diff options
Diffstat (limited to 'Lib/fractions.py')
| -rw-r--r-- | Lib/fractions.py | 79 |
1 files changed, 46 insertions, 33 deletions
diff --git a/Lib/fractions.py b/Lib/fractions.py index 49a3f2841a..f718b35639 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): # 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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 @@ class Fraction(numbers.Rational): 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)""" |