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"""Tests for binary operators on subtypes of built-in types."""
import unittest
from test import support
def gcd(a, b):
"""Greatest common divisor using Euclid's algorithm."""
while a:
a, b = b%a, a
return b
def isint(x):
"""Test whether an object is an instance of int or long."""
return isinstance(x, int) or isinstance(x, int)
def isnum(x):
"""Test whether an object is an instance of a built-in numeric type."""
for T in int, int, float, complex:
if isinstance(x, T):
return 1
return 0
def isRat(x):
"""Test wheter an object is an instance of the Rat class."""
return isinstance(x, Rat)
class Rat(object):
"""Rational number implemented as a normalized pair of longs."""
__slots__ = ['_Rat__num', '_Rat__den']
def __init__(self, num=0, den=1):
"""Constructor: Rat([num[, den]]).
The arguments must be ints or longs, and default to (0, 1)."""
if not isint(num):
raise TypeError("Rat numerator must be int or long (%r)" % num)
if not isint(den):
raise TypeError("Rat denominator must be int or long (%r)" % den)
# But the zero is always on
if den == 0:
raise ZeroDivisionError("zero denominator")
g = gcd(den, num)
self.__num = int(num//g)
self.__den = int(den//g)
def _get_num(self):
"""Accessor function for read-only 'num' attribute of Rat."""
return self.__num
num = property(_get_num, None)
def _get_den(self):
"""Accessor function for read-only 'den' attribute of Rat."""
return self.__den
den = property(_get_den, None)
def __repr__(self):
"""Convert a Rat to an string resembling a Rat constructor call."""
return "Rat(%d, %d)" % (self.__num, self.__den)
def __str__(self):
"""Convert a Rat to a string resembling a decimal numeric value."""
return str(float(self))
def __float__(self):
"""Convert a Rat to a float."""
return self.__num*1.0/self.__den
def __int__(self):
"""Convert a Rat to an int; self.den must be 1."""
if self.__den == 1:
try:
return int(self.__num)
except OverflowError:
raise OverflowError("%s too large to convert to int" %
repr(self))
raise ValueError("can't convert %s to int" % repr(self))
def __add__(self, other):
"""Add two Rats, or a Rat and a number."""
if isint(other):
other = Rat(other)
if isRat(other):
return Rat(self.__num*other.__den + other.__num*self.__den,
self.__den*other.__den)
if isnum(other):
return float(self) + other
return NotImplemented
__radd__ = __add__
def __sub__(self, other):
"""Subtract two Rats, or a Rat and a number."""
if isint(other):
other = Rat(other)
if isRat(other):
return Rat(self.__num*other.__den - other.__num*self.__den,
self.__den*other.__den)
if isnum(other):
return float(self) - other
return NotImplemented
def __rsub__(self, other):
"""Subtract two Rats, or a Rat and a number (reversed args)."""
if isint(other):
other = Rat(other)
if isRat(other):
return Rat(other.__num*self.__den - self.__num*other.__den,
self.__den*other.__den)
if isnum(other):
return other - float(self)
return NotImplemented
def __mul__(self, other):
"""Multiply two Rats, or a Rat and a number."""
if isRat(other):
return Rat(self.__num*other.__num, self.__den*other.__den)
if isint(other):
return Rat(self.__num*other, self.__den)
if isnum(other):
return float(self)*other
return NotImplemented
__rmul__ = __mul__
def __truediv__(self, other):
"""Divide two Rats, or a Rat and a number."""
if isRat(other):
return Rat(self.__num*other.__den, self.__den*other.__num)
if isint(other):
return Rat(self.__num, self.__den*other)
if isnum(other):
return float(self) / other
return NotImplemented
def __rtruediv__(self, other):
"""Divide two Rats, or a Rat and a number (reversed args)."""
if isRat(other):
return Rat(other.__num*self.__den, other.__den*self.__num)
if isint(other):
return Rat(other*self.__den, self.__num)
if isnum(other):
return other / float(self)
return NotImplemented
def __floordiv__(self, other):
"""Divide two Rats, returning the floored result."""
if isint(other):
other = Rat(other)
elif not isRat(other):
return NotImplemented
x = self/other
return x.__num // x.__den
def __rfloordiv__(self, other):
"""Divide two Rats, returning the floored result (reversed args)."""
x = other/self
return x.__num // x.__den
def __divmod__(self, other):
"""Divide two Rats, returning quotient and remainder."""
if isint(other):
other = Rat(other)
elif not isRat(other):
return NotImplemented
x = self//other
return (x, self - other * x)
def __rdivmod__(self, other):
"""Divide two Rats, returning quotient and remainder (reversed args)."""
if isint(other):
other = Rat(other)
elif not isRat(other):
return NotImplemented
return divmod(other, self)
def __mod__(self, other):
"""Take one Rat modulo another."""
return divmod(self, other)[1]
def __rmod__(self, other):
"""Take one Rat modulo another (reversed args)."""
return divmod(other, self)[1]
def __eq__(self, other):
"""Compare two Rats for equality."""
if isint(other):
return self.__den == 1 and self.__num == other
if isRat(other):
return self.__num == other.__num and self.__den == other.__den
if isnum(other):
return float(self) == other
return NotImplemented
def __ne__(self, other):
"""Compare two Rats for inequality."""
return not self == other
class RatTestCase(unittest.TestCase):
"""Unit tests for Rat class and its support utilities."""
def test_gcd(self):
self.assertEqual(gcd(10, 12), 2)
self.assertEqual(gcd(10, 15), 5)
self.assertEqual(gcd(10, 11), 1)
self.assertEqual(gcd(100, 15), 5)
self.assertEqual(gcd(-10, 2), -2)
self.assertEqual(gcd(10, -2), 2)
self.assertEqual(gcd(-10, -2), -2)
for i in range(1, 20):
for j in range(1, 20):
self.assertTrue(gcd(i, j) > 0)
self.assertTrue(gcd(-i, j) < 0)
self.assertTrue(gcd(i, -j) > 0)
self.assertTrue(gcd(-i, -j) < 0)
def test_constructor(self):
a = Rat(10, 15)
self.assertEqual(a.num, 2)
self.assertEqual(a.den, 3)
a = Rat(10, 15)
self.assertEqual(a.num, 2)
self.assertEqual(a.den, 3)
a = Rat(10, -15)
self.assertEqual(a.num, -2)
self.assertEqual(a.den, 3)
a = Rat(-10, 15)
self.assertEqual(a.num, -2)
self.assertEqual(a.den, 3)
a = Rat(-10, -15)
self.assertEqual(a.num, 2)
self.assertEqual(a.den, 3)
a = Rat(7)
self.assertEqual(a.num, 7)
self.assertEqual(a.den, 1)
try:
a = Rat(1, 0)
except ZeroDivisionError:
pass
else:
self.fail("Rat(1, 0) didn't raise ZeroDivisionError")
for bad in "0", 0.0, 0j, (), [], {}, None, Rat, unittest:
try:
a = Rat(bad)
except TypeError:
pass
else:
self.fail("Rat(%r) didn't raise TypeError" % bad)
try:
a = Rat(1, bad)
except TypeError:
pass
else:
self.fail("Rat(1, %r) didn't raise TypeError" % bad)
def test_add(self):
self.assertEqual(Rat(2, 3) + Rat(1, 3), 1)
self.assertEqual(Rat(2, 3) + 1, Rat(5, 3))
self.assertEqual(1 + Rat(2, 3), Rat(5, 3))
self.assertEqual(1.0 + Rat(1, 2), 1.5)
self.assertEqual(Rat(1, 2) + 1.0, 1.5)
def test_sub(self):
self.assertEqual(Rat(7, 2) - Rat(7, 5), Rat(21, 10))
self.assertEqual(Rat(7, 5) - 1, Rat(2, 5))
self.assertEqual(1 - Rat(3, 5), Rat(2, 5))
self.assertEqual(Rat(3, 2) - 1.0, 0.5)
self.assertEqual(1.0 - Rat(1, 2), 0.5)
def test_mul(self):
self.assertEqual(Rat(2, 3) * Rat(5, 7), Rat(10, 21))
self.assertEqual(Rat(10, 3) * 3, 10)
self.assertEqual(3 * Rat(10, 3), 10)
self.assertEqual(Rat(10, 5) * 0.5, 1.0)
self.assertEqual(0.5 * Rat(10, 5), 1.0)
def test_div(self):
self.assertEqual(Rat(10, 3) / Rat(5, 7), Rat(14, 3))
self.assertEqual(Rat(10, 3) / 3, Rat(10, 9))
self.assertEqual(2 / Rat(5), Rat(2, 5))
self.assertEqual(3.0 * Rat(1, 2), 1.5)
self.assertEqual(Rat(1, 2) * 3.0, 1.5)
def test_floordiv(self):
self.assertEqual(Rat(10) // Rat(4), 2)
self.assertEqual(Rat(10, 3) // Rat(4, 3), 2)
self.assertEqual(Rat(10) // 4, 2)
self.assertEqual(10 // Rat(4), 2)
def test_eq(self):
self.assertEqual(Rat(10), Rat(20, 2))
self.assertEqual(Rat(10), 10)
self.assertEqual(10, Rat(10))
self.assertEqual(Rat(10), 10.0)
self.assertEqual(10.0, Rat(10))
def test_true_div(self):
self.assertEqual(Rat(10, 3) / Rat(5, 7), Rat(14, 3))
self.assertEqual(Rat(10, 3) / 3, Rat(10, 9))
self.assertEqual(2 / Rat(5), Rat(2, 5))
self.assertEqual(3.0 * Rat(1, 2), 1.5)
self.assertEqual(Rat(1, 2) * 3.0, 1.5)
self.assertEqual(eval('1/2'), 0.5)
# XXX Ran out of steam; TO DO: divmod, div, future division
def test_main():
support.run_unittest(RatTestCase)
if __name__ == "__main__":
test_main()
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