#10255: improve karatsuba multiplication of univariate polynomials
--------------------------------+-------------------------------------------
Reporter: lftabera | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.6.1
Component: basic arithmetic | Keywords: karatsuba, multiplication,
polynomial
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by jdemeyer):
One can actually a speedup of more than a factor 10 by using PARI:
The following function converts a polynomial over a number field to a PARI
object:
{{{
def nfpol_to_pari(f):
return pari([c._pari_('a') for c in f.list()]).Polrev()
}}}
Now let's try your example:
{{{
sage: K=QQ[I][x]
sage: f=K.random_element(1500)
sage: g=K.random_element(1500)
sage: %time _ = f._mul_generic(g)
CPU times: user 3.57 s, sys: 0.00 s, total: 3.57 s
Wall time: 3.59 s
sage: %time _ = f._mul_karatsuba(g)
CPU times: user 5.06 s, sys: 0.05 s, total: 5.11 s
Wall time: 5.12 s
sage: fpari = nfpol_to_pari(f)
sage: gpari = nfpol_to_pari(g)
sage: %time _ = fpari*gpari
CPU times: user 0.26 s, sys: 0.00 s, total: 0.26 s
Wall time: 0.26 s
}}}
Since PARI is written completely in C, it's obvious why one could expect
such a speedup. Obviously, writing specialized code to deal with number
field polynomials would even be better.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10255#comment:8>
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