"""Tests for Lib/fractions.py."""

from decimal import Decimal
from test.support import requires_IEEE_754
import math
import numbers
import operator
import fractions
import functools
import sys
import unittest
import warnings
from copy import copy, deepcopy
from pickle import dumps, loads
F = fractions.Fraction
gcd = fractions.gcd

class DummyFloat(object):
    """Dummy float class for testing comparisons with Fractions"""

    def __init__(self, value):
        if not isinstance(value, float):
            raise TypeError("DummyFloat can only be initialized from float")
        self.value = value

    def _richcmp(self, other, op):
        if isinstance(other, numbers.Rational):
            return op(F.from_float(self.value), other)
        elif isinstance(other, DummyFloat):
            return op(self.value, other.value)
        else:
            return NotImplemented

    def __eq__(self, other): return self._richcmp(other, operator.eq)
    def __le__(self, other): return self._richcmp(other, operator.le)
    def __lt__(self, other): return self._richcmp(other, operator.lt)
    def __ge__(self, other): return self._richcmp(other, operator.ge)
    def __gt__(self, other): return self._richcmp(other, operator.gt)

    # shouldn't be calling __float__ at all when doing comparisons
    def __float__(self):
        assert False, "__float__ should not be invoked for comparisons"

    # same goes for subtraction
    def __sub__(self, other):
        assert False, "__sub__ should not be invoked for comparisons"
    __rsub__ = __sub__


class DummyRational(object):
    """Test comparison of Fraction with a naive rational implementation."""

    def __init__(self, num, den):
        g = math.gcd(num, den)
        self.num = num // g
        self.den = den // g

    def __eq__(self, other):
        if isinstance(other, fractions.Fraction):
            return (self.num == other._numerator and
                    self.den == other._denominator)
        else:
            return NotImplemented

    def __lt__(self, other):
        return(self.num * other._denominator < self.den * other._numerator)

    def __gt__(self, other):
        return(self.num * other._denominator > self.den * other._numerator)

    def __le__(self, other):
        return(self.num * other._denominator <= self.den * other._numerator)

    def __ge__(self, other):
        return(self.num * other._denominator >= self.den * other._numerator)

    # this class is for testing comparisons; conversion to float
    # should never be used for a comparison, since it loses accuracy
    def __float__(self):
        assert False, "__float__ should not be invoked"

class DummyFraction(fractions.Fraction):
    """Dummy Fraction subclass for copy and deepcopy testing."""

class GcdTest(unittest.TestCase):

    def testMisc(self):
        # fractions.gcd() is deprecated
        with self.assertWarnsRegex(DeprecationWarning, r'fractions\.gcd'):
            gcd(1, 1)
        with warnings.catch_warnings():
            warnings.filterwarnings('ignore', r'fractions\.gcd',
                                    DeprecationWarning)
            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(gcd(120.0, 84), 12.0)
            self.assertEqual(gcd(120, 84.0), 12.0)
            self.assertEqual(gcd(F(120), F(84)), F(12))
            self.assertEqual(gcd(F(120, 77), F(84, 55)), F(12, 385))


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.assertTupleEqual(expected, actual)
        self.assertListEqual(list(map(type, expected)), list(map(type, 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)

    @requires_IEEE_754
    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, 3125), _components(F("32.e-5")))
        self.assertEqual((1000000, 1), _components(F("1E+06")))
        self.assertEqual((-12300, 1), _components(F("-1.23e4")))
        self.assertEqual((0, 1), _components(F(" .0e+0\t")))
        self.assertEqual((0, 1), _components(F("-0.000e0")))

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

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

        # 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 Infinity to integer ratio",
            F.from_float, inf)
        self.assertRaisesMessage(
            OverflowError, "cannot convert Infinity to integer ratio",
            F.from_float, -inf)
        self.assertRaisesMessage(
            ValueError, "cannot convert NaN to integer ratio",
            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 integer ratio",
            F.from_decimal, Decimal("inf"))
        self.assertRaisesMessage(
            OverflowError, "cannot convert Infinity to integer ratio",
            F.from_decimal, Decimal("-inf"))
        self.assertRaisesMessage(
            ValueError, "cannot convert NaN to integer ratio",
            F.from_decimal, Decimal("nan"))
        self.assertRaisesMessage(
            ValueError, "cannot convert NaN to integer ratio",
            F.from_decimal, Decimal("snan"))

    def test_as_integer_ratio(self):
        self.assertEqual(F(4, 6).as_integer_ratio(), (2, 3))
        self.assertEqual(F(-4, 6).as_integer_ratio(), (-2, 3))
        self.assertEqual(F(4, -6).as_integer_ratio(), (-2, 3))
        self.assertEqual(F(0, 6).as_integer_ratio(), (0, 1))

    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)))
        self.assertTypedEquals(-2, math.floor(F(-11, 10)))
        self.assertTypedEquals(-1, math.ceil(F(-11, 10)))
        self.assertTypedEquals(-1, math.ceil(F(-10, 10)))
        self.assertTypedEquals(-1, int(F(-11, 10)))
        self.assertTypedEquals(0, round(F(-1, 10)))
        self.assertTypedEquals(0, round(F(-5, 10)))
        self.assertTypedEquals(-2, round(F(-15, 10)))
        self.assertTypedEquals(-1, round(F(-7, 10)))

        self.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,