"""Tests for Lib/rational.py.""" from decimal import Decimal from test.test_support import run_unittest, verbose import math import operator import rational import unittest R = rational.Rational def _components(r): return (r.numerator, r.denominator) class RationalTest(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 as e: self.assertEquals(message, str(e)) else: self.fail("%s not raised" % exc_type.__name__) def testInit(self): self.assertEquals((0, 1), _components(R())) self.assertEquals((7, 1), _components(R(7))) self.assertEquals((7, 3), _components(R(R(7, 3)))) self.assertEquals((-1, 1), _components(R(-1, 1))) self.assertEquals((-1, 1), _components(R(1, -1))) self.assertEquals((1, 1), _components(R(-2, -2))) self.assertEquals((1, 2), _components(R(5, 10))) self.assertEquals((7, 15), _components(R(7, 15))) self.assertEquals((10**23, 1), _components(R(10**23))) self.assertRaisesMessage(ZeroDivisionError, "Rational(12, 0)", R, 12, 0) self.assertRaises(TypeError, R, 1.5) self.assertRaises(TypeError, R, 1.5 + 3j) self.assertRaises(TypeError, R, R(1, 2), 3) self.assertRaises(TypeError, R, "3/2", 3) def testFromString(self): self.assertEquals((5, 1), _components(R("5"))) self.assertEquals((3, 2), _components(R("3/2"))) self.assertEquals((3, 2), _components(R(" \n +3/2"))) self.assertEquals((-3, 2), _components(R("-3/2 "))) self.assertEquals((3, 2), _components(R(" 03/02 \n "))) self.assertEquals((3, 2), _components(R(" 03/02 \n "))) self.assertRaisesMessage( ZeroDivisionError, "Rational(3, 0)", R, "3/0") self.assertRaisesMessage( ValueError, "Invalid literal for Rational: 3/", R, "3/") self.assertRaisesMessage( ValueError, "Invalid literal for Rational: 3 /2", R, "3 /2") self.assertRaisesMessage( # Denominators don't need a sign. ValueError, "Invalid literal for Rational: 3/+2", R, "3/+2") self.assertRaisesMessage( # Imitate float's parsing. ValueError, "Invalid literal for Rational: + 3/2", R, "+ 3/2") self.assertRaisesMessage( # Only parse fractions, not decimals. ValueError, "Invalid literal for Rational: 3.2", R, "3.2") def testImmutable(self): r = R(7, 3) r.__init__(2, 15) self.assertEquals((7, 3), _components(r)) def testFromFloat(self): self.assertRaisesMessage( TypeError, "Rational.from_float() only takes floats, not 3 (int)", R.from_float, 3) self.assertEquals((0, 1), _components(R.from_float(-0.0))) self.assertEquals((10, 1), _components(R.from_float(10.0))) self.assertEquals((-5, 2), _components(R.from_float(-2.5))) self.assertEquals((99999999999999991611392, 1), _components(R.from_float(1e23))) self.assertEquals(float(10**23), float(R.from_float(1e23))) self.assertEquals((3602879701896397, 1125899906842624), _components(R.from_float(3.2))) self.assertEquals(3.2, float(R.from_float(3.2))) inf = 1e1000 nan = inf - inf self.assertRaisesMessage( TypeError, "Cannot convert inf to Rational.", R.from_float, inf) self.assertRaisesMessage( TypeError, "Cannot convert -inf to Rational.", R.from_float, -inf) self.assertRaisesMessage( TypeError, "Cannot convert nan to Rational.", R.from_float, nan) def testFromDecimal(self): self.assertRaisesMessage( TypeError, "Rational.from_decimal() only takes Decimals, not 3 (int)", R.from_decimal, 3) self.assertEquals(R(0), R.from_decimal(Decimal("-0"))) self.assertEquals(R(5, 10), R.from_decimal(Decimal("0.5"))) self.assertEquals(R(5, 1000), R.from_decimal(Decimal("5e-3"))) self.assertEquals(R(5000), R.from_decimal(Decimal("5e3"))) self.assertEquals(1 - R(1, 10**30), R.from_decimal(Decimal("0." + "9" * 30))) self.assertRaisesMessage( TypeError, "Cannot convert Infinity to Rational.", R.from_decimal, Decimal("inf")) self.assertRaisesMessage( TypeError, "Cannot convert -Infinity to Rational.", R.from_decimal, Decimal("-inf")) self.assertRaisesMessage( TypeError, "Cannot convert NaN to Rational.", R.from_decimal, Decimal("nan")) self.assertRaisesMessage( TypeError, "Cannot convert sNaN to Rational.", R.from_decimal, Decimal("snan")) def testConversions(self): self.assertTypedEquals(-1, trunc(R(-11, 10))) self.assertTypedEquals(-2, math.floor(R(-11, 10))) self.assertTypedEquals(-1, math.ceil(R(-11, 10))) self.assertTypedEquals(-1, math.ceil(R(-10, 10))) self.assertTypedEquals(0, round(R(-1, 10))) self.assertTypedEquals(0, round(R(-5, 10))) self.assertTypedEquals(-2, round(R(-15, 10))) self.assertTypedEquals(-1, round(R(-7, 10))) self.assertEquals(False, bool(R(0, 1))) self.assertEquals(True, bool(R(3, 2))) self.assertTypedEquals(0.1, float(R(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.assertAlmostEquals(2.0/3, float(R(int('2'*400+'7'), int('3'*400+'1')))) self.assertTypedEquals(0.1+0j, complex(R(1,10))) def testRound(self): self.assertTypedEquals(R(-200), round(R(-150), -2)) self.assertTypedEquals(R(-200), round(R(-250), -2)) self.assertTypedEquals(R(30), round(R(26), -1)) self.assertTypedEquals(R(-2, 10), round(R(-15, 100), 1)) self.assertTypedEquals(R(-2, 10), round(R(-25, 100), 1)) def testArithmetic(self): self.assertEquals(R(1, 2), R(1, 10) + R(2, 5)) self.assertEquals(R(-3, 10), R(1, 10) - R(2, 5)) self.assertEquals(R(1, 25), R(1, 10) * R(2, 5)) self.assertEquals(R(1, 4), R(1, 10) / R(2, 5)) self.assertTypedEquals(2, R(9, 10) // R(2, 5)) self.assertTypedEquals(10**23, R(10**23, 1) // R(1)) self.assertEquals(R(2, 3), R(-7, 3) % R(3, 2)) self.assertEquals(R(8, 27), R(2, 3) ** R(3)) self.assertEquals(R(27, 8), R(2, 3) ** R(-3)) self.assertTypedEquals(2.0, R(4) ** R(1, 2)) z = pow(R(-1), R(1, 2)) self.assertAlmostEquals(z.real, 0) self.assertEquals(z.imag, 1) def testMixedArithmetic(self): self.assertTypedEquals(R(11, 10), R(1, 10) + 1) self.assertTypedEquals(1.1, R(1, 10) + 1.0) self.assertTypedEquals(1.1 + 0j, R(1, 10) + (1.0 + 0j)) self.assertTypedEquals(R(11, 10), 1 + R(1, 10)) self.assertTypedEquals(1.1, 1.0 + R(1, 10)) self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + R(1, 10)) self.assertTypedEquals(R(-9, 10), R(1, 10) - 1) self.assertTypedEquals(-0.9, R(1, 10) - 1.0) self.assertTypedEquals(-0.9 + 0j, R(1, 10) - (1.0 + 0j)) self.assertTypedEquals(R(9, 10), 1 - R(1, 10)) self.assertTypedEquals(0.9, 1.0 - R(1, 10)) self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - R(1, 10)) self.assertTypedEquals(R(1, 10), R(1, 10) * 1) self.assertTypedEquals(0.1, R(1, 10) * 1.0) self.assertTypedEquals(0.1 + 0j, R(1, 10) * (1.0 + 0j)) self.assertTypedEquals(R(1, 10), 1 * R(1, 10)) self.assertTypedEquals(0.1, 1.0 * R(1, 10)) self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * R(1, 10)) self.assertTypedEquals(R(1, 10), R(1, 10) / 1) self.assertTypedEquals(0.1, R(1, 10) / 1.0) self.assertTypedEquals(0.1 + 0j, R(1, 10) / (1.0 + 0j)) self.assertTypedEquals(R(10, 1), 1 / R(1, 10)) self.assertTypedEquals(10.0, 1.0 / R(1, 10)) self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / R(1, 10)) self.assertTypedEquals(0, R(1, 10) // 1) self.assertTypedEquals(0, R(1, 10) // 1.0) self.assertTypedEquals(10, 1 // R(1, 10)) self.assertTypedEquals(10**23, 10**22 // R(1, 10)) self.assertTypedEquals(10, 1.0 // R(1, 10)) self.assertTypedEquals(R(1, 10), R(1, 10) % 1) self.assertTypedEquals(0.1, R(1, 10) % 1.0) self.assertTypedEquals(R(0, 1), 1 % R(1, 10)) self.assertTypedEquals(0.0, 1.0 % R(1, 10)) # No need for divmod since we don't override it. # ** has more interesting conversion rules. self.assertTypedEquals(R(100, 1), R(1, 10) ** -2) self.assertTypedEquals(R(100, 1), R(10, 1) ** 2) self.assertTypedEquals(0.1, R(1, 10) ** 1.0) self.assertTypedEquals(0.1 + 0j, R(1, 10) ** (1.0 + 0j)) self.assertTypedEquals(4 , 2 ** R(2, 1)) z = pow(-1, R(1, 2)) self.assertAlmostEquals(0, z.real) self.assertEquals(1, z.imag) self.assertTypedEquals(R(1, 4) , 2 ** R(-2, 1)) self.assertTypedEquals(2.0 , 4 ** R(1, 2)) self.assertTypedEquals(0.25, 2.0 ** R(-2, 1)) self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** R(1, 10)) def testMixingWithDecimal(self): # Decimal refuses mixed comparisons. self.assertRaisesMessage( TypeError, "unsupported operand type(s) for +: 'Rational' and 'Decimal'", operator.add, R(3,11), Decimal('3.1415926')) self.assertNotEquals(R(5, 2), Decimal('2.5')) def testComparisons(self): self.assertTrue(R(1, 2) < R(2, 3)) self.assertFalse(R(1, 2) < R(1, 2)) self.assertTrue(R(1, 2) <= R(2, 3)) self.assertTrue(R(1, 2) <= R(1, 2)) self.assertFalse(R(2, 3) <= R(1, 2)) self.assertTrue(R(1, 2) == R(1, 2)) self.assertFalse(R(1, 2) == R(1, 3)) def testMixedLess(self): self.assertTrue(2 < R(5, 2)) self.assertFalse(2 < R(4, 2)) self.assertTrue(R(5, 2) < 3) self.assertFalse(R(4, 2) < 2) self.assertTrue(R(1, 2) < 0.6) self.assertFalse(R(1, 2) < 0.4) self.assertTrue(0.4 < R(1, 2)) self.assertFalse(0.5 < R(1, 2)) def testMixedLessEqual(self): self.assertTrue(0.5 <= R(1, 2)) self.assertFalse(0.6 <= R(1, 2)) self.assertTrue(R(1, 2) <= 0.5) self.assertFalse(R(1, 2) <= 0.4) self.assertTrue(2 <= R(4, 2)) self.assertFalse(2 <= R(3, 2)) self.assertTrue(R(4, 2) <= 2) self.assertFalse(R(5, 2) <= 2) def testBigFloatComparisons(self): # Because 10**23 can't be represented exactly as a float: self.assertFalse(R(10**23) == float(10**23)) # The first test demonstrates why these are important. self.assertFalse(1e23 < float(R(trunc(1e23) + 1))) self.assertTrue(1e23 < R(trunc(1e23) + 1)) self.assertFalse(1e23 <= R(trunc(1e23) - 1)) self.assertTrue(1e23 > R(trunc(1e23) - 1)) self.assertFalse(1e23 >= R(trunc(1e23) + 1)) def testBigComplexComparisons(self): self.assertFalse(R(10**23) == complex(10**23)) self.assertTrue(R(10**23) > complex(10**23)) self.assertFalse(R(10**23) <= complex(10**23)) def testMixedEqual(self): self.assertTrue(0.5 == R(1, 2)) self.assertFalse(0.6 == R(1, 2)) self.assertTrue(R(1, 2) == 0.5) self.assertFalse(R(1, 2) == 0.4) self.assertTrue(2 == R(4, 2)) self.assertFalse(2 == R(3, 2)) self.assertTrue(R(4, 2) == 2) self.assertFalse(R(5, 2) == 2) def testStringification(self): self.assertEquals("Rational(7,3)", repr(R(7, 3))) self.assertEquals("7/3", str(R(7, 3))) self.assertEquals("7", str(R(7, 1))) def testHash(self): self.assertEquals(hash(2.5), hash(R(5, 2))) self.assertEquals(hash(10**50), hash(R(10**50))) self.assertNotEquals(hash(float(10**23)), hash(R(10**23))) def testApproximatePi(self): # Algorithm borrowed from # http://docs.python.org/lib/decimal-recipes.html three = R(3) lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 while abs(s - lasts) > R(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 = R(1) i, lasts, s, fact, num, sign = 0, 0, R(1), 1, 1, 1 while abs(s - lasts) > R(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_main(): run_unittest(RationalTest) if __name__ == '__main__': test_main()