| """Tests for Lib/fractions.py.""" |
| |
| from decimal import Decimal |
| from test.test_support import run_unittest |
| import math |
| import operator |
| import fractions |
| import unittest |
| from copy import copy, deepcopy |
| from cPickle import dumps, loads |
| F = fractions.Fraction |
| gcd = fractions.gcd |
| |
| |
| class GcdTest(unittest.TestCase): |
| |
| def testMisc(self): |
| self.assertEquals(0, gcd(0, 0)) |
| self.assertEquals(1, gcd(1, 0)) |
| self.assertEquals(-1, gcd(-1, 0)) |
| self.assertEquals(1, gcd(0, 1)) |
| self.assertEquals(-1, gcd(0, -1)) |
| self.assertEquals(1, gcd(7, 1)) |
| self.assertEquals(-1, gcd(7, -1)) |
| self.assertEquals(1, gcd(-23, 15)) |
| self.assertEquals(12, gcd(120, 84)) |
| self.assertEquals(-12, gcd(84, -120)) |
| |
| |
| 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.assertEquals(type(expected), type(actual)) |
| self.assertEquals(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, e: |
| self.assertEquals(message, str(e)) |
| else: |
| self.fail("%s not raised" % exc_type.__name__) |
| |
| def testInit(self): |
| self.assertEquals((0, 1), _components(F())) |
| self.assertEquals((7, 1), _components(F(7))) |
| self.assertEquals((7, 3), _components(F(F(7, 3)))) |
| |
| self.assertEquals((-1, 1), _components(F(-1, 1))) |
| self.assertEquals((-1, 1), _components(F(1, -1))) |
| self.assertEquals((1, 1), _components(F(-2, -2))) |
| self.assertEquals((1, 2), _components(F(5, 10))) |
| self.assertEquals((7, 15), _components(F(7, 15))) |
| self.assertEquals((10**23, 1), _components(F(10**23))) |
| |
| self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)", |
| F, 12, 0) |
| self.assertRaises(AttributeError, F, 1.5) |
| self.assertRaises(AttributeError, F, 1.5 + 3j) |
| |
| self.assertRaises(AttributeError, F, F(1, 2), 3) |
| self.assertRaises(AttributeError, F, "3/2", 3) |
| |
| def testFromString(self): |
| self.assertEquals((5, 1), _components(F("5"))) |
| self.assertEquals((3, 2), _components(F("3/2"))) |
| self.assertEquals((3, 2), _components(F(" \n +3/2"))) |
| self.assertEquals((-3, 2), _components(F("-3/2 "))) |
| self.assertEquals((13, 2), _components(F(" 013/02 \n "))) |
| self.assertEquals((13, 2), _components(F(u" 013/02 \n "))) |
| |
| self.assertEquals((16, 5), _components(F(" 3.2 "))) |
| self.assertEquals((-16, 5), _components(F(u" -3.2 "))) |
| self.assertEquals((-3, 1), _components(F(u" -3. "))) |
| self.assertEquals((3, 5), _components(F(u" .6 "))) |
| |
| |
| 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: 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( |
| # Only parse ordinary decimals, not scientific form. |
| ValueError, "Invalid literal for Fraction: 3.2e4", |
| F, "3.2e4") |
| self.assertRaisesMessage( |
| # Don't accept combinations of decimals and fractions. |
| ValueError, "Invalid literal for Fraction: 3/7.2", |
| F, "3/7.2") |
| self.assertRaisesMessage( |
| # Don't accept combinations of decimals and fractions. |
| 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.assertEquals((7, 3), _components(r)) |
| |
| self.assertRaises(AttributeError, setattr, r, 'numerator', 12) |
| self.assertRaises(AttributeError, setattr, r, 'denominator', 6) |
| self.assertEquals((7, 3), _components(r)) |
| |
| # But if you _really_ need to: |
| r._numerator = 4 |
| r._denominator = 2 |
| self.assertEquals((4, 2), _components(r)) |
| # Which breaks some important operations: |
| self.assertNotEquals(F(4, 2), r) |
| |
| def testFromFloat(self): |
| self.assertRaisesMessage( |
| TypeError, "Fraction.from_float() only takes floats, not 3 (int)", |
| F.from_float, 3) |
| |
| self.assertEquals((0, 1), _components(F.from_float(-0.0))) |
| self.assertEquals((10, 1), _components(F.from_float(10.0))) |
| self.assertEquals((-5, 2), _components(F.from_float(-2.5))) |
| self.assertEquals((99999999999999991611392, 1), |
| _components(F.from_float(1e23))) |
| self.assertEquals(float(10**23), float(F.from_float(1e23))) |
| self.assertEquals((3602879701896397, 1125899906842624), |
| _components(F.from_float(3.2))) |
| self.assertEquals(3.2, float(F.from_float(3.2))) |
| |
| inf = 1e1000 |
| nan = inf - inf |
| self.assertRaisesMessage( |
| TypeError, "Cannot convert inf to Fraction.", |
| F.from_float, inf) |
| self.assertRaisesMessage( |
| TypeError, "Cannot convert -inf to Fraction.", |
| F.from_float, -inf) |
| self.assertRaisesMessage( |
| TypeError, "Cannot convert nan to Fraction.", |
| F.from_float, nan) |
| |
| def testFromDecimal(self): |
| self.assertRaisesMessage( |
| TypeError, |
| "Fraction.from_decimal() only takes Decimals, not 3 (int)", |
| F.from_decimal, 3) |
| self.assertEquals(F(0), F.from_decimal(Decimal("-0"))) |
| self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5"))) |
| self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3"))) |
| self.assertEquals(F(5000), F.from_decimal(Decimal("5e3"))) |
| self.assertEquals(1 - F(1, 10**30), |
| F.from_decimal(Decimal("0." + "9" * 30))) |
| |
| self.assertRaisesMessage( |
| TypeError, "Cannot convert Infinity to Fraction.", |
| F.from_decimal, Decimal("inf")) |
| self.assertRaisesMessage( |
| TypeError, "Cannot convert -Infinity to Fraction.", |
| F.from_decimal, Decimal("-inf")) |
| self.assertRaisesMessage( |
| TypeError, "Cannot convert NaN to Fraction.", |
| F.from_decimal, Decimal("nan")) |
| self.assertRaisesMessage( |
| TypeError, "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)) |
| |
| def testConversions(self): |
| self.assertTypedEquals(-1, math.trunc(F(-11, 10))) |
| self.assertTypedEquals(-1, int(F(-11, 10))) |
| |
| self.assertEquals(False, bool(F(0, 1))) |
| self.assertEquals(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, long('2'*400+'7')) |
| self.assertAlmostEquals(2.0/3, |
| float(F(long('2'*400+'7'), long('3'*400+'1')))) |
| |
| self.assertTypedEquals(0.1+0j, complex(F(1,10))) |
| |
| |
| def testArithmetic(self): |
| self.assertEquals(F(1, 2), F(1, 10) + F(2, 5)) |
| self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5)) |
| self.assertEquals(F(1, 25), F(1, 10) * F(2, 5)) |
| self.assertEquals(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.assertEquals(F(2, 3), F(-7, 3) % F(3, 2)) |
| self.assertEquals(F(8, 27), F(2, 3) ** F(3)) |
| self.assertEquals(F(27, 8), F(2, 3) ** F(-3)) |
| self.assertTypedEquals(2.0, F(4) ** F(1, 2)) |
| # Will return 1j in 3.0: |
| self.assertRaises(ValueError, pow, F(-1), F(1, 2)) |
| |
| 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(10.0, 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)) |
| |
| # No need for divmod since we don't override it. |
| |
| # ** 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)) |
| # Will return 1j in 3.0: |
| self.assertRaises(ValueError, pow, (-1), F(1, 2)) |
| 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)) |
| |
| def testMixingWithDecimal(self): |
| # Decimal refuses mixed comparisons. |
| self.assertRaisesMessage( |
| TypeError, |
| "unsupported operand type(s) for +: 'Fraction' and 'Decimal'", |
| operator.add, F(3,11), Decimal('3.1415926')) |
| self.assertNotEquals(F(5, 2), Decimal('2.5')) |
| |
| 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 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)) |
| |
| 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) |
| |
| 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.assertTrue(F(10**23) > complex(10**23)) |
| self.assertFalse(F(10**23) <= complex(10**23)) |
| |
| 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) |
| |
| def testStringification(self): |
| self.assertEquals("Fraction(7, 3)", repr(F(7, 3))) |
| self.assertEquals("7/3", str(F(7, 3))) |
| self.assertEquals("7", str(F(7, 1))) |
| |
| def testHash(self): |
| self.assertEquals(hash(2.5), hash(F(5, 2))) |
| self.assertEquals(hash(10**50), hash(F(10**50))) |
| self.assertNotEquals(hash(float(10**23)), hash(F(10**23))) |
| |
| 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.assertAlmostEquals(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.assertAlmostEquals(math.cos(1), s) |
| |
| def test_copy_deepcopy_pickle(self): |
| r = F(13, 7) |
| self.assertEqual(r, loads(dumps(r))) |
| self.assertEqual(id(r), id(copy(r))) |
| self.assertEqual(id(r), id(deepcopy(r))) |
| |
| def test_main(): |
| run_unittest(FractionTest, GcdTest) |
| |
| if __name__ == '__main__': |
| test_main() |