#11115: Rewrite cached_method in Cython
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: jason
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7
Component: misc | Keywords: category cython cache
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
In order to be on the safe side, I made some timings for the patches from
#9138 (on top of #9944), and I'd like to repeat these timings here, with
this patch applied additionally.
{{{
$ ./sage -startuptime
...
== Slowest (including children) ==
1.244 sage.all (None)
0.280 sage.schemes.all (sage.all)
0.243 sage.misc.all (sage.all)
0.162 elliptic_curves.all (sage.schemes.all)
...
}}}
So, there is no slow-down, compared with the timings from an unpatched
Sage on the same machine, as reported on #9138.
Here is an arithmetical example:
{{{
sage: B.<t> = PolynomialRing(Integers(125))
sage: R = monsky_washnitzer.SpecialCubicQuotientRing(t^3 - t + B(1/4))
sage: x, T = R.gens()
sage: timeit('x*T')
625 loops, best of 3: 893 µs per loop
}}}
That is about the same as with the patches from #9944 and #9138, but
slower than with an unpatched Sage.
I found that one can use the improved cached_methods to considerably speed
up the arithmetics. Namely, in the multiplication, the method `modulus()`
from sage.rings.polynomial.polynomial_ring is called repeatedly. The
`modulus()` method returns ´self.basering().characteristic()`. When I put
that method under a cached_method decorator, the timing looks much better:
{{{
sage: B.<t> = PolynomialRing(Integers(125))
sage: R = monsky_washnitzer.SpecialCubicQuotientRing(t^3 - t + B(1/4))
sage: x, T = R.gens()
sage: timeit('x*T')
625 loops, best of 3: 253 µs per loop
}}}
That is much faster than without patches, which is 501 µs!!.
Currently, I try to find some places where using a cached_method might be
beneficial. As I have demonstrated in previous posts, there are chances to
speed methods up that do nothing more but "`return self.__some_argument`".
But independent of that possible second patch, I think the first patch can
be reviewed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11115#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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