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

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Merged
mdickinson merged 13 commits intopython:mainfromskirpichev:opt-fractions-new
Feb 27, 2023
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9cc62f7
gh-101773: Optimize creation of Fraction's in private methods
skirpichevFeb 10, 2023
836d3a6
Merge branch 'main' into opt-fractions-new
skirpichevFeb 10, 2023
3625d34
Adjust signature of _from_pair() and add docstring
skirpichevFeb 11, 2023
9e66b5a
Use new helper in from_float/Decimal
skirpichevFeb 11, 2023
4324391
Restore back _normalize kwarg for the Fraction.__new__()
skirpichevFeb 11, 2023
b0dca38
Amend 3625d34155
skirpichevFeb 11, 2023
3a8506d
Nitpick on docstring (int's -> ints)
skirpichevFeb 27, 2023
13262af
Revert "Restore back _normalize kwarg for the Fraction.__new__()"
skirpichevFeb 27, 2023
4e8977a
Rename: _from_pair -> _from_coprime_ints
skirpichevFeb 27, 2023
57ac373
Merge branch 'main' into opt-fractions-new
skirpichevFeb 27, 2023
4b4a386
Update Misc/NEWS.d/next/Library/2023-02-10-11-59-13.gh-issue-101773.J…
skirpichevFeb 27, 2023
580b1be
+1
skirpichevFeb 27, 2023
53d5e94
Tweak docstring wording
mdickinsonFeb 27, 2023
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gh-101773: Optimize creation of Fraction's in private methods
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@skirpichev
skirpichev committedFeb 10, 2023
commit9cc62f7c849f4e0d60efb71f8eec6bd4933ec1d7
70 changes: 39 additions & 31 deletionsLib/fractions.py
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Expand Up@@ -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
Expand DownExpand Up@@ -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
Expand DownExpand Up@@ -315,6 +314,13 @@ def from_decimal(cls, dec):
(cls.__name__, dec, type(dec).__name__))
return cls(*dec.as_integer_ratio())

@classmethod
def _from_pair(cls, num, den):
obj = super(Fraction, cls).__new__(cls)
obj._numerator = num
obj._denominator = den
return obj

def is_integer(self):
"""Return True if the Fraction is an integer."""
return self._denominator == 1
Expand DownExpand Up@@ -380,9 +386,9 @@ 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_pair(p1, q1)
else:
return Fraction(p0+k*p1, q0+k*q1, _normalize=False)
return Fraction._from_pair(p0+k*p1, q0+k*q1)

@property
def numerator(a):
Expand DownExpand Up@@ -703,13 +709,13 @@ 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_pair(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_pair(t, s * db)
return Fraction._from_pair(t // g2, s * (db // g2))

__add__, __radd__ = _operator_fallbacks(_add, operator.add)

Expand All@@ -719,13 +725,13 @@ 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_pair(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_pair(t, s * db)
return Fraction._from_pair(t // g2, s * (db // g2))

__sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)

Expand All@@ -741,15 +747,17 @@ def _mul(a, b):
if g2 > 1:
nb //= g2
da //= g2
return Fraction(na * nb, db * da, _normalize=False)
return Fraction._from_pair(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
Expand All@@ -761,7 +769,7 @@ 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_pair(n, d)

__truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)

Expand DownExpand Up@@ -798,17 +806,17 @@ 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_pair(a._numerator ** power,
a._denominator ** power)
elif a._numerator > 0:
return Fraction._from_pair(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_pair((-a._denominator) ** -power,
(-a._numerator) ** -power)
else:
# A fractional power will generally produce an
# irrational number.
Expand All@@ -832,15 +840,15 @@ 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_pair(a._numerator, a._denominator)

def __neg__(a):
"""-a"""
return Fraction(-a._numerator, a._denominator, _normalize=False)
return Fraction._from_pair(-a._numerator, a._denominator)

def __abs__(a):
"""abs(a)"""
return Fraction(abs(a._numerator), a._denominator, _normalize=False)
return Fraction._from_pair(abs(a._numerator), a._denominator)

def __int__(a, _index=operator.index):
"""int(a)"""
Expand Down
1 change: 1 addition & 0 deletionsLib/test/test_fractions.py
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Expand Up@@ -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))
Expand Down
2 changes: 1 addition & 1 deletionLib/test/test_numeric_tower.py
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Expand Up@@ -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_pair(DummyIntegral(1), DummyIntegral(2))
self.assertRaises(TypeError, lambda: x.numerator/x.denominator)
self.assertEqual(float(x), 0.5)

Expand Down
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@@ -0,0 +1 @@
Optimize:class:`fractions.Fraction` for small components.
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