#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):
Replying to [comment:35 leif]:
> Replying to [comment:33 rohana]:
> > I have verified that `prime_pi` gives correct output for `i*10**12`
with `0 <= i <= 1000` on x86_64 :).
>
> Besides a couple of other values on individual machines,
Which machines have you had issues with? Everything I have tested with v8
has worked (this includes x86 and x86_64 linux, 64bit Snow Leopard, and
Sparc Solaris 10).
----
> I wonder if `legendres_formula()` shouldn't be renamed to
`legendre_phi()` - better names appreciated, but the latter ( \phi(x,a) )
seems to be quite established in literature, and `legendre_phi` would be
analogous to e.g. `euler_phi` in Sage.
Makes sense to me, if no one has an objection to the idea, I'll make the
change.
> I'd also mention in its docstring it's called the ''partial sieve
function''.
Sounds good to me.
----
Replying to [comment:36 leif]:
> Also, there's a mixture of both kinds of exponentiation operators (`^`
and `**`) throughout the [doc]strings; I'm not sure if we shouldn't use
just one notation.
Will do -- probably `^` since it is more consumer friendly.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:37>
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