diff --git a/Lib/fractions.py b/Lib/fractions.py index 49a3f2841a2ed4..f718b35639beee 100644 --- a/Lib/fractions.py +++ b/Lib/fractions.py @@ -183,7 +183,7 @@ class Fraction(numbers.Rational): __slots__ = ('_numerator', '_denominator') # We're immutable, so use __new__ not __init__ - def __new__(cls, numerator=0, denominator=None, *, _normalize=True): + def __new__(cls, numerator=0, denominator=None): """Constructs a Rational. Takes a string like '3/2' or '1.5', another Rational instance, a @@ -279,12 +279,11 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True): if denominator == 0: raise ZeroDivisionError('Fraction(%s, 0)' % numerator) - if _normalize: - g = math.gcd(numerator, denominator) - if denominator < 0: - g = -g - numerator //= g - denominator //= g + g = math.gcd(numerator, denominator) + if denominator < 0: + g = -g + numerator //= g + denominator //= g self._numerator = numerator self._denominator = denominator return self @@ -301,7 +300,7 @@ def from_float(cls, f): elif not isinstance(f, float): raise TypeError("%s.from_float() only takes floats, not %r (%s)" % (cls.__name__, f, type(f).__name__)) - return cls(*f.as_integer_ratio()) + return cls._from_coprime_ints(*f.as_integer_ratio()) @classmethod def from_decimal(cls, dec): @@ -313,7 +312,19 @@ def from_decimal(cls, dec): raise TypeError( "%s.from_decimal() only takes Decimals, not %r (%s)" % (cls.__name__, dec, type(dec).__name__)) - return cls(*dec.as_integer_ratio()) + return cls._from_coprime_ints(*dec.as_integer_ratio()) + + @classmethod + def _from_coprime_ints(cls, numerator, denominator, /): + """Convert a pair of ints to a rational number, for internal use. + + The ratio of integers should be in lowest terms and the denominator + should be positive. + """ + obj = super(Fraction, cls).__new__(cls) + obj._numerator = numerator + obj._denominator = denominator + return obj def is_integer(self): """Return True if the Fraction is an integer.""" @@ -380,9 +391,9 @@ def limit_denominator(self, max_denominator=1000000): # the distance from p1/q1 to self is d/(q1*self._denominator). So we # need to compare 2*(q0+k*q1) with self._denominator/d. if 2*d*(q0+k*q1) <= self._denominator: - return Fraction(p1, q1, _normalize=False) + return Fraction._from_coprime_ints(p1, q1) else: - return Fraction(p0+k*p1, q0+k*q1, _normalize=False) + return Fraction._from_coprime_ints(p0+k*p1, q0+k*q1) @property def numerator(a): @@ -703,13 +714,13 @@ def _add(a, b): nb, db = b._numerator, b._denominator g = math.gcd(da, db) if g == 1: - return Fraction(na * db + da * nb, da * db, _normalize=False) + return Fraction._from_coprime_ints(na * db + da * nb, da * db) s = da // g t = na * (db // g) + nb * s g2 = math.gcd(t, g) if g2 == 1: - return Fraction(t, s * db, _normalize=False) - return Fraction(t // g2, s * (db // g2), _normalize=False) + return Fraction._from_coprime_ints(t, s * db) + return Fraction._from_coprime_ints(t // g2, s * (db // g2)) __add__, __radd__ = _operator_fallbacks(_add, operator.add) @@ -719,13 +730,13 @@ def _sub(a, b): nb, db = b._numerator, b._denominator g = math.gcd(da, db) if g == 1: - return Fraction(na * db - da * nb, da * db, _normalize=False) + return Fraction._from_coprime_ints(na * db - da * nb, da * db) s = da // g t = na * (db // g) - nb * s g2 = math.gcd(t, g) if g2 == 1: - return Fraction(t, s * db, _normalize=False) - return Fraction(t // g2, s * (db // g2), _normalize=False) + return Fraction._from_coprime_ints(t, s * db) + return Fraction._from_coprime_ints(t // g2, s * (db // g2)) __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub) @@ -741,15 +752,17 @@ def _mul(a, b): if g2 > 1: nb //= g2 da //= g2 - return Fraction(na * nb, db * da, _normalize=False) + return Fraction._from_coprime_ints(na * nb, db * da) __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul) def _div(a, b): """a / b""" # Same as _mul(), with inversed b. - na, da = a._numerator, a._denominator nb, db = b._numerator, b._denominator + if nb == 0: + raise ZeroDivisionError('Fraction(%s, 0)' % db) + na, da = a._numerator, a._denominator g1 = math.gcd(na, nb) if g1 > 1: na //= g1 @@ -761,7 +774,7 @@ def _div(a, b): n, d = na * db, nb * da if d < 0: n, d = -n, -d - return Fraction(n, d, _normalize=False) + return Fraction._from_coprime_ints(n, d) __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv) @@ -798,17 +811,17 @@ def __pow__(a, b): if b.denominator == 1: power = b.numerator if power >= 0: - return Fraction(a._numerator ** power, - a._denominator ** power, - _normalize=False) - elif a._numerator >= 0: - return Fraction(a._denominator ** -power, - a._numerator ** -power, - _normalize=False) + return Fraction._from_coprime_ints(a._numerator ** power, + a._denominator ** power) + elif a._numerator > 0: + return Fraction._from_coprime_ints(a._denominator ** -power, + a._numerator ** -power) + elif a._numerator == 0: + raise ZeroDivisionError('Fraction(%s, 0)' % + a._denominator ** -power) else: - return Fraction((-a._denominator) ** -power, - (-a._numerator) ** -power, - _normalize=False) + return Fraction._from_coprime_ints((-a._denominator) ** -power, + (-a._numerator) ** -power) else: # A fractional power will generally produce an # irrational number. @@ -832,15 +845,15 @@ def __rpow__(b, a): def __pos__(a): """+a: Coerces a subclass instance to Fraction""" - return Fraction(a._numerator, a._denominator, _normalize=False) + return Fraction._from_coprime_ints(a._numerator, a._denominator) def __neg__(a): """-a""" - return Fraction(-a._numerator, a._denominator, _normalize=False) + return Fraction._from_coprime_ints(-a._numerator, a._denominator) def __abs__(a): """abs(a)""" - return Fraction(abs(a._numerator), a._denominator, _normalize=False) + return Fraction._from_coprime_ints(abs(a._numerator), a._denominator) def __int__(a, _index=operator.index): """int(a)""" diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py index 3bc6b409e05dc3..e112f49d2e7944 100644 --- a/Lib/test/test_fractions.py +++ b/Lib/test/test_fractions.py @@ -488,6 +488,7 @@ def testArithmetic(self): self.assertEqual(F(5, 6), F(2, 3) * F(5, 4)) self.assertEqual(F(1, 4), F(1, 10) / F(2, 5)) self.assertEqual(F(-15, 8), F(3, 4) / F(-2, 5)) + self.assertRaises(ZeroDivisionError, operator.truediv, F(1), F(0)) self.assertTypedEquals(2, F(9, 10) // F(2, 5)) self.assertTypedEquals(10**23, F(10**23, 1) // F(1)) self.assertEqual(F(5, 6), F(7, 3) % F(3, 2)) diff --git a/Lib/test/test_numeric_tower.py b/Lib/test/test_numeric_tower.py index 9cd85e13634c2b..337682d6bac96c 100644 --- a/Lib/test/test_numeric_tower.py +++ b/Lib/test/test_numeric_tower.py @@ -145,7 +145,7 @@ def test_fractions(self): # The numbers ABC doesn't enforce that the "true" division # of integers produces a float. This tests that the # Rational.__float__() method has required type conversions. - x = F(DummyIntegral(1), DummyIntegral(2), _normalize=False) + x = F._from_coprime_ints(DummyIntegral(1), DummyIntegral(2)) self.assertRaises(TypeError, lambda: x.numerator/x.denominator) self.assertEqual(float(x), 0.5) diff --git a/Misc/NEWS.d/next/Library/2023-02-10-11-59-13.gh-issue-101773.J_kI7y.rst b/Misc/NEWS.d/next/Library/2023-02-10-11-59-13.gh-issue-101773.J_kI7y.rst new file mode 100644 index 00000000000000..b577d93d28c2ae --- /dev/null +++ b/Misc/NEWS.d/next/Library/2023-02-10-11-59-13.gh-issue-101773.J_kI7y.rst @@ -0,0 +1,2 @@ +Optimize :class:`fractions.Fraction` for small components. The private argument +``_normalize`` of the :class:`fractions.Fraction` constructor has been removed.