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58a7da9e12
* bpo-26680: Adds support for int.is_integer() for compatibility with float.is_integer(). The int.is_integer() method always returns True. * bpo-26680: Adds a test to ensure that False.is_integer() and True.is_integer() are always True. * bpo-26680: Adds Real.is_integer() with a trivial implementation using conversion to int. This default implementation is intended to reduce the workload for subclass implementers. It is not robust in the presence of infinities or NaNs and may have suboptimal performance for other types. * bpo-26680: Adds Rational.is_integer which returns True if the denominator is one. This implementation assumes the Rational is represented in it's lowest form, as required by the class docstring. * bpo-26680: Adds Integral.is_integer which always returns True. * bpo-26680: Adds tests for Fraction.is_integer called as an instance method. The tests for the Rational abstract base class use an unbound method to sidestep the inability to directly instantiate Rational. These tests check that everything works correct as an instance method. * bpo-26680: Updates documentation for Real.is_integer and built-ins int and float. The call x.is_integer() is now listed in the table of operations which apply to all numeric types except complex, with a reference to the full documentation for Real.is_integer(). Mention of is_integer() has been removed from the section 'Additional Methods on Float'. The documentation for Real.is_integer() describes its purpose, and mentions that it should be overridden for performance reasons, or to handle special values like NaN. * bpo-26680: Adds Decimal.is_integer to the Python and C implementations. The C implementation of Decimal already implements and uses mpd_isinteger internally, we just expose the existing function to Python. The Python implementation uses internal conversion to integer using to_integral_value(). In both cases, the corresponding context methods are also implemented. Tests and documentation are included. * bpo-26680: Updates the ACKS file. * bpo-26680: NEWS entries for int, the numeric ABCs and Decimal. Co-authored-by: Robert Smallshire <rob@sixty-north.com>
740 lines
30 KiB
Python
740 lines
30 KiB
Python
"""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):
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self.value = value
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def __bool__(self):
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return bool(self.value)
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@property
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def numerator(self):
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# required to preserve `self` during instantiation
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return self
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def __eq__(self, other):
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raise AssertionError("Avoid comparisons in Fraction.__bool__")
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__lt__ = __eq__
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# We did not implement all abstract methods, so register:
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numbers.Rational.register(CustomValue)
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numerator = CustomValue(1)
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r = F(numerator)
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# ensure the numerator was not lost during instantiation:
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self.assertIs(r.numerator, numerator)
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self.assertIs(bool(r), True)
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numerator = CustomValue(0)
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r = F(numerator)
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self.assertIs(bool(r), False)
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def testRound(self):
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self.assertTypedEquals(F(-200), round(F(-150), -2))
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self.assertTypedEquals(F(-200), round(F(-250), -2))
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self.assertTypedEquals(F(30), round(F(26), -1))
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self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1))
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self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1))
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def testArithmetic(self):
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self.assertEqual(F(1, 2), F(1, 10) + F(2, 5))
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self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5))
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self.assertEqual(F(1, 25), F(1, 10) * F(2, 5))
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self.assertEqual(F(1, 4), F(1, 10) / F(2, 5))
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self.assertTypedEquals(2, F(9, 10) // F(2, 5))
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self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
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self.assertEqual(F(5, 6), F(7, 3) % F(3, 2))
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self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2))
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self.assertEqual((F(1), F(5, 6)), divmod(F(7, 3), F(3, 2)))
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self.assertEqual((F(-2), F(2, 3)), divmod(F(-7, 3), F(3, 2)))
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self.assertEqual(F(8, 27), F(2, 3) ** F(3))
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self.assertEqual(F(27, 8), F(2, 3) ** F(-3))
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self.assertTypedEquals(2.0, F(4) ** F(1, 2))
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self.assertEqual(F(1, 1), +F(1, 1))
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z = pow(F(-1), F(1, 2))
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self.assertAlmostEqual(z.real, 0)
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self.assertEqual(z.imag, 1)
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# Regression test for #27539.
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p = F(-1, 2) ** 0
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self.assertEqual(p, F(1, 1))
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self.assertEqual(p.numerator, 1)
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self.assertEqual(p.denominator, 1)
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p = F(-1, 2) ** -1
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self.assertEqual(p, F(-2, 1))
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self.assertEqual(p.numerator, -2)
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self.assertEqual(p.denominator, 1)
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p = F(-1, 2) ** -2
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self.assertEqual(p, F(4, 1))
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self.assertEqual(p.numerator, 4)
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self.assertEqual(p.denominator, 1)
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def testLargeArithmetic(self):
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self.assertTypedEquals(
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F(10101010100808080808080808101010101010000000000000000,
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1010101010101010101010101011111111101010101010101010101010101),
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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)
|
|
|
|
def test_is_integer(self):
|
|
# Issue #26680: Incorporating number.is_integer into Fraction
|
|
self.assertTrue(F(-1, 1).is_integer())
|
|
self.assertTrue(F(0, 1).is_integer())
|
|
self.assertTrue(F(1, 1).is_integer())
|
|
self.assertTrue(F(42, 1).is_integer())
|
|
self.assertTrue(F(2, 2).is_integer())
|
|
self.assertTrue(F(8, 4).is_integer())
|
|
self.assertFalse(F(1, 2).is_integer())
|
|
self.assertFalse(F(1, 3).is_integer())
|
|
self.assertFalse(F(2, 3).is_integer())
|
|
|
|
if __name__ == '__main__':
|
|
unittest.main()
|