"""Tests for binary operators on subtypes of built-in types.""" import test_support import unittest class getset(object): """Define a get/set attribute descriptor. This will eventually become a built-in.""" def __init__(self, get, set=None): self.__get = get self.__set = set def __get__(self, inst, type=None): return self.__get(inst) def __set__(self, inst, value): if self.__set is None: raise AttributeError, "this attribute is read-only" return self.__set(inst, value) 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, long) def isnum(x): """Test whether an object is an instance of a built-in numeric type.""" for T in int, long, 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=0L, den=1L): """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 = long(num/g) self.__den = long(den/g) def _get_num(self): """Accessor function for read-only 'num' attribute of Rat.""" return self.__num num = getset(_get_num, None) def _get_den(self): """Accessor function for read-only 'den' attribute of Rat.""" return self.__den den = getset(_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 __long__(self): """Convert a Rat to an long; self.den must be 1.""" if self.__den == 1: return long(self.__num) raise ValueError, "can't convert %s to long" % 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 __div__ = __truediv__ 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 __rdiv__ = __rtruediv__ 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.assert_(gcd(i, j) > 0) self.assert_(gcd(-i, j) < 0) self.assert_(gcd(i, -j) > 0) self.assert_(gcd(-i, -j) < 0) def test_constructor(self): a = Rat(10, 15) self.assertEqual(a.num, 2) self.assertEqual(a.den, 3) a = Rat(10L, 15L) 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_future_div(self): exec future_test # XXX Ran out of steam; TO DO: divmod, div, future division future_test = """ from __future__ import division 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) """ test_support.run_unittest(RatTestCase)