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Minor optimization for Fractions.limit_denominator (GH-93730)

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When we construct the upper and lower candidates in limit_denominator,
the numerator and denominator are already relatively prime (and the
denominator positive) by construction, so there's no need to go through
the usual normalisation in the constructor. This saves a couple of
potentially expensive gcd calls.

Suggested by Michael Scott Asato Cuthbert in GH-93477.
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Mark Dickinson 2022-06-21 20:36:35 +01:00 committed by GitHub
parent 830513754d
commit 420f0df862
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1 changed files with 8 additions and 6 deletions
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14
Lib/fractions.py
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@ -245,14 +245,16 @@ def limit_denominator(self, max_denominator=1000000):
break
p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
n, d = d, n-a*d
k = (max_denominator-q0)//q1
bound1 = Fraction(p0+k*p1, q0+k*q1)
bound2 = Fraction(p1, q1)
if abs(bound2 - self) <= abs(bound1-self):
return bound2
# Determine which of the candidates (p0+k*p1)/(q0+k*q1) and p1/q1 is
# closer to self. The distance between them is 1/(q1*(q0+k*q1)), while
# 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)
else:
return bound1
return Fraction(p0+k*p1, q0+k*q1, _normalize=False)
@property
def numerator(a):