Staging
v0.5.1
v0.5.1
https://github.com/python/cpython
Tip revision: 1da43e5e916949c8e849e656d9d05fa4b9d6836c authored by Benjamin Peterson on 26 June 2009, 13:21:52 UTC
rearrange the sections of the README, so they'll hopefully be more in the order people will interested in
rearrange the sections of the README, so they'll hopefully be more in the order people will interested in
Tip revision: 1da43e5
test_fractions.py
"""Tests for Lib/fractions.py."""
from decimal import Decimal
from test.support import run_unittest
import math
import operator
import fractions
import unittest
from copy import copy, deepcopy
from pickle import dumps, loads
F = fractions.Fraction
gcd = fractions.gcd
class GcdTest(unittest.TestCase):
def testMisc(self):
self.assertEquals(0, gcd(0, 0))
self.assertEquals(1, gcd(1, 0))
self.assertEquals(-1, gcd(-1, 0))
self.assertEquals(1, gcd(0, 1))
self.assertEquals(-1, gcd(0, -1))
self.assertEquals(1, gcd(7, 1))
self.assertEquals(-1, gcd(7, -1))
self.assertEquals(1, gcd(-23, 15))
self.assertEquals(12, gcd(120, 84))
self.assertEquals(-12, gcd(84, -120))
def _components(r):
return (r.numerator, r.denominator)
class FractionTest(unittest.TestCase):
def assertTypedEquals(self, expected, actual):
"""Asserts that both the types and values are the same."""
self.assertEquals(type(expected), type(actual))
self.assertEquals(expected, actual)
def assertRaisesMessage(self, exc_type, message,
callable, *args, **kwargs):
"""Asserts that callable(*args, **kwargs) raises exc_type(message)."""
try:
callable(*args, **kwargs)
except exc_type as e:
self.assertEquals(message, str(e))
else:
self.fail("%s not raised" % exc_type.__name__)
def testInit(self):
self.assertEquals((0, 1), _components(F()))
self.assertEquals((7, 1), _components(F(7)))
self.assertEquals((7, 3), _components(F(F(7, 3))))
self.assertEquals((-1, 1), _components(F(-1, 1)))
self.assertEquals((-1, 1), _components(F(1, -1)))
self.assertEquals((1, 1), _components(F(-2, -2)))
self.assertEquals((1, 2), _components(F(5, 10)))
self.assertEquals((7, 15), _components(F(7, 15)))
self.assertEquals((10**23, 1), _components(F(10**23)))
self.assertEquals((3, 77), _components(F(F(3, 7), 11)))
self.assertEquals((-9, 5), _components(F(2, F(-10, 9))))
self.assertEquals((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)
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)
def testFromString(self):
self.assertEquals((5, 1), _components(F("5")))
self.assertEquals((3, 2), _components(F("3/2")))
self.assertEquals((3, 2), _components(F(" \n +3/2")))
self.assertEquals((-3, 2), _components(F("-3/2 ")))
self.assertEquals((13, 2), _components(F(" 013/02 \n ")))
self.assertEquals((16, 5), _components(F(" 3.2 ")))
self.assertEquals((-16, 5), _components(F(" -3.2 ")))
self.assertEquals((-3, 1), _components(F(" -3. ")))
self.assertEquals((3, 5), _components(F(" .6 ")))
self.assertEquals((1, 3125), _components(F("32.e-5")))
self.assertEquals((1000000, 1), _components(F("1E+06")))
self.assertEquals((-12300, 1), _components(F("-1.23e4")))
self.assertEquals((0, 1), _components(F(" .0e+0\t")))
self.assertEquals((0, 1), _components(F("-0.000e0")))
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 testImmutable(self):
r = F(7, 3)
r.__init__(2, 15)
self.assertEquals((7, 3), _components(r))
self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
self.assertEquals((7, 3), _components(r))
# But if you _really_ need to:
r._numerator = 4
r._denominator = 2
self.assertEquals((4, 2), _components(r))
# Which breaks some important operations:
self.assertNotEquals(F(4, 2), r)
def testFromFloat(self):
self.assertRaises(TypeError, F.from_float, 3+4j)
self.assertEquals((10, 1), _components(F.from_float(10)))
bigint = 1234567890123456789
self.assertEquals((bigint, 1), _components(F.from_float(bigint)))
self.assertEquals((0, 1), _components(F.from_float(-0.0)))
self.assertEquals((10, 1), _components(F.from_float(10.0)))
self.assertEquals((-5, 2), _components(F.from_float(-2.5)))
self.assertEquals((99999999999999991611392, 1),
_components(F.from_float(1e23)))
self.assertEquals(float(10**23), float(F.from_float(1e23)))
self.assertEquals((3602879701896397, 1125899906842624),
_components(F.from_float(3.2)))
self.assertEquals(3.2, float(F.from_float(3.2)))
inf = 1e1000
nan = inf - inf
self.assertRaisesMessage(
TypeError, "Cannot convert inf to Fraction.",
F.from_float, inf)
self.assertRaisesMessage(
TypeError, "Cannot convert -inf to Fraction.",
F.from_float, -inf)
self.assertRaisesMessage(
TypeError, "Cannot convert nan to Fraction.",
F.from_float, nan)
def testFromDecimal(self):
self.assertRaises(TypeError, F.from_decimal, 3+4j)
self.assertEquals(F(10, 1), F.from_decimal(10))
self.assertEquals(F(0), F.from_decimal(Decimal("-0")))
self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5")))
self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3")))
self.assertEquals(F(5000), F.from_decimal(Decimal("5e3")))
self.assertEquals(1 - F(1, 10**30),
F.from_decimal(Decimal("0." + "9" * 30)))
self.assertRaisesMessage(
TypeError, "Cannot convert Infinity to Fraction.",
F.from_decimal, Decimal("inf"))
self.assertRaisesMessage(
TypeError, "Cannot convert -Infinity to Fraction.",
F.from_decimal, Decimal("-inf"))
self.assertRaisesMessage(
TypeError, "Cannot convert NaN to Fraction.",
F.from_decimal, Decimal("nan"))
self.assertRaisesMessage(
TypeError, "Cannot convert sNaN to Fraction.",
F.from_decimal, Decimal("snan"))
def testLimitDenominator(self):
rpi = F('3.1415926535897932')
self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
self.assertEqual(rpi.limit_denominator(113), F(355, 113))
self.assertEqual(rpi.limit_denominator(112), F(333, 106))
self.assertEqual(F(201, 200).limit_denominator(100), F(1))
self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
self.assertEqual(F(0).limit_denominator(10000), F(0))
def testConversions(self):
self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
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)))
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.assertEquals(False, bool(F(0, 1)))
self.assertEquals(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.assertAlmostEquals(2.0/3,
float(F(int('2'*400+'7'), int('3'*400+'1'))))
self.assertTypedEquals(0.1+0j, complex(F(1,10)))
def testRound(self):
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 testArithmetic(self):
self.assertEquals(F(1, 2), F(1, 10) + F(2, 5))
self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5))
self.assertEquals(F(1, 25), F(1, 10) * F(2, 5))
self.assertEquals(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.assertEquals(F(2, 3), F(-7, 3) % F(3, 2))
self.assertEquals(F(8, 27), F(2, 3) ** F(3))
self.assertEquals(F(27, 8), F(2, 3) ** F(-3))
self.assertTypedEquals(2.0, F(4) ** F(1, 2))
z = pow(F(-1), F(1, 2))
self.assertAlmostEquals(z.real, 0)
self.assertEquals(z.imag, 1)
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, F(1, 10) // 1.0)
self.assertTypedEquals(10, 1 // F(1, 10))
self.assertTypedEquals(10**23, 10**22 // F(1, 10))
self.assertTypedEquals(10, 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))
# No need for divmod since we don't override it.
# ** 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))
z = pow(-1, F(1, 2))
self.assertAlmostEquals(0, z.real)
self.assertEquals(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))
def testMixingWithDecimal(self):
# Decimal refuses mixed comparisons.
self.assertRaisesMessage(
TypeError,
"unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
operator.add, F(3,11), Decimal('3.1415926'))
self.assertNotEquals(F(5, 2), Decimal('2.5'))
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 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))
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)
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 testBigComplexComparisons(self):
self.assertFalse(F(10**23) == complex(10**23))
self.assertTrue(F(10**23) > complex(10**23))
self.assertFalse(F(10**23) <= complex(10**23))
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)
def testStringification(self):
self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))
self.assertEquals("Fraction(6283185307, 2000000000)",
repr(F('3.1415926535')))
self.assertEquals("Fraction(-1, 100000000000000000000)",
repr(F(1, -10**20)))
self.assertEquals("7/3", str(F(7, 3)))
self.assertEquals("7", str(F(7, 1)))
def testHash(self):
self.assertEquals(hash(2.5), hash(F(5, 2)))
self.assertEquals(hash(10**50), hash(F(10**50)))
self.assertNotEquals(hash(float(10**23)), hash(F(10**23)))
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.assertAlmostEquals(math.pi, s)
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.assertAlmostEquals(math.cos(1), s)
def test_copy_deepcopy_pickle(self):
r = F(13, 7)
self.assertEqual(r, loads(dumps(r)))
self.assertEqual(id(r), id(copy(r)))
self.assertEqual(id(r), id(deepcopy(r)))
def test_slots(self):
# Issue 4998
r = F(13, 7)
self.assertRaises(AttributeError, setattr, r, 'a', 10)
def test_main():
run_unittest(FractionTest, GcdTest)
if __name__ == '__main__':
test_main()