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cpython/Lib/test/test_fractions.py
Mark Dickinson 8d15643a4b Merged revisions 74078 via svnmerge from 
svn+ssh://pythondev@www.python.org/python/branches/py3k

........
  r74078 | mark.dickinson | 2009-07-18 15:41:42 +0100 (Sat, 18 Jul 2009) | 5 lines

  Issue #6431: Fix Fraction comparisons to return NotImplemented when
  the Fraction type doesn't know how to handle the comparison without
  loss of accuracy.  Also, make sure that comparisons between Fractions
  and float infinities or nans do the right thing.
........
2009-07-18 14:43:10 +00:00

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"""Tests for Lib/fractions.py."""
from decimal import Decimal
from test.support import run_unittest
import math
import numbers
import operator
import fractions
import unittest
from copy import copy, deepcopy
from pickle import dumps, loads
F = fractions.Fraction
gcd = fractions.gcd
class DummyFloat(object):
"""Dummy float class for testing comparisons with Fractions"""
def __init__(self, value):
if not isinstance(value, float):
raise TypeError("DummyFloat can only be initialized from float")
self.value = value
def _richcmp(self, other, op):
if isinstance(other, numbers.Rational):
return op(F.from_float(self.value), other)
elif isinstance(other, DummyFloat):
return op(self.value, other.value)
else:
return NotImplemented
def __eq__(self, other): return self._richcmp(other, operator.eq)
def __le__(self, other): return self._richcmp(other, operator.le)
def __lt__(self, other): return self._richcmp(other, operator.lt)
def __ge__(self, other): return self._richcmp(other, operator.ge)
def __gt__(self, other): return self._richcmp(other, operator.gt)
# shouldn't be calling __float__ at all when doing comparisons
def __float__(self):
assert False, "__float__ should not be invoked for comparisons"
# same goes for subtraction
def __sub__(self, other):
assert False, "__sub__ should not be invoked for comparisons"
__rsub__ = __sub__
class DummyRational(object):
"""Test comparison of Fraction with a naive rational implementation."""
def __init__(self, num, den):
g = gcd(num, den)
self.num = num // g
self.den = den // g
def __eq__(self, other):
if isinstance(other, fractions.Fraction):
return (self.num == other._numerator and
self.den == other._denominator)
else:
return NotImplemented
def __lt__(self, other):
return(self.num * other._denominator < self.den * other._numerator)
def __gt__(self, other):
return(self.num * other._denominator > self.den * other._numerator)
def __le__(self, other):
return(self.num * other._denominator <= self.den * other._numerator)
def __ge__(self, other):
return(self.num * other._denominator >= self.den * other._numerator)
# this class is for testing comparisons; conversion to float
# should never be used for a comparison, since it loses accuracy
def __float__(self):
assert False, "__float__ should not be invoked"
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 testComparisonsDummyRational(self):
self.assertTrue(F(1, 2) == DummyRational(1, 2))
self.assertTrue(DummyRational(1, 2) == F(1, 2))
self.assertFalse(F(1, 2) == DummyRational(3, 4))
self.assertFalse(DummyRational(3, 4) == F(1, 2))
self.assertTrue(F(1, 2) < DummyRational(3, 4))
self.assertFalse(F(1, 2) < DummyRational(1, 2))
self.assertFalse(F(1, 2) < DummyRational(1, 7))
self.assertFalse(F(1, 2) > DummyRational(3, 4))
self.assertFalse(F(1, 2) > DummyRational(1, 2))
self.assertTrue(F(1, 2) > DummyRational(1, 7))
self.assertTrue(F(1, 2) <= DummyRational(3, 4))
self.assertTrue(F(1, 2) <= DummyRational(1, 2))
self.assertFalse(F(1, 2) <= DummyRational(1, 7))
self.assertFalse(F(1, 2) >= DummyRational(3, 4))
self.assertTrue(F(1, 2) >= DummyRational(1, 2))
self.assertTrue(F(1, 2) >= DummyRational(1, 7))
self.assertTrue(DummyRational(1, 2) < F(3, 4))
self.assertFalse(DummyRational(1, 2) < F(1, 2))
self.assertFalse(DummyRational(1, 2) < F(1, 7))
self.assertFalse(DummyRational(1, 2) > F(3, 4))
self.assertFalse(DummyRational(1, 2) > F(1, 2))
self.assertTrue(DummyRational(1, 2) > F(1, 7))
self.assertTrue(DummyRational(1, 2) <= F(3, 4))
self.assertTrue(DummyRational(1, 2) <= F(1, 2))
self.assertFalse(DummyRational(1, 2) <= F(1, 7))
self.assertFalse(DummyRational(1, 2) >= F(3, 4))
self.assertTrue(DummyRational(1, 2) >= F(1, 2))
self.assertTrue(DummyRational(1, 2) >= F(1, 7))
def testComparisonsDummyFloat(self):
x = DummyFloat(1./3.)
y = F(1, 3)
self.assertTrue(x != y)
self.assertTrue(x < y or x > y)
self.assertFalse(x == y)
self.assertFalse(x <= y and x >= y)
self.assertTrue(y != x)
self.assertTrue(y < x or y > x)
self.assertFalse(y == x)
self.assertFalse(y <= x and y >= x)
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 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 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)
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 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()
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