#7719: Improvements to complex AGM
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Reporter: cremona | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.3.1
Component: basic arithmetic | Keywords: complex agm
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by was):
Watch out. The following is a much more accurate reflection of how fast
PARI is at this computation (and even then there is still a tiny bit of
overhead):
{{{
sage: timeit('pari("agm(-0.95-0.65*I,0.683+0.747*I)")')
625 loops, best of 3: 33.2 µs per loop
}}}
versus
{{{
sage: CC = ComplexField(200)
sage: a = CC(-0.95,-0.65)
sage: b = CC(0.683,0.747)
sage: z = pari(a)
sage: timeit('z.agm(b)')
625 loops, best of 3: 309 µs per loop
}}}
To avoid overhead from caching:
{{{
sage: time z = pari("for(i=1,10^5,agm(-0.95-I*0.65,0.683+I*0.747))")
CPU times: user 2.49 s, sys: 0.00 s, total: 2.49 s
Wall time: 2.49 s
}}}
which is about 25 microseconds.
Conclusions:
(1) How did you come up with an algorithm="pari" that takes 7ms? That's
really long.
(2) What we do in Sage should hopefully take at most 25 microseconds in
just order to be competitive to PARI.
Here's some more to worry about. Magma evidently does not even have a
*complex* AGM. However, it has a real AGM, and it is an order of
magnitude faster than PARI's:
{{{
age: time z = pari("for(i=1,10^5,agm(-0.95,0.683))")
CPU times: user 2.07 s, sys: 0.00 s, total: 2.07 s
Wall time: 2.07 s
sage: magma.eval("time for n in [1..10^5] do z := AGM(0.95,0.683); end
for;")
'Time: 0.170'
sage: 2.07/0.170
12.1764705882353
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7719#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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