#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 leif):
Replying to [comment:35 leif]:
> Replying to [comment:33 rohana]:
> > I am probably going to remove the bound flag and instead put a warning
about larger values not being well tested if/when they are called.
>
> Yes, I also think we can or should drop any "artificial" limit now,
though I must admit I haven't really looked at the code yet...
Ah, I see, you already removed the restriction in patch v8 (and also added
warnings w.r.t. seemingly "endless" computations, which I also wanted to
suggest).
There's a small typo in `__call__()`'s docstring (the `2**32` should read
`2**64`):
{{{
This implementation uses unsigned 64-bit ints and thus does not
support `x >= 2**32`::
sage: prime_pi(2^64)
Traceback (most recent call last):
...
NotImplementedError: computation of prime_pi for x >= 2^64 is
not implemented
}}}
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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:36>
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