#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 robertwb):
The speed disparity between AGM over CC and over CDF was bugging me, so I
decided to code the arbitrary-precision case directly against mpfr
tonight. Made me wish we had mpc ;), or even better if sage/cython could
unroll CC arithmetic like this already (though there are several other
optimizations)
In any case, now we have
{{{
sage: a = CC(-0.95,-0.65)
sage: b = CC(0.683,0.747)
sage: %timeit a.agm(b, algorithm="optimal")
10000 loops, best of 3: 37.9 µs per loop
sage: %timeit aa.agm(bb)
10000 loops, best of 3: 35.2 µs per loop
}}}
The difference may be due to pari's stack-based rather than heap-based
memory management. Note, we're getting closer to optimal with this
algorithm as good chunk of the time is due to just taking the square
roots:
{{{
sage: %timeit [a.sqrt() for k in range(6)]
10000 loops, best of 3: 25.9 µs per loop
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7719#comment:8>
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