345 lines
14 KiB
Python
345 lines
14 KiB
Python
"""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()
|