730 lines
30 KiB
Python
730 lines
30 KiB
Python
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"""Tests for Lib/fractions.py."""
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from decimal import Decimal
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from test.support import requires_IEEE_754
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import math
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import numbers
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import operator
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import fractions
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import functools
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import sys
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import unittest
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from copy import copy, deepcopy
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from pickle import dumps, loads
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F = fractions.Fraction
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class DummyFloat(object):
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"""Dummy float class for testing comparisons with Fractions"""
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def __init__(self, value):
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if not isinstance(value, float):
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raise TypeError("DummyFloat can only be initialized from float")
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self.value = value
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def _richcmp(self, other, op):
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if isinstance(other, numbers.Rational):
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return op(F.from_float(self.value), other)
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elif isinstance(other, DummyFloat):
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return op(self.value, other.value)
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else:
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return NotImplemented
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def __eq__(self, other): return self._richcmp(other, operator.eq)
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def __le__(self, other): return self._richcmp(other, operator.le)
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def __lt__(self, other): return self._richcmp(other, operator.lt)
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def __ge__(self, other): return self._richcmp(other, operator.ge)
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def __gt__(self, other): return self._richcmp(other, operator.gt)
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# shouldn't be calling __float__ at all when doing comparisons
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def __float__(self):
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assert False, "__float__ should not be invoked for comparisons"
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# same goes for subtraction
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def __sub__(self, other):
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assert False, "__sub__ should not be invoked for comparisons"
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__rsub__ = __sub__
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class DummyRational(object):
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"""Test comparison of Fraction with a naive rational implementation."""
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def __init__(self, num, den):
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g = math.gcd(num, den)
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self.num = num // g
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self.den = den // g
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def __eq__(self, other):
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if isinstance(other, fractions.Fraction):
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return (self.num == other._numerator and
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self.den == other._denominator)
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else:
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return NotImplemented
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def __lt__(self, other):
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return(self.num * other._denominator < self.den * other._numerator)
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def __gt__(self, other):
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return(self.num * other._denominator > self.den * other._numerator)
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def __le__(self, other):
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return(self.num * other._denominator <= self.den * other._numerator)
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def __ge__(self, other):
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return(self.num * other._denominator >= self.den * other._numerator)
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# this class is for testing comparisons; conversion to float
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# should never be used for a comparison, since it loses accuracy
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def __float__(self):
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assert False, "__float__ should not be invoked"
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class DummyFraction(fractions.Fraction):
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"""Dummy Fraction subclass for copy and deepcopy testing."""
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def _components(r):
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return (r.numerator, r.denominator)
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class FractionTest(unittest.TestCase):
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def assertTypedEquals(self, expected, actual):
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"""Asserts that both the types and values are the same."""
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self.assertEqual(type(expected), type(actual))
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self.assertEqual(expected, actual)
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def assertTypedTupleEquals(self, expected, actual):
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"""Asserts that both the types and values in the tuples are the same."""
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self.assertTupleEqual(expected, actual)
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self.assertListEqual(list(map(type, expected)), list(map(type, actual)))
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def assertRaisesMessage(self, exc_type, message,
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callable, *args, **kwargs):
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"""Asserts that callable(*args, **kwargs) raises exc_type(message)."""
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try:
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callable(*args, **kwargs)
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except exc_type as e:
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self.assertEqual(message, str(e))
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else:
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self.fail("%s not raised" % exc_type.__name__)
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def testInit(self):
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self.assertEqual((0, 1), _components(F()))
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self.assertEqual((7, 1), _components(F(7)))
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self.assertEqual((7, 3), _components(F(F(7, 3))))
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self.assertEqual((-1, 1), _components(F(-1, 1)))
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self.assertEqual((-1, 1), _components(F(1, -1)))
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self.assertEqual((1, 1), _components(F(-2, -2)))
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self.assertEqual((1, 2), _components(F(5, 10)))
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self.assertEqual((7, 15), _components(F(7, 15)))
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self.assertEqual((10**23, 1), _components(F(10**23)))
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self.assertEqual((3, 77), _components(F(F(3, 7), 11)))
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self.assertEqual((-9, 5), _components(F(2, F(-10, 9))))
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self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113))))
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self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
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F, 12, 0)
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self.assertRaises(TypeError, F, 1.5 + 3j)
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self.assertRaises(TypeError, F, "3/2", 3)
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self.assertRaises(TypeError, F, 3, 0j)
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self.assertRaises(TypeError, F, 3, 1j)
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self.assertRaises(TypeError, F, 1, 2, 3)
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@requires_IEEE_754
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def testInitFromFloat(self):
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self.assertEqual((5, 2), _components(F(2.5)))
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self.assertEqual((0, 1), _components(F(-0.0)))
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self.assertEqual((3602879701896397, 36028797018963968),
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_components(F(0.1)))
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# bug 16469: error types should be consistent with float -> int
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self.assertRaises(ValueError, F, float('nan'))
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self.assertRaises(OverflowError, F, float('inf'))
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self.assertRaises(OverflowError, F, float('-inf'))
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def testInitFromDecimal(self):
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self.assertEqual((11, 10),
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_components(F(Decimal('1.1'))))
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self.assertEqual((7, 200),
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_components(F(Decimal('3.5e-2'))))
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self.assertEqual((0, 1),
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_components(F(Decimal('.000e20'))))
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# bug 16469: error types should be consistent with decimal -> int
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self.assertRaises(ValueError, F, Decimal('nan'))
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self.assertRaises(ValueError, F, Decimal('snan'))
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self.assertRaises(OverflowError, F, Decimal('inf'))
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self.assertRaises(OverflowError, F, Decimal('-inf'))
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def testFromString(self):
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self.assertEqual((5, 1), _components(F("5")))
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self.assertEqual((3, 2), _components(F("3/2")))
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self.assertEqual((3, 2), _components(F(" \n +3/2")))
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self.assertEqual((-3, 2), _components(F("-3/2 ")))
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self.assertEqual((13, 2), _components(F(" 013/02 \n ")))
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self.assertEqual((16, 5), _components(F(" 3.2 ")))
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self.assertEqual((-16, 5), _components(F(" -3.2 ")))
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self.assertEqual((-3, 1), _components(F(" -3. ")))
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self.assertEqual((3, 5), _components(F(" .6 ")))
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self.assertEqual((1, 3125), _components(F("32.e-5")))
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self.assertEqual((1000000, 1), _components(F("1E+06")))
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self.assertEqual((-12300, 1), _components(F("-1.23e4")))
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self.assertEqual((0, 1), _components(F(" .0e+0\t")))
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self.assertEqual((0, 1), _components(F("-0.000e0")))
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self.assertRaisesMessage(
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ZeroDivisionError, "Fraction(3, 0)",
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F, "3/0")
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self.assertRaisesMessage(
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ValueError, "Invalid literal for Fraction: '3/'",
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F, "3/")
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self.assertRaisesMessage(
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ValueError, "Invalid literal for Fraction: '/2'",
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F, "/2")
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self.assertRaisesMessage(
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ValueError, "Invalid literal for Fraction: '3 /2'",
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F, "3 /2")
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self.assertRaisesMessage(
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# Denominators don't need a sign.
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ValueError, "Invalid literal for Fraction: '3/+2'",
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F, "3/+2")
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self.assertRaisesMessage(
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# Imitate float's parsing.
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ValueError, "Invalid literal for Fraction: '+ 3/2'",
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F, "+ 3/2")
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self.assertRaisesMessage(
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# Avoid treating '.' as a regex special character.
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ValueError, "Invalid literal for Fraction: '3a2'",
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F, "3a2")
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self.assertRaisesMessage(
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# Don't accept combinations of decimals and rationals.
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ValueError, "Invalid literal for Fraction: '3/7.2'",
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F, "3/7.2")
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self.assertRaisesMessage(
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# Don't accept combinations of decimals and rationals.
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ValueError, "Invalid literal for Fraction: '3.2/7'",
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F, "3.2/7")
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self.assertRaisesMessage(
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# Allow 3. and .3, but not .
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ValueError, "Invalid literal for Fraction: '.'",
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F, ".")
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def testImmutable(self):
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r = F(7, 3)
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r.__init__(2, 15)
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self.assertEqual((7, 3), _components(r))
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self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
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self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
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self.assertEqual((7, 3), _components(r))
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# But if you _really_ need to:
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r._numerator = 4
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r._denominator = 2
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self.assertEqual((4, 2), _components(r))
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# Which breaks some important operations:
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self.assertNotEqual(F(4, 2), r)
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def testFromFloat(self):
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self.assertRaises(TypeError, F.from_float, 3+4j)
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self.assertEqual((10, 1), _components(F.from_float(10)))
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bigint = 1234567890123456789
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self.assertEqual((bigint, 1), _components(F.from_float(bigint)))
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self.assertEqual((0, 1), _components(F.from_float(-0.0)))
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self.assertEqual((10, 1), _components(F.from_float(10.0)))
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self.assertEqual((-5, 2), _components(F.from_float(-2.5)))
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self.assertEqual((99999999999999991611392, 1),
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_components(F.from_float(1e23)))
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self.assertEqual(float(10**23), float(F.from_float(1e23)))
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self.assertEqual((3602879701896397, 1125899906842624),
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_components(F.from_float(3.2)))
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self.assertEqual(3.2, float(F.from_float(3.2)))
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inf = 1e1000
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nan = inf - inf
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# bug 16469: error types should be consistent with float -> int
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self.assertRaisesMessage(
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OverflowError, "cannot convert Infinity to integer ratio",
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F.from_float, inf)
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self.assertRaisesMessage(
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OverflowError, "cannot convert Infinity to integer ratio",
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F.from_float, -inf)
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self.assertRaisesMessage(
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ValueError, "cannot convert NaN to integer ratio",
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F.from_float, nan)
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def testFromDecimal(self):
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self.assertRaises(TypeError, F.from_decimal, 3+4j)
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self.assertEqual(F(10, 1), F.from_decimal(10))
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self.assertEqual(F(0), F.from_decimal(Decimal("-0")))
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self.assertEqual(F(5, 10), F.from_decimal(Decimal("0.5")))
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self.assertEqual(F(5, 1000), F.from_decimal(Decimal("5e-3")))
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self.assertEqual(F(5000), F.from_decimal(Decimal("5e3")))
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self.assertEqual(1 - F(1, 10**30),
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F.from_decimal(Decimal("0." + "9" * 30)))
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# bug 16469: error types should be consistent with decimal -> int
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self.assertRaisesMessage(
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OverflowError, "cannot convert Infinity to integer ratio",
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F.from_decimal, Decimal("inf"))
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self.assertRaisesMessage(
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OverflowError, "cannot convert Infinity to integer ratio",
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F.from_decimal, Decimal("-inf"))
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self.assertRaisesMessage(
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ValueError, "cannot convert NaN to integer ratio",
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F.from_decimal, Decimal("nan"))
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self.assertRaisesMessage(
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ValueError, "cannot convert NaN to integer ratio",
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F.from_decimal, Decimal("snan"))
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def test_as_integer_ratio(self):
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self.assertEqual(F(4, 6).as_integer_ratio(), (2, 3))
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self.assertEqual(F(-4, 6).as_integer_ratio(), (-2, 3))
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self.assertEqual(F(4, -6).as_integer_ratio(), (-2, 3))
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self.assertEqual(F(0, 6).as_integer_ratio(), (0, 1))
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def testLimitDenominator(self):
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rpi = F('3.1415926535897932')
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self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
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self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
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self.assertEqual(rpi.limit_denominator(113), F(355, 113))
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self.assertEqual(rpi.limit_denominator(112), F(333, 106))
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self.assertEqual(F(201, 200).limit_denominator(100), F(1))
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self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
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self.assertEqual(F(0).limit_denominator(10000), F(0))
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for i in (0, -1):
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self.assertRaisesMessage(
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ValueError, "max_denominator should be at least 1",
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F(1).limit_denominator, i)
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def testConversions(self):
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self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
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self.assertTypedEquals(1, math.trunc(F(11, 10)))
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self.assertTypedEquals(-2, math.floor(F(-11, 10)))
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self.assertTypedEquals(-1, math.ceil(F(-11, 10)))
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self.assertTypedEquals(-1, math.ceil(F(-10, 10)))
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self.assertTypedEquals(-1, int(F(-11, 10)))
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self.assertTypedEquals(0, round(F(-1, 10)))
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self.assertTypedEquals(0, round(F(-5, 10)))
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self.assertTypedEquals(-2, round(F(-15, 10)))
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self.assertTypedEquals(-1, round(F(-7, 10)))
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self.assertEqual(False, bool(F(0, 1)))
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self.assertEqual(True, bool(F(3, 2)))
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self.assertTypedEquals(0.1, float(F(1, 10)))
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# Check that __float__ isn't implemented by converting the
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# numerator and denominator to float before dividing.
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self.assertRaises(OverflowError, float, int('2'*400+'7'))
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self.assertAlmostEqual(2.0/3,
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float(F(int('2'*400+'7'), int('3'*400+'1'))))
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self.assertTypedEquals(0.1+0j, complex(F(1,10)))
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def testBoolGuarateesBoolReturn(self):
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# Ensure that __bool__ is used on numerator which guarantees a bool
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# return. See also bpo-39274.
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@functools.total_ordering
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class CustomValue:
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denominator = 1
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def __init__(self, value):
|
||
|
|
self.value = value
|
||
|
|
|
||
|
|
def __bool__(self):
|
||
|
|
return bool(self.value)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def numerator(self):
|
||
|
|
# required to preserve `self` during instantiation
|
||
|
|
return self
|
||
|
|
|
||
|
|
def __eq__(self, other):
|
||
|
|
raise AssertionError("Avoid comparisons in Fraction.__bool__")
|
||
|
|
|
||
|
|
__lt__ = __eq__
|
||
|
|
|
||
|
|
# We did not implement all abstract methods, so register:
|
||
|
|
numbers.Rational.register(CustomValue)
|
||
|
|
|
||
|
|
numerator = CustomValue(1)
|
||
|
|
r = F(numerator)
|
||
|
|
# ensure the numerator was not lost during instantiation:
|
||
|
|
self.assertIs(r.numerator, numerator)
|
||
|
|
self.assertIs(bool(r), True)
|
||
|
|
|
||
|
|
numerator = CustomValue(0)
|
||
|
|
r = F(numerator)
|
||
|
|
self.assertIs(bool(r), False)
|
||
|
|
|
||
|
|
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.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))
|
||
|
|
z = pow(F(-1), F(1, 2))
|
||
|
|
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,
|
||
|
|
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,
|
||
|
|
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 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(1.0 % 0.1, 1.0 % F(1, 10))
|
||
|
|
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)))
|
||
|
|
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))
|
||
|
|
z = pow(-1, F(1, 2))
|
||
|
|
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 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 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.assertRaises(TypeError, operator.gt, F(10**23), complex(10**23))
|
||
|
|
self.assertRaises(TypeError, operator.le, F(10**23), complex(10**23))
|
||
|
|
|
||
|
|
x = F(3, 8)
|
||
|
|
z = complex(0.375, 0.0)
|
||
|
|
w = complex(0.375, 0.2)
|
||
|
|
self.assertTrue(x == z)
|
||
|
|
self.assertFalse(x != z)
|
||
|
|
self.assertFalse(x == w)
|
||
|
|
self.assertTrue(x != w)
|
||
|
|
for op in operator.lt, operator.le, operator.gt, operator.ge:
|
||
|
|
self.assertRaises(TypeError, op, x, z)
|
||
|
|
self.assertRaises(TypeError, op, z, x)
|
||
|
|
self.assertRaises(TypeError, op, x, w)
|
||
|
|
self.assertRaises(TypeError, op, w, x)
|
||
|
|
|
||
|
|
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.assertEqual("Fraction(7, 3)", repr(F(7, 3)))
|
||
|
|
self.assertEqual("Fraction(6283185307, 2000000000)",
|
||
|
|
repr(F('3.1415926535')))
|
||
|
|
self.assertEqual("Fraction(-1, 100000000000000000000)",
|
||
|
|
repr(F(1, -10**20)))
|
||
|
|
self.assertEqual("7/3", str(F(7, 3)))
|
||
|
|
self.assertEqual("7", str(F(7, 1)))
|
||
|
|
|
||
|
|
def testHash(self):
|
||
|
|
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 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 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 test_copy_deepcopy_pickle(self):
|
||
|
|
r = F(13, 7)
|
||
|
|
dr = DummyFraction(13, 7)
|
||
|
|
self.assertEqual(r, loads(dumps(r)))
|
||
|
|
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_slots(self):
|
||
|
|
# Issue 4998
|
||
|
|
r = F(13, 7)
|
||
|
|
self.assertRaises(AttributeError, setattr, r, 'a', 10)
|
||
|
|
|
||
|
|
def test_int_subclass(self):
|
||
|
|
class myint(int):
|
||
|
|
def __mul__(self, other):
|
||
|
|
return type(self)(int(self) * int(other))
|
||
|
|
def __floordiv__(self, other):
|
||
|
|
return type(self)(int(self) // int(other))
|
||
|
|
def __mod__(self, other):
|
||
|
|
x = type(self)(int(self) % int(other))
|
||
|
|
return x
|
||
|
|
@property
|
||
|
|
def numerator(self):
|
||
|
|
return type(self)(int(self))
|
||
|
|
@property
|
||
|
|
def denominator(self):
|
||
|
|
return type(self)(1)
|
||
|
|
|
||
|
|
f = fractions.Fraction(myint(1 * 3), myint(2 * 3))
|
||
|
|
self.assertEqual(f.numerator, 1)
|
||
|
|
self.assertEqual(f.denominator, 2)
|
||
|
|
self.assertEqual(type(f.numerator), myint)
|
||
|
|
self.assertEqual(type(f.denominator), myint)
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
unittest.main()
|