| """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 typing |
| import unittest |
| from copy import copy, deepcopy |
| import pickle |
| from pickle import dumps, loads |
| F = fractions.Fraction |
| |
| |
| 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.""" |
| |
| |
| 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("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.assertEqual((123, 1), _components(F("1_2_3"))) |
| self.assertEqual((41, 107), _components(F("1_2_3/3_2_1"))) |
| self.assertEqual((6283, 2000), _components(F("3.14_15"))) |
| self.assertEqual((6283, 2*10**13), _components(F("3.14_15e-1_0"))) |
| self.assertEqual((101, 100), _components(F("1.01"))) |
| self.assertEqual((101, 100), _components(F("1.0_1"))) |
| |
| 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( |
| # 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, ".") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '_'", |
| F, "_") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '_1'", |
| F, "_1") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1__2'", |
| F, "1__2") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '/_'", |
| F, "/_") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1_/'", |
| F, "1_/") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '_1/'", |
| F, "_1/") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1__2/'", |
| F, "1__2/") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1/_'", |
| F, "1/_") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1/_1'", |
| F, "1/_1") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1/1__2'", |
| F, "1/1__2") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1._111'", |
| F, "1._111") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1.1__1'", |
| F, "1.1__1") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1.1e+_1'", |
| F, "1.1e+_1") |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1.1e+1__1'", |
| F, "1.1e+1__1") |
| # Test catastrophic backtracking. |
| val = "9"*50 + "_" |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '" + val + "'", |
| F, val) |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1/" + val + "'", |
| F, "1/" + val) |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1." + val + "'", |
| F, "1." + val) |
| self.assertRaisesMessage( |
| ValueError, "Invalid literal for Fraction: '1.1+e" + val + "'", |
| F, "1.1+e" + val) |
| |
| 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_is_integer(self): |
| self.assertTrue(F(1, 1).is_integer()) |
| self.assertTrue(F(-1, 1).is_integer()) |
| self.assertTrue(F(1, -1).is_integer()) |
| self.assertTrue(F(2, 2).is_integer()) |
| self.assertTrue(F(-2, 2).is_integer()) |
| self.assertTrue(F(2, -2).is_integer()) |
| |
| self.assertFalse(F(1, 2).is_integer()) |
| self.assertFalse(F(-1, 2).is_integer()) |
| self.assertFalse(F(1, -2).is_integer()) |
| self.assertFalse(F(-1, -2).is_integer()) |
| |
| 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, |
| float(F(int('2'*400+'7'), int('3'*400+'1')))) |
| |
| self.assertTypedEquals(0.1+0j, complex(F(1,10))) |
| |
| def testSupportsInt(self): |
| # See bpo-44547. |
| f = F(3, 2) |
| self.assertIsInstance(f, typing.SupportsInt) |
| self.assertEqual(int(f), 1) |
| self.assertEqual(type(int(f)), int) |
| |
| def testIntGuaranteesIntReturn(self): |
| # Check that int(some_fraction) gives a result of exact type `int` |
| # even if the fraction is using some other Integral type for its |
| # numerator and denominator. |
| |
| class CustomInt(int): |
| """ |
| Subclass of int with just enough machinery to convince the Fraction |
| constructor to produce something with CustomInt numerator and |
| denominator. |
| """ |
| |
| @property |
| def numerator(self): |
| return self |
| |
| @property |
| def denominator(self): |
| return CustomInt(1) |
| |
| def __mul__(self, other): |
| return CustomInt(int(self) * int(other)) |
| |
| def __floordiv__(self, other): |
| return CustomInt(int(self) // int(other)) |
| |
| f = F(CustomInt(13), CustomInt(5)) |
| |
| self.assertIsInstance(f.numerator, CustomInt) |
| self.assertIsInstance(f.denominator, CustomInt) |
| self.assertIsInstance(f, typing.SupportsInt) |
| self.assertEqual(int(f), 2) |
| self.assertEqual(type(int(f)), int) |
| |
| def testBoolGuarateesBoolReturn(self): |
| # Ensure that __bool__ is used on numerator which guarantees a bool |
| # return. See also bpo-39274. |
| @functools.total_ordering |
| class CustomValue: |
| denominator = 1 |
| |
| def __init__(self, value): |
| self.value = value |
| |
| def __bool__(self): |
| return bool(self.value) |
| |
| @property |
| def numerator(self): |
| # required to preserve `self` during instantiation |
| return self |
| |
| def __eq__(self, other): |
| raise AssertionError("Avoid comparisons in Fraction.__bool__") |
| |
| __lt__ = __eq__ |
| |
| # We did not implement all abstract methods, so register: |
| numbers.Rational.register(CustomValue) |
| |
| numerator = CustomValue(1) |
| r = F(numerator) |
| # ensure the numerator was not lost during instantiation: |
| self.assertIs(r.numerator, numerator) |
| self.assertIs(bool(r), True) |
| |
| numerator = CustomValue(0) |
| r = F(numerator) |
| self.assertIs(bool(r), False) |
| |
| def testRound(self): |
| self.assertTypedEquals(F(-200), round(F(-150), -2)) |
| self.assertTypedEquals(F(-200), round(F(-250), -2)) |
| self.assertTypedEquals(F(30), round(F(26), -1)) |
| self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1)) |
| self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1)) |
| |
| def testArithmetic(self): |
| self.assertEqual(F(1, 2), F(1, 10) + F(2, 5)) |
| self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5)) |
| self.assertEqual(F(1, 25), F(1, 10) * F(2, 5)) |
| self.assertEqual(F(5, 6), F(2, 3) * F(5, 4)) |
| self.assertEqual(F(1, 4), F(1, 10) / F(2, 5)) |
| self.assertEqual(F(-15, 8), F(3, 4) / F(-2, 5)) |
| self.assertTypedEquals(2, F(9, 10) // F(2, 5)) |
| self.assertTypedEquals(10**23, F(10**23, 1) // F(1)) |
| self.assertEqual(F(5, 6), F(7, 3) % F(3, 2)) |
| self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2)) |
| self.assertEqual((F(1), F(5, 6)), divmod(F(7, 3), F(3, 2))) |
| self.assertEqual((F(-2), F(2, 3)), divmod(F(-7, 3), F(3, 2))) |
| self.assertEqual(F(8, 27), F(2, 3) ** F(3)) |
| self.assertEqual(F(27, 8), F(2, 3) ** F(-3)) |
| self.assertTypedEquals(2.0, F(4) ** F(1, 2)) |
| self.assertEqual(F(1, 1), +F(1, 1)) |
| z = pow(F(-1), F(1, 2)) |
| self.assertAlmostEqual(z.real, 0) |
| self.assertEqual(z.imag, 1) |
| # Regression test for #27539. |
| p = F(-1, 2) ** 0 |
| self.assertEqual(p, F(1, 1)) |
| self.assertEqual(p.numerator, 1) |
| self.assertEqual(p.denominator, 1) |
| p = F(-1, 2) ** -1 |
| self.assertEqual(p, F(-2, 1)) |
| self.assertEqual(p.numerator, -2) |
| self.assertEqual(p.denominator, 1) |
| p = F(-1, 2) ** -2 |
| self.assertEqual(p, F(4, 1)) |
| self.assertEqual(p.numerator, 4) |
| self.assertEqual(p.denominator, 1) |
| |
| def testLargeArithmetic(self): |
| self.assertTypedEquals( |
| F(10101010100808080808080808101010101010000000000000000, |
| 1010101010101010101010101011111111101010101010101010101010101), |
| F(10**35+1, 10**27+1) % F(10**27+1, 10**35-1) |
| ) |
| self.assertTypedEquals( |
| F(7, 1901475900342344102245054808064), |
| F(-2**100, 3) % F(5, 2**100) |
| ) |
| self.assertTypedTupleEquals( |
| (9999999999999999, |
| F(10101010100808080808080808101010101010000000000000000, |
| 1010101010101010101010101011111111101010101010101010101010101)), |
| divmod(F(10**35+1, 10**27+1), F(10**27+1, 10**35-1)) |
| ) |
| self.assertTypedEquals( |
| -2 ** 200 // 15, |
| F(-2**100, 3) // F(5, 2**100) |
| ) |
| self.assertTypedEquals( |
| 1, |
| F(5, 2**100) // F(3, 2**100) |
| ) |
| self.assertTypedEquals( |
| (1, F(2, 2**100)), |
| divmod(F(5, 2**100), F(3, 2**100)) |
| ) |
| self.assertTypedTupleEquals( |
| (-2 ** 200 // 15, |
| F(7, 1901475900342344102245054808064)), |
| divmod(F(-2**100, 3), F(5, 2**100)) |
| ) |
| |
| def testMixedArithmetic(self): |
| self.assertTypedEquals(F(11, 10), F(1, 10) + 1) |
| self.assertTypedEquals(1.1, F(1, 10) + 1.0) |
| self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j)) |
| self.assertTypedEquals(F(11, 10), 1 + F(1, 10)) |
| self.assertTypedEquals(1.1, 1.0 + F(1, 10)) |
| self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10)) |
| |
| self.assertTypedEquals(F(-9, 10), F(1, 10) - 1) |
| self.assertTypedEquals(-0.9, F(1, 10) - 1.0) |
| self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j)) |
| self.assertTypedEquals(F(9, 10), 1 - F(1, 10)) |
| self.assertTypedEquals(0.9, 1.0 - F(1, 10)) |
| self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10)) |
| |
| self.assertTypedEquals(F(1, 10), F(1, 10) * 1) |
| self.assertTypedEquals(0.1, F(1, 10) * 1.0) |
| self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j)) |
| self.assertTypedEquals(F(1, 10), 1 * F(1, 10)) |
| self.assertTypedEquals(0.1, 1.0 * F(1, 10)) |
| self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10)) |
| |
| self.assertTypedEquals(F(1, 10), F(1, 10) / 1) |
| self.assertTypedEquals(0.1, F(1, 10) / 1.0) |
| self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j)) |
| self.assertTypedEquals(F(10, 1), 1 / F(1, 10)) |
| self.assertTypedEquals(10.0, 1.0 / F(1, 10)) |
| self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10)) |
| |
| self.assertTypedEquals(0, F(1, 10) // 1) |
| self.assertTypedEquals(0.0, F(1, 10) // 1.0) |
| self.assertTypedEquals(10, 1 // F(1, 10)) |
| self.assertTypedEquals(10**23, 10**22 // F(1, 10)) |
| self.assertTypedEquals(1.0 // 0.1, 1.0 // F(1, 10)) |
| |
| self.assertTypedEquals(F(1, 10), F(1, 10) % 1) |
| self.assertTypedEquals(0.1, F(1, 10) % 1.0) |
| self.assertTypedEquals(F(0, 1), 1 % F(1, 10)) |
| self.assertTypedEquals(1.0 % 0.1, 1.0 % F(1, 10)) |
| self.assertTypedEquals(0.1, F(1, 10) % float('inf')) |
| self.assertTypedEquals(float('-inf'), F(1, 10) % float('-inf')) |
| self.assertTypedEquals(float('inf'), F(-1, 10) % float('inf')) |
| self.assertTypedEquals(-0.1, F(-1, 10) % float('-inf')) |
| |
| self.assertTypedTupleEquals((0, F(1, 10)), divmod(F(1, 10), 1)) |
| self.assertTypedTupleEquals(divmod(0.1, 1.0), divmod(F(1, 10), 1.0)) |
| self.assertTypedTupleEquals((10, F(0)), divmod(1, F(1, 10))) |
| self.assertTypedTupleEquals(divmod(1.0, 0.1), divmod(1.0, F(1, 10))) |
| self.assertTypedTupleEquals(divmod(0.1, float('inf')), divmod(F(1, 10), float('inf'))) |
| self.assertTypedTupleEquals(divmod(0.1, float('-inf')), divmod(F(1, 10), float('-inf'))) |
| self.assertTypedTupleEquals(divmod(-0.1, float('inf')), divmod(F(-1, 10), float('inf'))) |
| self.assertTypedTupleEquals(divmod(-0.1, float('-inf')), divmod(F(-1, 10), float('-inf'))) |
| |
| # ** has more interesting conversion rules. |
| self.assertTypedEquals(F(100, 1), F(1, 10) ** -2) |
| self.assertTypedEquals(F(100, 1), F(10, 1) ** 2) |
| self.assertTypedEquals(0.1, F(1, 10) ** 1.0) |
| self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j)) |
| self.assertTypedEquals(4 , 2 ** F(2, 1)) |
| z = pow(-1, F(1, 2)) |
| self.assertAlmostEqual(0, z.real) |
| self.assertEqual(1, z.imag) |
| self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1)) |
| self.assertTypedEquals(2.0 , 4 ** F(1, 2)) |
| self.assertTypedEquals(0.25, 2.0 ** F(-2, 1)) |
| self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10)) |
| self.assertRaises(ZeroDivisionError, operator.pow, |
| F(0, 1), -2) |
| |
| def testMixingWithDecimal(self): |
| # Decimal refuses mixed arithmetic (but not mixed comparisons) |
| self.assertRaises(TypeError, operator.add, |
| F(3,11), Decimal('3.1415926')) |
| self.assertRaises(TypeError, operator.add, |
| Decimal('3.1415926'), F(3,11)) |
| |
| def testComparisons(self): |
| self.assertTrue(F(1, 2) < F(2, 3)) |
| self.assertFalse(F(1, 2) < F(1, 2)) |
| self.assertTrue(F(1, 2) <= F(2, 3)) |
| self.assertTrue(F(1, 2) <= F(1, 2)) |
| self.assertFalse(F(2, 3) <= F(1, 2)) |
| self.assertTrue(F(1, 2) == F(1, 2)) |
| self.assertFalse(F(1, 2) == F(1, 3)) |
| self.assertFalse(F(1, 2) != F(1, 2)) |
| self.assertTrue(F(1, 2) != F(1, 3)) |
| |
| def testComparisonsDummyRational(self): |
| self.assertTrue(F(1, 2) == DummyRational(1, 2)) |
| self.assertTrue(DummyRational(1, 2) == F(1, 2)) |
| self.assertFalse(F(1, 2) == DummyRational(3, 4)) |
| self.assertFalse(DummyRational(3, 4) == F(1, 2)) |
| |
| self.assertTrue(F(1, 2) < DummyRational(3, 4)) |
| self.assertFalse(F(1, 2) < DummyRational(1, 2)) |
| self.assertFalse(F(1, 2) < DummyRational(1, 7)) |
| self.assertFalse(F(1, 2) > DummyRational(3, 4)) |
| self.assertFalse(F(1, 2) > DummyRational(1, 2)) |
| self.assertTrue(F(1, 2) > DummyRational(1, 7)) |
| self.assertTrue(F(1, 2) <= DummyRational(3, 4)) |
| self.assertTrue(F(1, 2) <= DummyRational(1, 2)) |
| self.assertFalse(F(1, 2) <= DummyRational(1, 7)) |
| self.assertFalse(F(1, 2) >= DummyRational(3, 4)) |
| self.assertTrue(F(1, 2) >= DummyRational(1, 2)) |
| self.assertTrue(F(1, 2) >= DummyRational(1, 7)) |
| |
| self.assertTrue(DummyRational(1, 2) < F(3, 4)) |
| self.assertFalse(DummyRational(1, 2) < F(1, 2)) |
| self.assertFalse(DummyRational(1, 2) < F(1, 7)) |
| self.assertFalse(DummyRational(1, 2) > F(3, 4)) |
| self.assertFalse(DummyRational(1, 2) > F(1, 2)) |
| self.assertTrue(DummyRational(1, 2) > F(1, 7)) |
| self.assertTrue(DummyRational(1, 2) <= F(3, 4)) |
| self.assertTrue(DummyRational(1, 2) <= F(1, 2)) |
| self.assertFalse(DummyRational(1, 2) <= F(1, 7)) |
| self.assertFalse(DummyRational(1, 2) >= F(3, 4)) |
| self.assertTrue(DummyRational(1, 2) >= F(1, 2)) |
| self.assertTrue(DummyRational(1, 2) >= F(1, 7)) |
| |
| def testComparisonsDummyFloat(self): |
| x = DummyFloat(1./3.) |
| y = F(1, 3) |
| self.assertTrue(x != y) |
| self.assertTrue(x < y or x > y) |
| self.assertFalse(x == y) |
| self.assertFalse(x <= y and x >= y) |
| self.assertTrue(y != x) |
| self.assertTrue(y < x or y > x) |
| self.assertFalse(y == x) |
| self.assertFalse(y <= x and y >= x) |
| |
| def testMixedLess(self): |
| self.assertTrue(2 < F(5, 2)) |
| self.assertFalse(2 < F(4, 2)) |
| self.assertTrue(F(5, 2) < 3) |
| self.assertFalse(F(4, 2) < 2) |
| |
| self.assertTrue(F(1, 2) < 0.6) |
| self.assertFalse(F(1, 2) < 0.4) |
| self.assertTrue(0.4 < F(1, 2)) |
| self.assertFalse(0.5 < F(1, 2)) |
| |
| self.assertFalse(float('inf') < F(1, 2)) |
| self.assertTrue(float('-inf') < F(0, 10)) |
| self.assertFalse(float('nan') < F(-3, 7)) |
| self.assertTrue(F(1, 2) < float('inf')) |
| self.assertFalse(F(17, 12) < float('-inf')) |
| self.assertFalse(F(144, -89) < float('nan')) |
| |
| def testMixedLessEqual(self): |
| self.assertTrue(0.5 <= F(1, 2)) |
| self.assertFalse(0.6 <= F(1, 2)) |
| self.assertTrue(F(1, 2) <= 0.5) |
| self.assertFalse(F(1, 2) <= 0.4) |
| self.assertTrue(2 <= F(4, 2)) |
| self.assertFalse(2 <= F(3, 2)) |
| self.assertTrue(F(4, 2) <= 2) |
| self.assertFalse(F(5, 2) <= 2) |
| |
| self.assertFalse(float('inf') <= F(1, 2)) |
| self.assertTrue(float('-inf') <= F(0, 10)) |
| self.assertFalse(float('nan') <= F(-3, 7)) |
| self.assertTrue(F(1, 2) <= float('inf')) |
| self.assertFalse(F(17, 12) <= float('-inf')) |
| self.assertFalse(F(144, -89) <= float('nan')) |
| |
| def testBigFloatComparisons(self): |
| # Because 10**23 can't be represented exactly as a float: |
| self.assertFalse(F(10**23) == float(10**23)) |
| # The first test demonstrates why these are important. |
| self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1))) |
| self.assertTrue(1e23 < F(math.trunc(1e23) + 1)) |
| self.assertFalse(1e23 <= F(math.trunc(1e23) - 1)) |
| self.assertTrue(1e23 > F(math.trunc(1e23) - 1)) |
| self.assertFalse(1e23 >= F(math.trunc(1e23) + 1)) |
| |
| def testBigComplexComparisons(self): |
| self.assertFalse(F(10**23) == complex(10**23)) |
| self.assertRaises(TypeError, operator.gt, F(10**23), complex(10**23)) |
| self.assertRaises(TypeError, operator.le, F(10**23), complex(10**23)) |
| |
| x = F(3, 8) |
| z = complex(0.375, 0.0) |
| w = complex(0.375, 0.2) |
| self.assertTrue(x == z) |
| self.assertFalse(x != z) |
| self.assertFalse(x == w) |
| self.assertTrue(x != w) |
| for op in operator.lt, operator.le, operator.gt, operator.ge: |
| self.assertRaises(TypeError, op, x, z) |
| self.assertRaises(TypeError, op, z, x) |
| self.assertRaises(TypeError, op, x, w) |
| self.assertRaises(TypeError, op, w, x) |
| |
| def testMixedEqual(self): |
| self.assertTrue(0.5 == F(1, 2)) |
| self.assertFalse(0.6 == F(1, 2)) |
| self.assertTrue(F(1, 2) == 0.5) |
| self.assertFalse(F(1, 2) == 0.4) |
| self.assertTrue(2 == F(4, 2)) |
| self.assertFalse(2 == F(3, 2)) |
| self.assertTrue(F(4, 2) == 2) |
| self.assertFalse(F(5, 2) == 2) |
| self.assertFalse(F(5, 2) == float('nan')) |
| self.assertFalse(float('nan') == F(3, 7)) |
| self.assertFalse(F(5, 2) == float('inf')) |
| self.assertFalse(float('-inf') == F(2, 5)) |
| |
| def testStringification(self): |
| self.assertEqual("Fraction(7, 3)", repr(F(7, 3))) |
| self.assertEqual("Fraction(6283185307, 2000000000)", |
| repr(F('3.1415926535'))) |
| self.assertEqual("Fraction(-1, 100000000000000000000)", |
| repr(F(1, -10**20))) |
| self.assertEqual("7/3", str(F(7, 3))) |
| self.assertEqual("7", str(F(7, 1))) |
| |
| def testHash(self): |
| hmod = sys.hash_info.modulus |
| hinf = sys.hash_info.inf |
| self.assertEqual(hash(2.5), hash(F(5, 2))) |
| self.assertEqual(hash(10**50), hash(F(10**50))) |
| self.assertNotEqual(hash(float(10**23)), hash(F(10**23))) |
| self.assertEqual(hinf, hash(F(1, hmod))) |
| # Check that __hash__ produces the same value as hash(), for |
| # consistency with int and Decimal. (See issue #10356.) |
| self.assertEqual(hash(F(-1)), F(-1).__hash__()) |
| |
| def testApproximatePi(self): |
| # Algorithm borrowed from |
| # http://docs.python.org/lib/decimal-recipes.html |
| three = F(3) |
| lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 |
| while abs(s - lasts) > F(1, 10**9): |
| lasts = s |
| n, na = n+na, na+8 |
| d, da = d+da, da+32 |
| t = (t * n) / d |
| s += t |
| self.assertAlmostEqual(math.pi, s) |
| |
| def testApproximateCos1(self): |
| # Algorithm borrowed from |
| # http://docs.python.org/lib/decimal-recipes.html |
| x = F(1) |
| i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1 |
| while abs(s - lasts) > F(1, 10**9): |
| lasts = s |
| i += 2 |
| fact *= i * (i-1) |
| num *= x * x |
| sign *= -1 |
| s += num / fact * sign |
| self.assertAlmostEqual(math.cos(1), s) |
| |
| def test_copy_deepcopy_pickle(self): |
| r = F(13, 7) |
| dr = DummyFraction(13, 7) |
| for proto in range(0, pickle.HIGHEST_PROTOCOL + 1): |
| self.assertEqual(r, loads(dumps(r, proto))) |
| 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_format_no_presentation_type(self): |
| # Triples (fraction, specification, expected_result) |
| testcases = [ |
| (F(1, 3), '', '1/3'), |
| (F(-1, 3), '', '-1/3'), |
| (F(3), '', '3'), |
| (F(-3), '', '-3'), |
| ] |
| for fraction, spec, expected in testcases: |
| with self.subTest(fraction=fraction, spec=spec): |
| self.assertEqual(format(fraction, spec), expected) |
| |
| def test_format_e_presentation_type(self): |
| # Triples (fraction, specification, expected_result) |
| testcases = [ |
| (F(2, 3), '.6e', '6.666667e-01'), |
| (F(3, 2), '.6e', '1.500000e+00'), |
| (F(2, 13), '.6e', '1.538462e-01'), |
| (F(2, 23), '.6e', '8.695652e-02'), |
| (F(2, 33), '.6e', '6.060606e-02'), |
| (F(13, 2), '.6e', '6.500000e+00'), |
| (F(20, 2), '.6e', '1.000000e+01'), |
| (F(23, 2), '.6e', '1.150000e+01'), |
| (F(33, 2), '.6e', '1.650000e+01'), |
| (F(2, 3), '.6e', '6.666667e-01'), |
| (F(3, 2), '.6e', '1.500000e+00'), |
| # Zero |
| (F(0), '.3e', '0.000e+00'), |
| # Powers of 10, to exercise the log10 boundary logic |
| (F(1, 1000), '.3e', '1.000e-03'), |
| (F(1, 100), '.3e', '1.000e-02'), |
| (F(1, 10), '.3e', '1.000e-01'), |
| (F(1, 1), '.3e', '1.000e+00'), |
| (F(10), '.3e', '1.000e+01'), |
| (F(100), '.3e', '1.000e+02'), |
| (F(1000), '.3e', '1.000e+03'), |
| # Boundary where we round up to the next power of 10 |
| (F('99.999994999999'), '.6e', '9.999999e+01'), |
| (F('99.999995'), '.6e', '1.000000e+02'), |
| (F('99.999995000001'), '.6e', '1.000000e+02'), |
| # Negatives |
| (F(-2, 3), '.6e', '-6.666667e-01'), |
| (F(-3, 2), '.6e', '-1.500000e+00'), |
| (F(-100), '.6e', '-1.000000e+02'), |
| # Large and small |
| (F('1e1000'), '.3e', '1.000e+1000'), |
| (F('1e-1000'), '.3e', '1.000e-1000'), |
| # Using 'E' instead of 'e' should give us a capital 'E' |
| (F(2, 3), '.6E', '6.666667E-01'), |
| # Tiny precision |
| (F(2, 3), '.1e', '6.7e-01'), |
| (F('0.995'), '.0e', '1e+00'), |
| # Default precision is 6 |
| (F(22, 7), 'e', '3.142857e+00'), |
| # Alternate form forces a decimal point |
| (F('0.995'), '#.0e', '1.e+00'), |
| # Check that padding takes the exponent into account. |
| (F(22, 7), '11.6e', '3.142857e+00'), |
| (F(22, 7), '12.6e', '3.142857e+00'), |
| (F(22, 7), '13.6e', ' 3.142857e+00'), |
| # Thousands separators |
| (F('1234567.123456'), ',.5e', '1.23457e+06'), |
| (F('123.123456'), '012_.2e', '0_001.23e+02'), |
| # z flag is legal, but never makes a difference to the output |
| (F(-1, 7**100), 'z.6e', '-3.091690e-85'), |
| ] |
| for fraction, spec, expected in testcases: |
| with self.subTest(fraction=fraction, spec=spec): |
| self.assertEqual(format(fraction, spec), expected) |
| |
| def test_format_f_presentation_type(self): |
| # Triples (fraction, specification, expected_result) |
| testcases = [ |
| # Simple .f formatting |
| (F(0, 1), '.2f', '0.00'), |
| (F(1, 3), '.2f', '0.33'), |
| (F(2, 3), '.2f', '0.67'), |
| (F(4, 3), '.2f', '1.33'), |
| (F(1, 8), '.2f', '0.12'), |
| (F(3, 8), '.2f', '0.38'), |
| (F(1, 13), '.2f', '0.08'), |
| (F(1, 199), '.2f', '0.01'), |
| (F(1, 200), '.2f', '0.00'), |
| (F(22, 7), '.5f', '3.14286'), |
| (F('399024789'), '.2f', '399024789.00'), |
| # Large precision (more than float can provide) |
| (F(104348, 33215), '.50f', |
| '3.14159265392142104470871594159265392142104470871594'), |
| # Precision defaults to 6 if not given |
| (F(22, 7), 'f', '3.142857'), |
| (F(0), 'f', '0.000000'), |
| (F(-22, 7), 'f', '-3.142857'), |
| # Round-ties-to-even checks |
| (F('1.225'), '.2f', '1.22'), |
| (F('1.2250000001'), '.2f', '1.23'), |
| (F('1.2349999999'), '.2f', '1.23'), |
| (F('1.235'), '.2f', '1.24'), |
| (F('1.245'), '.2f', '1.24'), |
| (F('1.2450000001'), '.2f', '1.25'), |
| (F('1.2549999999'), '.2f', '1.25'), |
| (F('1.255'), '.2f', '1.26'), |
| (F('-1.225'), '.2f', '-1.22'), |
| (F('-1.2250000001'), '.2f', '-1.23'), |
| (F('-1.2349999999'), '.2f', '-1.23'), |
| (F('-1.235'), '.2f', '-1.24'), |
| (F('-1.245'), '.2f', '-1.24'), |
| (F('-1.2450000001'), '.2f', '-1.25'), |
| (F('-1.2549999999'), '.2f', '-1.25'), |
| (F('-1.255'), '.2f', '-1.26'), |
| # Negatives and sign handling |
| (F(2, 3), '.2f', '0.67'), |
| (F(2, 3), '-.2f', '0.67'), |
| (F(2, 3), '+.2f', '+0.67'), |
| (F(2, 3), ' .2f', ' 0.67'), |
| (F(-2, 3), '.2f', '-0.67'), |
| (F(-2, 3), '-.2f', '-0.67'), |
| (F(-2, 3), '+.2f', '-0.67'), |
| (F(-2, 3), ' .2f', '-0.67'), |
| # Formatting to zero places |
| (F(1, 2), '.0f', '0'), |
| (F(-1, 2), '.0f', '-0'), |
| (F(22, 7), '.0f', '3'), |
| (F(-22, 7), '.0f', '-3'), |
| # Formatting to zero places, alternate form |
| (F(1, 2), '#.0f', '0.'), |
| (F(-1, 2), '#.0f', '-0.'), |
| (F(22, 7), '#.0f', '3.'), |
| (F(-22, 7), '#.0f', '-3.'), |
| # z flag for suppressing negative zeros |
| (F('-0.001'), 'z.2f', '0.00'), |
| (F('-0.001'), '-z.2f', '0.00'), |
| (F('-0.001'), '+z.2f', '+0.00'), |
| (F('-0.001'), ' z.2f', ' 0.00'), |
| (F('0.001'), 'z.2f', '0.00'), |
| (F('0.001'), '-z.2f', '0.00'), |
| (F('0.001'), '+z.2f', '+0.00'), |
| (F('0.001'), ' z.2f', ' 0.00'), |
| # Specifying a minimum width |
| (F(2, 3), '6.2f', ' 0.67'), |
| (F(12345), '6.2f', '12345.00'), |
| (F(12345), '12f', '12345.000000'), |
| # Fill and alignment |
| (F(2, 3), '>6.2f', ' 0.67'), |
| (F(2, 3), '<6.2f', '0.67 '), |
| (F(2, 3), '^3.2f', '0.67'), |
| (F(2, 3), '^4.2f', '0.67'), |
| (F(2, 3), '^5.2f', '0.67 '), |
| (F(2, 3), '^6.2f', ' 0.67 '), |
| (F(2, 3), '^7.2f', ' 0.67 '), |
| (F(2, 3), '^8.2f', ' 0.67 '), |
| # '=' alignment |
| (F(-2, 3), '=+8.2f', '- 0.67'), |
| (F(2, 3), '=+8.2f', '+ 0.67'), |
| # Fill character |
| (F(-2, 3), 'X>3.2f', '-0.67'), |
| (F(-2, 3), 'X>7.2f', 'XX-0.67'), |
| (F(-2, 3), 'X<7.2f', '-0.67XX'), |
| (F(-2, 3), 'X^7.2f', 'X-0.67X'), |
| (F(-2, 3), 'X=7.2f', '-XX0.67'), |
| (F(-2, 3), ' >7.2f', ' -0.67'), |
| # Corner cases: weird fill characters |
| (F(-2, 3), '\x00>7.2f', '\x00\x00-0.67'), |
| (F(-2, 3), '\n>7.2f', '\n\n-0.67'), |
| (F(-2, 3), '\t>7.2f', '\t\t-0.67'), |
| (F(-2, 3), '>>7.2f', '>>-0.67'), |
| (F(-2, 3), '<>7.2f', '<<-0.67'), |
| (F(-2, 3), '→>7.2f', '→→-0.67'), |
| # Zero-padding |
| (F(-2, 3), '07.2f', '-000.67'), |
| (F(-2, 3), '-07.2f', '-000.67'), |
| (F(2, 3), '+07.2f', '+000.67'), |
| (F(2, 3), ' 07.2f', ' 000.67'), |
| # An isolated zero is a minimum width, not a zero-pad flag. |
| # So unlike zero-padding, it's legal in combination with alignment. |
| (F(2, 3), '0.2f', '0.67'), |
| (F(2, 3), '>0.2f', '0.67'), |
| (F(2, 3), '<0.2f', '0.67'), |
| (F(2, 3), '^0.2f', '0.67'), |
| (F(2, 3), '=0.2f', '0.67'), |
| # Corner case: zero-padding _and_ a zero minimum width. |
| (F(2, 3), '00.2f', '0.67'), |
| # Thousands separator (only affects portion before the point) |
| (F(2, 3), ',.2f', '0.67'), |
| (F(2, 3), ',.7f', '0.6666667'), |
| (F('123456.789'), ',.2f', '123,456.79'), |
| (F('1234567'), ',.2f', '1,234,567.00'), |
| (F('12345678'), ',.2f', '12,345,678.00'), |
| (F('12345678'), ',f', '12,345,678.000000'), |
| # Underscore as thousands separator |
| (F(2, 3), '_.2f', '0.67'), |
| (F(2, 3), '_.7f', '0.6666667'), |
| (F('123456.789'), '_.2f', '123_456.79'), |
| (F('1234567'), '_.2f', '1_234_567.00'), |
| (F('12345678'), '_.2f', '12_345_678.00'), |
| # Thousands and zero-padding |
| (F('1234.5678'), '07,.2f', '1,234.57'), |
| (F('1234.5678'), '08,.2f', '1,234.57'), |
| (F('1234.5678'), '09,.2f', '01,234.57'), |
| (F('1234.5678'), '010,.2f', '001,234.57'), |
| (F('1234.5678'), '011,.2f', '0,001,234.57'), |
| (F('1234.5678'), '012,.2f', '0,001,234.57'), |
| (F('1234.5678'), '013,.2f', '00,001,234.57'), |
| (F('1234.5678'), '014,.2f', '000,001,234.57'), |
| (F('1234.5678'), '015,.2f', '0,000,001,234.57'), |
| (F('1234.5678'), '016,.2f', '0,000,001,234.57'), |
| (F('-1234.5678'), '07,.2f', '-1,234.57'), |
| (F('-1234.5678'), '08,.2f', '-1,234.57'), |
| (F('-1234.5678'), '09,.2f', '-1,234.57'), |
| (F('-1234.5678'), '010,.2f', '-01,234.57'), |
| (F('-1234.5678'), '011,.2f', '-001,234.57'), |
| (F('-1234.5678'), '012,.2f', '-0,001,234.57'), |
| (F('-1234.5678'), '013,.2f', '-0,001,234.57'), |
| (F('-1234.5678'), '014,.2f', '-00,001,234.57'), |
| (F('-1234.5678'), '015,.2f', '-000,001,234.57'), |
| (F('-1234.5678'), '016,.2f', '-0,000,001,234.57'), |
| # Corner case: no decimal point |
| (F('-1234.5678'), '06,.0f', '-1,235'), |
| (F('-1234.5678'), '07,.0f', '-01,235'), |
| (F('-1234.5678'), '08,.0f', '-001,235'), |
| (F('-1234.5678'), '09,.0f', '-0,001,235'), |
| # Corner-case - zero-padding specified through fill and align |
| # instead of the zero-pad character - in this case, treat '0' as a |
| # regular fill character and don't attempt to insert commas into |
| # the filled portion. This differs from the int and float |
| # behaviour. |
| (F('1234.5678'), '0=12,.2f', '00001,234.57'), |
| # Corner case where it's not clear whether the '0' indicates zero |
| # padding or gives the minimum width, but there's still an obvious |
| # answer to give. We want this to work in case the minimum width |
| # is being inserted programmatically: spec = f'{width}.2f'. |
| (F('12.34'), '0.2f', '12.34'), |
| (F('12.34'), 'X>0.2f', '12.34'), |
| # 'F' should work identically to 'f' |
| (F(22, 7), '.5F', '3.14286'), |
| # %-specifier |
| (F(22, 7), '.2%', '314.29%'), |
| (F(1, 7), '.2%', '14.29%'), |
| (F(1, 70), '.2%', '1.43%'), |
| (F(1, 700), '.2%', '0.14%'), |
| (F(1, 7000), '.2%', '0.01%'), |
| (F(1, 70000), '.2%', '0.00%'), |
| (F(1, 7), '.0%', '14%'), |
| (F(1, 7), '#.0%', '14.%'), |
| (F(100, 7), ',.2%', '1,428.57%'), |
| (F(22, 7), '7.2%', '314.29%'), |
| (F(22, 7), '8.2%', ' 314.29%'), |
| (F(22, 7), '08.2%', '0314.29%'), |
| # Test cases from #67790 and discuss.python.org Ideas thread. |
| (F(1, 3), '.2f', '0.33'), |
| (F(1, 8), '.2f', '0.12'), |
| (F(3, 8), '.2f', '0.38'), |
| (F(2545, 1000), '.2f', '2.54'), |
| (F(2549, 1000), '.2f', '2.55'), |
| (F(2635, 1000), '.2f', '2.64'), |
| (F(1, 100), '.1f', '0.0'), |
| (F(49, 1000), '.1f', '0.0'), |
| (F(51, 1000), '.1f', '0.1'), |
| (F(149, 1000), '.1f', '0.1'), |
| (F(151, 1000), '.1f', '0.2'), |
| ] |
| for fraction, spec, expected in testcases: |
| with self.subTest(fraction=fraction, spec=spec): |
| self.assertEqual(format(fraction, spec), expected) |
| |
| def test_format_g_presentation_type(self): |
| # Triples (fraction, specification, expected_result) |
| testcases = [ |
| (F('0.000012345678'), '.6g', '1.23457e-05'), |
| (F('0.00012345678'), '.6g', '0.000123457'), |
| (F('0.0012345678'), '.6g', '0.00123457'), |
| (F('0.012345678'), '.6g', '0.0123457'), |
| (F('0.12345678'), '.6g', '0.123457'), |
| (F('1.2345678'), '.6g', '1.23457'), |
| (F('12.345678'), '.6g', '12.3457'), |
| (F('123.45678'), '.6g', '123.457'), |
| (F('1234.5678'), '.6g', '1234.57'), |
| (F('12345.678'), '.6g', '12345.7'), |
| (F('123456.78'), '.6g', '123457'), |
| (F('1234567.8'), '.6g', '1.23457e+06'), |
| # Rounding up cases |
| (F('9.99999e+2'), '.4g', '1000'), |
| (F('9.99999e-8'), '.4g', '1e-07'), |
| (F('9.99999e+8'), '.4g', '1e+09'), |
| # Check round-ties-to-even behaviour |
| (F('-0.115'), '.2g', '-0.12'), |
| (F('-0.125'), '.2g', '-0.12'), |
| (F('-0.135'), '.2g', '-0.14'), |
| (F('-0.145'), '.2g', '-0.14'), |
| (F('0.115'), '.2g', '0.12'), |
| (F('0.125'), '.2g', '0.12'), |
| (F('0.135'), '.2g', '0.14'), |
| (F('0.145'), '.2g', '0.14'), |
| # Trailing zeros and decimal point suppressed by default ... |
| (F(0), '.6g', '0'), |
| (F('123.400'), '.6g', '123.4'), |
| (F('123.000'), '.6g', '123'), |
| (F('120.000'), '.6g', '120'), |
| (F('12000000'), '.6g', '1.2e+07'), |
| # ... but not when alternate form is in effect |
| (F(0), '#.6g', '0.00000'), |
| (F('123.400'), '#.6g', '123.400'), |
| (F('123.000'), '#.6g', '123.000'), |
| (F('120.000'), '#.6g', '120.000'), |
| (F('12000000'), '#.6g', '1.20000e+07'), |
| # 'G' format (uses 'E' instead of 'e' for the exponent indicator) |
| (F('123.45678'), '.6G', '123.457'), |
| (F('1234567.8'), '.6G', '1.23457E+06'), |
| # Default precision is 6 significant figures |
| (F('3.1415926535'), 'g', '3.14159'), |
| # Precision 0 is treated the same as precision 1. |
| (F('0.000031415'), '.0g', '3e-05'), |
| (F('0.00031415'), '.0g', '0.0003'), |
| (F('0.31415'), '.0g', '0.3'), |
| (F('3.1415'), '.0g', '3'), |
| (F('3.1415'), '#.0g', '3.'), |
| (F('31.415'), '.0g', '3e+01'), |
| (F('31.415'), '#.0g', '3.e+01'), |
| (F('0.000031415'), '.1g', '3e-05'), |
| (F('0.00031415'), '.1g', '0.0003'), |
| (F('0.31415'), '.1g', '0.3'), |
| (F('3.1415'), '.1g', '3'), |
| (F('3.1415'), '#.1g', '3.'), |
| (F('31.415'), '.1g', '3e+01'), |
| # Thousands separator |
| (F(2**64), '_.25g', '18_446_744_073_709_551_616'), |
| # As with 'e' format, z flag is legal, but has no effect |
| (F(-1, 7**100), 'zg', '-3.09169e-85'), |
| ] |
| for fraction, spec, expected in testcases: |
| with self.subTest(fraction=fraction, spec=spec): |
| self.assertEqual(format(fraction, spec), expected) |
| |
| def test_invalid_formats(self): |
| fraction = F(2, 3) |
| with self.assertRaises(TypeError): |
| format(fraction, None) |
| |
| invalid_specs = [ |
| 'Q6f', # regression test |
| # illegal to use fill or alignment when zero padding |
| 'X>010f', |
| 'X<010f', |
| 'X^010f', |
| 'X=010f', |
| '0>010f', |
| '0<010f', |
| '0^010f', |
| '0=010f', |
| '>010f', |
| '<010f', |
| '^010f', |
| '=010e', |
| '=010f', |
| '=010g', |
| '=010%', |
| '>00.2f', |
| '>00f', |
| # Too many zeros - minimum width should not have leading zeros |
| '006f', |
| # Leading zeros in precision |
| '.010f', |
| '.02f', |
| '.000f', |
| # Missing precision |
| '.e', |
| '.f', |
| '.g', |
| '.%', |
| # Z instead of z for negative zero suppression |
| 'Z.2f' |
| ] |
| for spec in invalid_specs: |
| with self.subTest(spec=spec): |
| with self.assertRaises(ValueError): |
| format(fraction, spec) |
| |
| |
| if __name__ == '__main__': |
| unittest.main() |
