#11475: improve prime_pi (speedup + small fixes)
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Reporter: rohana | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: number theory | Keywords: primes, prime counting, prime_pi
Work_issues: | Upstream: N/A
Reviewer: | Author: R. Andrew Ohana
Merged: | Dependencies:
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Comment(by ylchapuy):
> A lot of the speed of this algorithm relies on the __cached_count
method, which is essentially a binary search (with a simple adjustment in
the beginning that takes advantage of the density of the primes)
Something like this should give you a 10% speedup for big inputs.
{{{
if p < 200:
pos = p>>2
size = 5
else:
size = self.__numPrimes>>1
# Use the expected density of primes for expected inputs to
make an
# educated guess
if p>>3 < size:
size = p>>3
pos = size
}}}
(beware to make sure there are enough primes cached for small inputs)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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