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Minor optimization for Fractions.limit_denominator (GH-93730)
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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@ -245,14 +245,16 @@ def limit_denominator(self, max_denominator=1000000):
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break
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p0, q0, p1, q1 = p1, q1, p0+a*p1, q2
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n, d = d, n-a*d
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k = (max_denominator-q0)//q1
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bound1 = Fraction(p0+k*p1, q0+k*q1)
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bound2 = Fraction(p1, q1)
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if abs(bound2 - self) <= abs(bound1-self):
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return bound2
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# Determine which of the candidates (p0+k*p1)/(q0+k*q1) and p1/q1 is
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# closer to self. The distance between them is 1/(q1*(q0+k*q1)), while
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# the distance from p1/q1 to self is d/(q1*self._denominator). So we
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# need to compare 2*(q0+k*q1) with self._denominator/d.
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if 2*d*(q0+k*q1) <= self._denominator:
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return Fraction(p1, q1, _normalize=False)
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else:
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return bound1
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return Fraction(p0+k*p1, q0+k*q1, _normalize=False)
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@property
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def numerator(a):
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