-10, 9))))
self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113))))
self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)", F, 12,
0)
self.assertRaises(TypeError, F, 1.5 + 3j)
self.assertRaises(TypeError, F, "3/2", 3)
self.assertRaises(TypeError, F, 3, 0j)
self.assertRaises(TypeError, F, 3, 1j)
self.assertRaises(TypeError, F, 1, 2, 3)