#4302: [with patch, needs review] improve modular composition in GF(2)[x]
------------------------------+---------------------------------------------
Reporter: zimmerma | Owner: somebody
Type: task | Status: new
Priority: major | Milestone: sage-3.2
Component: basic arithmetic | Resolution:
Keywords: |
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Comment (by malb):
This is what I sent to Paul earlier about the patch
>I've improved said implementation on my train ride after Sage Days. The
result
>is faster than Magma but only competitive with NTL. It seems NTL is
already
>faster than Magma for this problem and that the runtime is dominated by
the
>construction of the matrices (ntl.GF2X arithmetic mainly) and the
recovery of
>the result (ntl.GF2X arithmetic mainly). There is room for improvements
>w.r.t. the conversion between ntl.GF2X and M4RI but I didn't bother yet
>because ntl.GF2X arithmetic seems to be the main bottleneck for now. Note
>that matrix multiplication takes up only a tiny fraction of the overall
>runtime, it is almost negligible.
>
>Maybe, once we switch to the GF2X library things will look different
enough to
>motivate a better tuned conversion routine?
{{{
f = R.random_element(30000)
g = R.random_element(30000)
h = R.random_element(30000*10)
}}}
{{{
%time
set_verbose(1)
_ = f.modular_composition(g,h)
verbose 1 (1: , <module>) G 548 x 299999 16.331 s
verbose 1 (1: , <module>) F 55 x 548 0.000 s
verbose 1 (1: , <module>) H 55 x 299999 0.230 s
verbose 1 (1: , <module>) Res 6.359 s
CPU time: 22.98 s, Wall time: 23.42 s
}}}
{{{
%time _ = f.modular_composition(g,h,'ntl')
verbose 1 (1: , <module>) NTL 23.998 s
CPU time: 24.07 s, Wall time: 24.72 s
}}}
{{{
fm = f._magma_()
gm = g._magma_()
hm = h._magma_()
t = magma.cputime()
_ = fm.ModularComposition(gm,hm)
magma.cputime(t)
83.810000000000002
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4302#comment:3>
Sage <http://sagemath.org/>
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