#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 rohana):
So through the updates, I haven't been keeping `legendres_formula` up to
date. I am posting a patch that should fix the bugs that were present for
the past few versions (primarily, calling it with a relatively small `x`
in comparison to `a` would give an extremely wrong answer due to overflow
issues). I have also changed the name, so it now is called either
`legendre_phi` or `partial_sieve_function`.
The patch also makes all documentation use `^`, there are no longer any
instances of `**`.
The patch also touches up on `__phi` and `__phi32` -- cleaning up code,
adding a few comments, and makes a simple optimization to reduce boolean
checks for small `x` values (~10% speedup for large input).
I'm hoping this will be the final patch for this ticket, so that I don't
go into the double digits for version numbers :-).
Apply only trac_11475v9.patch
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:40>
Sage <http://www.sagemath.org>
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