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gh-93476: Fraction.limit_denominator speed increase #93477

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gh-93476: Fraction.limit_denominator speed increase #93477

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599c55b
gh-93476: Fraction.limit_denominator speed increases
mscuthbert Jun 3, 2022
70ca7ad
add NEWS.d item
mscuthbert Jun 3, 2022
a1a4fc8
Fix boundary case.
mscuthbert Jun 4, 2022
3c06ded
Review comments
mscuthbert Jun 5, 2022
e5ab32e
trailing space
mscuthbert Jun 5, 2022
40cbe78
return Fraction(self) for limit case
mscuthbert Jun 5, 2022
f5daa21
drop comment for now. can be separate PR
mscuthbert Jun 5, 2022
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24 changes: 18 additions & 6 deletions Lib/fractions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -234,10 +234,11 @@ def limit_denominator(self, max_denominator=1000000):
if max_denominator < 1:
raise ValueError("max_denominator should be at least 1")
if self._denominator <= max_denominator:
return Fraction(self)
return Fraction(self._numerator, self._denominator, _normalize=False)
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Does this change make a significant difference to performance? If not, I'd suggest reverting it, both for readability and for the purposes of keeping the PR focused. From looking at the code, a simple Fraction(self) shouldn't end up doing any gcd calculation here.

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It actually saves 30% on this case based on tests above -- however, I hadn't realized at the time that the return self was executed in this branch and no normalization was done. The speed increase is probably based on the isinstance() check, which just keeps getting faster and faster in subsequent versions, so it might eventually be the faster route. I've removed the change.

If Fractions are eventually to be truly immutable and hashable, then return self is the correct response here, but that is probably backwards incompatible with real code where people change _numerator or _denominator after instantiation.


p0, q0, p1, q1 = 0, 1, 1, 0
n, d = self._numerator, self._denominator
n_original, d_original = n, d
while True:
a = n//d
q2 = q0+a*q1
Expand All @@ -247,12 +248,23 @@ def limit_denominator(self, max_denominator=1000000):
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
bound1_n = p0 + k*p1
bound1_d = q0 + k*q1
bound2_n = p1
bound2_d = q1
bound1_minus_self_n = abs((bound1_n * d_original)
- (n_original * bound1_d))
bound1_minus_self_d = d_original * bound1_d
bound2_minus_self_n = abs((bound2_n * d_original)
- (n_original * bound2_d))
bound2_minus_self_d = d_original * bound2_d

difference = ((bound1_minus_self_n * bound2_minus_self_d)
- (bound2_minus_self_n * bound1_minus_self_d))
if difference >= 0:
return Fraction(bound2_n, bound2_d)
else:
return bound1
return Fraction(bound1_n, bound1_d)

@property
def numerator(a):
Expand Down
2 changes: 2 additions & 0 deletions Misc/NEWS.d/next/Library/2022-06-03-11-17-49.gh-issue-93476.vvjcGL.rst
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@@ -0,0 +1,2 @@
:meth:`fractions.Fraction.limit_denominator()` performance enhancements.
Patch by Michael Scott Asato Cuthbert.