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gh-101773: Optimize creation of Fractions in private methods (#101780) 

This PR adds a private `Fraction._from_coprime_ints` classmethod for internal creations of `Fraction` objects, replacing the use of `_normalize=False` in the existing constructor. This speeds up creation of `Fraction` objects arising from calculations. The `_normalize` argument to the `Fraction` constructor has been removed.

Co-authored-by: Pieter Eendebak <pieter.eendebak@gmail.com>
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
This commit is contained in:
Sergey B Kirpichev 2023-02-27 21:53:22 +03:00 committed by GitHub
parent bb0cf8fd60
commit 4f3786b761
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4 changed files with 50 additions and 34 deletions
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79
Lib/fractions.py
View File

@ -183,7 +183,7 @@ class Fraction(numbers.Rational):
__slots__ = ('_numerator', '_denominator') __slots__ = ('_numerator', '_denominator')
# We're immutable, so use __new__ not __init__ # 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. """Constructs a Rational.
Takes a string like '3/2' or '1.5', another Rational instance, a Takes a string like '3/2' or '1.5', another Rational instance, a
@ -279,12 +279,11 @@ class Fraction(numbers.Rational):
if denominator == 0: if denominator == 0:
raise ZeroDivisionError('Fraction(%s, 0)' % numerator) raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
if _normalize: g = math.gcd(numerator, denominator)
g = math.gcd(numerator, denominator) if denominator < 0:
if denominator < 0: g = -g
g = -g numerator //= g
numerator //= g denominator //= g
denominator //= g
self._numerator = numerator self._numerator = numerator
self._denominator = denominator self._denominator = denominator
return self return self
@ -301,7 +300,7 @@ class Fraction(numbers.Rational):
elif not isinstance(f, float): elif not isinstance(f, float):
raise TypeError("%s.from_float() only takes floats, not %r (%s)" % raise TypeError("%s.from_float() only takes floats, not %r (%s)" %
(cls.__name__, f, type(f).__name__)) (cls.__name__, f, type(f).__name__))
return cls(*f.as_integer_ratio()) return cls._from_coprime_ints(*f.as_integer_ratio())
@classmethod @classmethod
def from_decimal(cls, dec): def from_decimal(cls, dec):
@ -313,7 +312,19 @@ class Fraction(numbers.Rational):
raise TypeError( raise TypeError(
"%s.from_decimal() only takes Decimals, not %r (%s)" % "%s.from_decimal() only takes Decimals, not %r (%s)" %
(cls.__name__, dec, type(dec).__name__)) (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): def is_integer(self):
"""Return True if the Fraction is an integer.""" """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 # 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. # need to compare 2*(q0+k*q1) with self._denominator/d.
if 2*d*(q0+k*q1) <= self._denominator: if 2*d*(q0+k*q1) <= self._denominator:
return Fraction(p1, q1, _normalize=False) return Fraction._from_coprime_ints(p1, q1)
else: else:
return Fraction(p0+k*p1, q0+k*q1, _normalize=False) return Fraction._from_coprime_ints(p0+k*p1, q0+k*q1)
@property @property
def numerator(a): def numerator(a):
@ -703,13 +714,13 @@ class Fraction(numbers.Rational):
nb, db = b._numerator, b._denominator nb, db = b._numerator, b._denominator
g = math.gcd(da, db) g = math.gcd(da, db)
if g == 1: 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 s = da // g
t = na * (db // g) + nb * s t = na * (db // g) + nb * s
g2 = math.gcd(t, g) g2 = math.gcd(t, g)
if g2 == 1: if g2 == 1:
return Fraction(t, s * db, _normalize=False) return Fraction._from_coprime_ints(t, s * db)
return Fraction(t // g2, s * (db // g2), _normalize=False) return Fraction._from_coprime_ints(t // g2, s * (db // g2))
__add__, __radd__ = _operator_fallbacks(_add, operator.add) __add__, __radd__ = _operator_fallbacks(_add, operator.add)
@ -719,13 +730,13 @@ class Fraction(numbers.Rational):
nb, db = b._numerator, b._denominator nb, db = b._numerator, b._denominator
g = math.gcd(da, db) g = math.gcd(da, db)
if g == 1: 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 s = da // g
t = na * (db // g) - nb * s t = na * (db // g) - nb * s
g2 = math.gcd(t, g) g2 = math.gcd(t, g)
if g2 == 1: if g2 == 1:
return Fraction(t, s * db, _normalize=False) return Fraction._from_coprime_ints(t, s * db)
return Fraction(t // g2, s * (db // g2), _normalize=False) return Fraction._from_coprime_ints(t // g2, s * (db // g2))
__sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub) __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)
@ -741,15 +752,17 @@ class Fraction(numbers.Rational):
if g2 > 1: if g2 > 1:
nb //= g2 nb //= g2
da //= 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) __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul)
def _div(a, b): def _div(a, b):
"""a / b""" """a / b"""
# Same as _mul(), with inversed b. # Same as _mul(), with inversed b.
na, da = a._numerator, a._denominator
nb, db = b._numerator, b._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) g1 = math.gcd(na, nb)
if g1 > 1: if g1 > 1:
na //= g1 na //= g1
@ -761,7 +774,7 @@ class Fraction(numbers.Rational):
n, d = na * db, nb * da n, d = na * db, nb * da
if d < 0: if d < 0:
n, d = -n, -d n, d = -n, -d
return Fraction(n, d, _normalize=False) return Fraction._from_coprime_ints(n, d)
__truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv) __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)
@ -798,17 +811,17 @@ class Fraction(numbers.Rational):
if b.denominator == 1: if b.denominator == 1:
power = b.numerator power = b.numerator
if power >= 0: if power >= 0:
return Fraction(a._numerator ** power, return Fraction._from_coprime_ints(a._numerator ** power,
a._denominator ** power, a._denominator ** power)
_normalize=False) elif a._numerator > 0:
elif a._numerator >= 0: return Fraction._from_coprime_ints(a._denominator ** -power,
return Fraction(a._denominator ** -power, a._numerator ** -power)
a._numerator ** -power, elif a._numerator == 0:
_normalize=False) raise ZeroDivisionError('Fraction(%s, 0)' %
a._denominator ** -power)
else: else:
return Fraction((-a._denominator) ** -power, return Fraction._from_coprime_ints((-a._denominator) ** -power,
(-a._numerator) ** -power, (-a._numerator) ** -power)
_normalize=False)
else: else:
# A fractional power will generally produce an # A fractional power will generally produce an
# irrational number. # irrational number.
@ -832,15 +845,15 @@ class Fraction(numbers.Rational):
def __pos__(a): def __pos__(a):
"""+a: Coerces a subclass instance to Fraction""" """+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): def __neg__(a):
"""-a""" """-a"""
return Fraction(-a._numerator, a._denominator, _normalize=False) return Fraction._from_coprime_ints(-a._numerator, a._denominator)
def __abs__(a): def __abs__(a):
"""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): def __int__(a, _index=operator.index):
"""int(a)""" """int(a)"""

1
Lib/test/test_fractions.py
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@ -488,6 +488,7 @@ class FractionTest(unittest.TestCase):
self.assertEqual(F(5, 6), F(2, 3) * F(5, 4)) 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(1, 4), F(1, 10) / F(2, 5))
self.assertEqual(F(-15, 8), F(3, 4) / 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(2, F(9, 10) // F(2, 5))
self.assertTypedEquals(10**23, F(10**23, 1) // F(1)) self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
self.assertEqual(F(5, 6), F(7, 3) % F(3, 2)) self.assertEqual(F(5, 6), F(7, 3) % F(3, 2))

2
Lib/test/test_numeric_tower.py
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@ -145,7 +145,7 @@ class HashTest(unittest.TestCase):
# The numbers ABC doesn't enforce that the "true" division # The numbers ABC doesn't enforce that the "true" division
# of integers produces a float. This tests that the # of integers produces a float. This tests that the
# Rational.__float__() method has required type conversions. # 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.assertRaises(TypeError, lambda: x.numerator/x.denominator)
self.assertEqual(float(x), 0.5) self.assertEqual(float(x), 0.5)

2
Misc/NEWS.d/next/Library/2023-02-10-11-59-13.gh-issue-101773.J_kI7y.rst Normal file
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@ -0,0 +1,2 @@
Optimize :class:`fractions.Fraction` for small components. The private argument
``_normalize`` of the :class:`fractions.Fraction` constructor has been removed.