test_fractions.py

# coding: utf8

# Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
# 2011, 2012, 2013, 2014 Python Software Foundation; All Rights Reserved
#
# Based on the "test/test_fractions" module in CPython 3.4.
# https://hg.python.org/cpython/file/b18288f24501/Lib/test/test_fractions.py

"""Tests for Lib/fractions.py, slightly adapted for quicktions."""

from __future__ import division

import os
from decimal import Decimal
import math
import numbers
import operator
import fractions
import sys
import unittest
from copy import copy, deepcopy
from pickle import dumps, loads

import quicktions
F = quicktions.Fraction
gcd = quicktions._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)
        elif isinstance(other, quicktions.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 DummyFraction(fractions.Fraction):
    """Dummy Fraction subclass for copy and deepcopy testing."""


class GcdTest(unittest.TestCase):

    def testMisc(self):
        self.assertEqual(0, gcd(0, 0))
        self.assertEqual(1, gcd(1, 0))
        self.assertEqual(1, gcd(-1, 0))
        self.assertEqual(1, gcd(0, 1))
        self.assertEqual(1, gcd(0, -1))
        self.assertEqual(1, gcd(7, 1))
        self.assertEqual(1, gcd(7, -1))
        self.assertEqual(1, gcd(-23, 15))
        self.assertEqual(12, gcd(120, 84))
        self.assertEqual(12, gcd(84, -120))
        self.assertEqual(652560,
                         gcd(190738355881570558882299312308821696901058000,
                             76478560266291874249006856460326062498333440))
        self.assertEqual(
            286573572687563623189610484223662247799,
            gcd(83763289342793979220453055528167457860243376086879213707165435635135627040075,
                33585776402955145260404154387726204875807368546078094789530226423049489520976))

    def test_quicktions_limits(self):
        # specifially for quicktions:
        special_values = [
            -2**32-1, -2**64-1, -2**128-1,
            -2**32, -2**64, -2**128,
            -2**32+1, -2**64+1, -2**128+1,
            -2**31-1, -2**63-1, -2**127-1,
            -2**31, -2**63, -2**127,
            -2**31+1, -2**63+1, -2**127+1,
            2**31, 2**63, 2**127,
            2**31+1, 2**63+1, 2**127+1,
            2**32-1, 2**64-1, 2**128-1,
            2**32, 2**64, 2**128,
            2**32+1, 2**64+1, 2**128+1,
            ]
        special = None
        try:
            for special in special_values:
                self.assertEqual(1, gcd(special, 1))
                self.assertEqual(1, gcd(1, special))
                self.assertEqual(abs(special), gcd(special, special))
                self.assertEqual(abs(special), gcd(special, special*3))
                self.assertEqual(abs(special), gcd(special*3, special))

                special *= 5
                self.assertEqual(1, gcd(special, 1))
                self.assertEqual(1, gcd(1, special))
                self.assertEqual(5, gcd(special, 5))
                self.assertEqual(5, gcd(5, special))
                self.assertEqual(5 if special % 25 else 25, gcd(special, 125))
                self.assertEqual(5 if special % 25 else 25, gcd(125, special))
        except AssertionError as e:
            assert len(e.args) == 1
            e.args = ('[%s] %s' % (special, e),)
            raise


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.assertEqual(type(expected), type(actual))
        self.assertEqual(expected, actual)

    def assertTypedTupleEquals(self, expected, actual):
        """Asserts that both the types and values in the tuples are the same."""
        self.assertEqual(tuple, type(actual))
        self.assertEqual(list(map(type, expected)), list(map(type, actual)))
        self.assertEqual(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.assertEqual(message, str(e))
        else:
            self.fail("%s not raised" % exc_type.__name__)

    def testInit(self):
        self.assertEqual((0, 1), _components(F()))
        self.assertEqual((7, 1), _components(F(7)))
        self.assertEqual((7, 3), _components(F(F(7, 3))))

        self.assertEqual((-1, 1), _components(F(-1, 1)))
        self.assertEqual((-1, 1), _components(F(1, -1)))
        self.assertEqual((1, 1), _components(F(-2, -2)))
        self.assertEqual((1, 2), _components(F(5, 10)))
        self.assertEqual((7, 15), _components(F(7, 15)))
        self.assertEqual((10**23, 1), _components(F(10**23)))

        self.assertEqual((3, 77), _components(F(F(3, 7), 11)))
        self.assertEqual((-9, 5), _components(F(2, F(-10, 9))))
        self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113))))

        self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
                                 F, 12, 0)
        self.assertRaises(TypeError, F, 1.5 + 3j)

        self.assertRaises(TypeError, F, "3/2", 3)
        self.assertRaises(TypeError, F, 3, 0j)
        self.assertRaises(TypeError, F, 3, 1j)
        self.assertRaises(TypeError, F, 1, 2, 3)

    def testInitFromFloat(self):
        self.assertEqual((5, 2), _components(F(2.5)))
        self.assertEqual((0, 1), _components(F(-0.0)))
        self.assertEqual((3602879701896397, 36028797018963968),
                         _components(F(0.1)))
        # bug 16469: error types should be consistent with float -> int
        self.assertRaises(ValueError, F, float('nan'))
        self.assertRaises(OverflowError, F, float('inf'))
        self.assertRaises(OverflowError, F, float('-inf'))

    def testInitFromDecimal(self):
        self.assertEqual((11, 10),
                         _components(F(Decimal('1.1'))))
        self.assertEqual((7, 200),
                         _components(F(Decimal('3.5e-2'))))
        self.assertEqual((0, 1),
                         _components(F(Decimal('.000e20'))))
        # bug 16469: error types should be consistent with decimal -> int
        self.assertRaises(ValueError, F, Decimal('nan'))
        self.assertRaises(ValueError, F, Decimal('snan'))
        self.assertRaises(OverflowError, F, Decimal('inf'))
        self.assertRaises(OverflowError, F, Decimal('-inf'))

    def testFromString(self):
        self.assertEqual((5, 1), _components(F("5")))
        self.assertEqual((3, 2), _components(F("3/2")))
        self.assertEqual((3, 2), _components(F(" \n  +3/2")))
        self.assertEqual((-3, 2), _components(F("-3/2  ")))
        self.assertEqual((13, 2), _components(F("    013/02 \n  ")))
        self.assertEqual((16, 5), _components(F(" 3.2 ")))
        self.assertEqual((-16, 5), _components(F(" -3.2 ")))
        self.assertEqual((-3, 1), _components(F(" -3. ")))
        self.assertEqual((3, 5), _components(F(" .6 ")))
        self.assertEqual((-1, 8), _components(F(" -.125 ")))
        self.assertEqual((-5, 4), _components(F(" -.125e1 ")))
        self.assertEqual((-1, 80), _components(F(" -.125e-1 ")))
        self.assertEqual((1, 3125), _components(F("32.e-5")))
        self.assertEqual((1000000, 1), _components(F("1E+06")))
        self.assertEqual((-12300, 1), _components(F("-1.23e4")))
        self.assertEqual((-1, 800), _components(F("-.125e-2")))
        self.assertEqual((0, 1), _components(F(" .0e+0\t")))
        self.assertEqual((0, 1), _components(F("-0.000e0")))
        self.assertEqual((0, 1), _components(F("-.000e0")))
        self.assertEqual((123456789, 10000), _components(F(u"۱۲۳۴۵.۶۷۸۹")))
        self.assertEqual((123456789, 1000), _components(F(u"۱۲۳۴۵۶۷۸۹E-۳")))
        self.assertEqual((123456789, 1), _components(F(u"۱۲۳۴۵۶۷۸۹")))

        # Errors in fractions but not quicktions:
        self.assertEqual((3, 2), _components(F("3 / 2")))
        self.assertEqual((3, 2), _components(F("3 / +2")))
        self.assertEqual((-3, 2), _components(F("3 / -2")))

        # Errors in both:
        self.assertRaisesMessage(
            ZeroDivisionError, "Fraction(3, 0)",
            F, "3/0")
        self.assertRaisesMessage(
            ValueError, "Invalid literal for Fraction: '3/'",
            F, "3/")
        self.assertRaisesMessage(
            ValueError, "Invalid literal for Fraction: '/2'",
            F, "/2")
#        self.assertRaisesMessage(
#            ValueError, "Invalid literal for Fraction: '3 /2'",
#            F, "3 /2")
#        self.assertRaisesMessage(
#            # Denominators don't need a sign.
#            ValueError, "Invalid literal for Fraction: '3/+2'",
#            F, "3/+2")
        self.assertRaisesMessage(
            # Imitate float's parsing.
            ValueError, "Invalid literal for Fraction: '+ 3/2'",
            F, "+ 3/2")
        self.assertRaisesMessage(
            # Avoid treating '.' as a regex special character.
            ValueError, "Invalid literal for Fraction: '3a2'",
            F, "3a2")
        self.assertRaisesMessage(
            # Don't accept combinations of decimals and rationals.
            ValueError, "Invalid literal for Fraction: '3/7.2'",
            F, "3/7.2")
        self.assertRaisesMessage(
            # Don't accept combinations of decimals and rationals.
            ValueError, "Invalid literal for Fraction: '3.2/7'",
            F, "3.2/7")
        self.assertRaisesMessage(
            # Allow 3. and .3, but not .
            ValueError, "Invalid literal for Fraction: '.'",
            F, ".")

    def testImmutable(self):
        r = F(7, 3)
        r.__init__(2, 15)
        self.assertEqual((7, 3), _components(r))

        self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
        self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
        self.assertEqual((7, 3), _components(r))

        self.assertEqual(0, r.imag)
        self.assertRaises(AttributeError, setattr, r, 'imag', 12)
        self.assertEqual(0, r.imag)

        '''
        # But if you _really_ need to:
        r._numerator = 4
        r._denominator = 2
        self.assertEqual((4, 2), _components(r))
        # Which breaks some important operations:
        self.assertNotEqual(F(4, 2), r)
        '''

    def testFromFloat(self):
        self.assertRaises(TypeError, F.from_float, 3+4j)
        self.assertEqual((10, 1), _components(F.from_float(10)))
        bigint = 1234567890123456789
        self.assertEqual((bigint, 1), _components(F.from_float(bigint)))
        self.assertEqual((0, 1), _components(F.from_float(-0.0)))
        self.assertEqual((10, 1), _components(F.from_float(10.0)))
        self.assertEqual((-5, 2), _components(F.from_float(-2.5)))
        self.assertEqual((99999999999999991611392, 1),
                         _components(F.from_float(1e23)))
        self.assertEqual(float(10**23), float(F.from_float(1e23)))
        self.assertEqual((3602879701896397, 1125899906842624),
                         _components(F.from_float(3.2)))
        self.assertEqual(3.2, float(F.from_float(3.2)))

        inf = 1e1000
        nan = inf - inf
        # bug 16469: error types should be consistent with float -> int
        self.assertRaisesMessage(
            OverflowError, "Cannot convert inf to Fraction.",
            F.from_float, inf)
        self.assertRaisesMessage(
            OverflowError, "Cannot convert -inf to Fraction.",
            F.from_float, -inf)
        self.assertRaisesMessage(
            ValueError, "Cannot convert nan to Fraction.",
            F.from_float, nan)

    def testFromDecimal(self):
        self.assertRaises(TypeError, F.from_decimal, 3+4j)
        self.assertEqual(F(10, 1), F.from_decimal(10))
        self.assertEqual(F(0), F.from_decimal(Decimal("-0")))
        self.assertEqual(F(5, 10), F.from_decimal(Decimal("0.5")))
        self.assertEqual(F(5, 1000), F.from_decimal(Decimal("5e-3")))
        self.assertEqual(F(5000), F.from_decimal(Decimal("5e3")))
        self.assertEqual(1 - F(1, 10**30),
                         F.from_decimal(Decimal("0." + "9" * 30)))

        # bug 16469: error types should be consistent with decimal -> int
        self.assertRaisesMessage(
            OverflowError, "Cannot convert Infinity to Fraction.",
            F.from_decimal, Decimal("inf"))
        self.assertRaisesMessage(
            OverflowError, "Cannot convert -Infinity to Fraction.",
            F.from_decimal, Decimal("-inf"))
        self.assertRaisesMessage(
            ValueError, "Cannot convert NaN to Fraction.",
            F.from_decimal, Decimal("nan"))
        self.assertRaisesMessage(
            ValueError, "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))
        for i in (0, -1):
            self.assertRaisesMessage(
                ValueError, "max_denominator should be at least 1",
                F(1).limit_denominator, i)

    def testConversions(self):
        self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
        self.assertTypedEquals(1, math.trunc(F(11, 10)))
        if sys.version_info[0] >= 3:
            self.assertTypedEquals(-2, math.floor(F(-11, 10)))
            self.assertTypedEquals(-1, math.ceil(F(-11, 10)))
            self.assertTypedEquals(-1, math.ceil(F(-10, 10)))
        self.assertTypedEquals(-1, int(F(-11, 10)))
        if sys.version_info[0] >= 3:
            self.assertTypedEquals(0, round(F(-1, 10)))
            self.assertTypedEquals(0, round(F(-5, 10)))
            self.assertTypedEquals(-2, round(F(-15, 10)))
            self.assertTypedEquals(-1, round(F(-7, 10)))

        self.assertEqual(False, bool(F(0, 1)))
        self.assertEqual(True, bool(F(3, 2)))
        self.assertTypedEquals(0.1, float(F(1, 10)))

        # Check that __float__ isn't implemented by converting the
        # numerator and denominator to float before dividing.
        self.assertRaises(OverflowError, float, int('2'*400+'7'))
        self.assertAlmostEqual(2.0/3,
                               float(F(int('2'*400+'7'), int('3'*400+'1'))))

        self.assertTypedEquals(0.1+0j, complex(F(1,10)))

    def testRound(self):
        if sys.version_info[0] >= 3:
            self.assertTypedEquals(F(-200), round(F(-150), -2))
            self.assertTypedEquals(F(-200), round(F(-250), -2))
            self.assertTypedEquals(F(30), round(F(26), -1))
            self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1))
            self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1))

    def testArithmetic(self):
        self.assertEqual(F(1, 2), F(1, 10) + F(2, 5))
        self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5))
        self.assertEqual(F(1, 25), F(1, 10) * F(2, 5))
        self.assertEqual(F(1, 4), F(1, 10) / F(2, 5))
        self.assertTypedEquals(2, F(9, 10) // F(2, 5))
        self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
        self.assertEqual(F(5, 6), F(7, 3) % F(3, 2))
        self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2))
        self.assertEqual((F(1), F(5, 6)), divmod(F(7, 3), F(3, 2)))
        self.assertEqual((F(-2), F(2, 3)), divmod(F(-7, 3), F(3, 2)))
        self.assertEqual(F(8, 27), F(2, 3) ** F(3))
        self.assertEqual(F(27, 8), F(2, 3) ** F(-3))
        self.assertTypedEquals(2.0, F(4) ** F(1, 2))
        self.assertEqual(F(1, 1), +F(1, 1))
        try:
            z = pow(F(-1), F(1, 2))
        except ValueError:
            self.assertEqual(2, sys.version_info[0])
        else:
            self.assertAlmostEqual(z.real, 0)
            self.assertEqual(z.imag, 1)

        # Regression test for #27539.
        p = F(-1, 2) ** 0
        self.assertEqual(p, F(1, 1))
        self.assertEqual(p.numerator, 1)
        self.assertEqual(p.denominator, 1)
        p = F(-1, 2) ** -1
        self.assertEqual(p, F(-2, 1))
        self.assertEqual(p.numerator, -2)
        self.assertEqual(p.denominator, 1)
        p = F(-1, 2) ** -2
        self.assertEqual(p, F(4, 1))
        self.assertEqual(p.numerator, 4)
        self.assertEqual(p.denominator, 1)

    def testLargeArithmetic(self):
        self.assertTypedEquals(
            F(10101010100808080808080808101010101010000000000000000,
              1010101010101010101010101011111111101010101010101010101010101),
            F(10**35+1, 10**27+1) % F(10**27+1, 10**35-1)
        )
        self.assertTypedEquals(
            F(7, 1901475900342344102245054808064),
            F(-2**100, 3) % F(5, 2**100)
        )
        self.assertTypedTupleEquals(
            (9999999999999999 << 90 >> 90,  # Py2 requires long ...
             F(10101010100808080808080808101010101010000000000000000,
               1010101010101010101010101011111111101010101010101010101010101)),
            divmod(F(10**35+1, 10**27+1), F(10**27+1, 10**35-1))
        )
        self.assertTypedEquals(
            -2 ** 200 // 15,
            F(-2**100, 3) // F(5, 2**100)
        )
        self.assertTypedEquals(
            1 << 90 >> 90,  # Py2 requires long ...
            F(5, 2**100) // F(3, 2**100)
        )
        self.assertTypedEquals(
            (1, F(2, 2**100)),
            divmod(F(5, 2**100), F(3, 2**100))
        )
        self.assertTypedTupleEquals(
            (-2 ** 200 // 15,
             F(7, 1901475900342344102245054808064)),
            divmod(F(-2**100, 3), F(5, 2**100))
        )

    def testMixedArithmetic(self):
        self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
        self.assertTypedEquals(1.1, F(1, 10) + 1.0)
        self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
        self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
        self.assertTypedEquals(1.1, 1.0 + F(1, 10))
        self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))

        self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
        self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
        self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
        self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
        self.assertTypedEquals(0.9, 1.0 - F(1, 10))
        self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))

        self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
        self.assertTypedEquals(0.1, F(1, 10) * 1.0)
        self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
        self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
        self.assertTypedEquals(0.1, 1.0 * F(1, 10))
        self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))

        self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
        self.assertTypedEquals(0.1, F(1, 10) / 1.0)
        self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
        self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
        self.assertTypedEquals(10.0, 1.0 / F(1, 10))
        self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))

        self.assertTypedEquals(0, F(1, 10) // 1)
        self.assertTypedEquals(0.0, F(1, 10) // 1.0)
        self.assertTypedEquals(10, 1 // F(1, 10))
        self.assertTypedEquals(10**23, 10**22 // F(1, 10))
        self.assertTypedEquals(1.0 // 0.1, 1.0 // F(1, 10))

        self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
        self.assertTypedEquals(0.1, F(1, 10) % 1.0)
        self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
        #self.assertTypedEquals(0.0, 1.0 % F(1, 10))
        self.assertTypedEquals(1.0 % 0.1, 1.0 % F(1, 10))
        if sys.version_info >= (3, 5):
            self.assertTypedEquals(0.1, F(1, 10) % float('inf'))
            self.assertTypedEquals(float('-inf'), F(1, 10) % float('-inf'))
            self.assertTypedEquals(float('inf'), F(-1, 10) % float('inf'))
            self.assertTypedEquals(-0.1, F(-1, 10) % float('-inf'))

        self.assertTypedTupleEquals((0, F(1, 10)), divmod(F(1, 10), 1))
        self.assertTypedTupleEquals(divmod(0.1, 1.0), divmod(F(1, 10), 1.0))
        self.assertTypedTupleEquals((10, F(0)), divmod(1, F(1, 10)))
        self.assertTypedTupleEquals(divmod(1.0, 0.1), divmod(1.0, F(1, 10)))
        if sys.version_info >= (3, 5):
            self.assertTypedTupleEquals(divmod(0.1, float('inf')), divmod(F(1, 10), float('inf')))
            self.assertTypedTupleEquals(divmod(0.1, float('-inf')), divmod(F(1, 10), float('-inf')))
            self.assertTypedTupleEquals(divmod(-0.1, float('inf')), divmod(F(-1, 10), float('inf')))
            self.assertTypedTupleEquals(divmod(-0.1, float('-inf')), divmod(F(-1, 10), float('-inf')))

        # ** has more interesting conversion rules.
        self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
        self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
        self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
        self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
        self.assertTypedEquals(4 , 2 ** F(2, 1))
        try:
            z = pow(-1, F(1, 2))
        except ValueError:
            self.assertEqual(2, sys.version_info[0])
        else:
            self.assertAlmostEqual(0, z.real)
            self.assertEqual(1, z.imag)
        self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
        self.assertTypedEquals(2.0 , 4 ** F(1, 2))
        self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
        self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
        self.assertRaises(ZeroDivisionError, operator.pow,
                          F(0, 1), -2)

    def 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):
        if sys.version_info >= (3,2):
            hmod = sys.hash_info.modulus
            hinf = sys.hash_info.inf
            self.assertEqual(hash(2.5), hash(F(5, 2)))
            self.assertEqual(hash(10**50), hash(F(10**50)))
            self.assertNotEqual(hash(float(10**23)), hash(F(10**23)))
            self.assertEqual(hinf, hash(F(1, hmod)))
        # Check that __hash__ produces the same value as hash(), for
        # consistency with int and Decimal.  (See issue #10356.)
        self.assertEqual(hash(F(-1)), F(-1).__hash__())

    def testHash_compare(self):
        self.assertEqual(hash(fractions.Fraction(3, 2)), hash(F(3, 2)))
        self.assertEqual(hash(fractions.Fraction(1, 2)), hash(F(1, 2)))
        self.assertEqual(hash(fractions.Fraction(0, 2)), hash(F(0, 2)))
        self.assertEqual(hash(fractions.Fraction(0, 1)), hash(F(0, 1)))
        self.assertEqual(hash(fractions.Fraction(10, 1)), hash(F(10, 1)))
        self.assertEqual(hash(fractions.Fraction(-1, 1)), hash(F(-1, 1)))
        self.assertEqual(hash(fractions.Fraction(-1, 10)), hash(F(-1, 10)))
        if sys.version_info >= (2, 7):
            self.assertEqual(hash(fractions.Fraction(1.2)), hash(F(1.2)))
            self.assertEqual(hash(fractions.Fraction(1.5)), hash(F(1.5)))

    def 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_pi_digits(self):
        pi = (
            "3.141592653589793238462643383279502884197169399375105820974944592307816406286"
            "208998628034825342117067982148086513282306647093844609550582231725359408128481"
            "117450284102701938521105559644622948954930381964428810975665933446128475648233"
            "786783165271201909145648566923460348610454326648213393607260249141273724587006"
        )
        for i in range(2, len(pi)):
            s = pi[:i]
            ff = fractions.Fraction(s)
            qf = F(s)
            self.assertEqual(ff, qf)
            self.assertEqual(ff.numerator, qf.numerator)
            self.assertEqual(ff.denominator, qf.denominator)


def test_main():
    suite = unittest.TestSuite()
    suite.addTest(unittest.makeSuite(GcdTest))
    suite.addTest(unittest.makeSuite(FractionTest))
    import doctest
    suite.addTest(doctest.DocTestSuite('quicktions'))
    return suite


def main():
    suite = test_main()
    runner = unittest.TextTestRunner(sys.stdout, verbosity=2)
    result = runner.run(suite)
    sys.exit(not result.wasSuccessful())


if __name__ == '__main__':
    main()