#16878: faster is_prime
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers: Jeroen Demeyer
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16878 | d55dc6737936077eeee903687207f7af54588439
Dependencies: #15767 | Stopgaps:
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Old description:
> Right now to test if a Sage integer is prime it is faster to call
> `prime_range` rather than `.is_prime()`...
> {{{
> sage: timeit("bool(prime_range(121,122))", number=10000)
> 10000 loops, best of 3: 1.09 µs per loop
> sage: timeit("bool(prime_range(1009,1010))", number=10000)
> 10000 loops, best of 3: 1.2 µs per loop
> }}}
> versus
> {{{
> sage: timeit("121.is_prime()", number=10000)
> 10000 loops, best of 3: 5.3 µs per loop
> sage: timeit("1009.is_prime()", number=10000)
> 10000 loops, best of 3: 4.19 µs per loop
> }}}
>
> The patch does some tiny modifications in `integer.pyx` and we get
> {{{
> sage: timeit("121.is_prime()", number=10000)
> 10000 loops, best of 3: 812 ns per loop
> sage: timeit("1009.is_prime()", number=10000)
> 10000 loops, best of 3: 730 ns per loop
> }}}
New description:
Right now to test if a Sage integer is prime it is faster to call
`prime_range` rather than `.is_prime()`...
{{{
sage: timeit("bool(prime_range(121,122))", number=10000)
10000 loops, best of 3: 1.09 µs per loop
sage: timeit("bool(prime_range(1009,1010))", number=10000)
10000 loops, best of 3: 1.2 µs per loop
}}}
versus
{{{
sage: timeit("121.is_prime()", number=10000)
10000 loops, best of 3: 5.3 µs per loop
sage: timeit("1009.is_prime()", number=10000)
10000 loops, best of 3: 4.19 µs per loop
}}}
The patch does some tiny modifications in `integer.pyx` and we get
{{{
sage: timeit("121.is_prime()", number=10000)
10000 loops, best of 3: 812 ns per loop
sage: timeit("1009.is_prime()", number=10000)
10000 loops, best of 3: 730 ns per loop
}}}
We also modify `is_prime_power()` to return `False` for 1.
--
Comment (by jdemeyer):
Big reviewer patch coming up...
--
Ticket URL: <http://trac.sagemath.org/ticket/16878#comment:17>
Sage <http://www.sagemath.org>
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