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Minor optimization for Fractions.limit_denominator #93730

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Merged
ambv merged 4 commits into from
Jun 21, 2022
Merged

Minor optimization for Fractions.limit_denominator #93730

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f69321c
Minor optimization for Fractions.limit_denominator
mdickinson Jun 11, 2022
9ac09a1
More efficient comparison of candidates
mdickinson Jun 12, 2022
be8c332
Fix typo in comment
mdickinson Jun 12, 2022
6f70f58
Tweak to remove an extra operation
mdickinson Jun 12, 2022
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Tweak to remove an extra operation
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@mdickinson
mdickinson committed Jun 12, 2022
commit 6f70f586783b7c3ff6c23af1ac32f791332ebd00
11 changes: 5 additions & 6 deletions Lib/fractions.py
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Expand Up @@ -247,12 +247,11 @@ def limit_denominator(self, max_denominator=1000000):
n, d = d, n-a*d
k = (max_denominator-q0)//q1

# Determine which of the candidate fractions (p0+k*p1)/(q0+k*q1) and
# p1/q1 is closer to self. The distance between the two candidates is
# 1/(q1*(q0+k*q1)), while the distance from p1/q1 to self is
# 1/(q1*(q0+n/d*q1)). So we need to compare 2*(q0+k*q1) with q0+n/d*q1.
# That translates to the following comparison in integers.
if (q0+2*k*q1)*d <= q1*n:
# 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 Fraction(p0+k*p1, q0+k*q1, _normalize=False)
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