Hi,
Just to extend this thread some more, a few remarks.
(1) quaddouble has been included in SAGE for several months
now, thanks to the hard work of Didier Deshommes and Robert
Bradshaw.
sage: RQDF
Real Quad Double Field
sage: RQDF(2).sin()
0.909297426825681695396019865911744842702254971447890268378973011
(2) Great work on figuring out the problem with mpfr in SAGE!
I have fixed this for sage-2.7.3.
(3) Here are the latest timings of SAGE versus Mathematica
on (a) my Intel OS X laptop, and
(b) on an unloaded sage.math (64-bit opteron), both with
mathematica 5.2. This is after rebuilding mpfr with -O2.
On sage.math:
SAGE:
sage: time n = number_of_partitions(10^7)
CPU times: user 0.73 s, sys: 0.00 s, total: 0.73 s
Wall time: 0.73
sage: time n = number_of_partitions(10^8)
CPU times: user 8.42 s, sys: 0.00 s, total: 8.42 s
Wall time: 8.42
sage: time n = number_of_partitions(10^9)
CPU times: user 105.82 s, sys: 0.00 s, total: 105.82 s
Wall time: 105.81
Mathematica:
sage: time s=mathematica.eval('PartitionsP[10^7]')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 1.90
sage: time s=mathematica.eval('PartitionsP[10^8]')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 9.91
sage: time s=mathematica.eval('PartitionsP[10^9]')
CPU times: user 0.03 s, sys: 0.01 s, total: 0.04 s
Wall time: 70.43
Interesting, SAGE seems better at Mathematica for
smaller input.)
On my OS X core 2 duo 2.33Ghz laptop:
SAGE:
sage: time n=number_of_partitions(10^7)
CPU times: user 0.62 s, sys: 0.00 s, total: 0.62 s
Wall time: 0.62
sage: time n=number_of_partitions(10^8)
CPU times: user 6.99 s, sys: 0.02 s, total: 7.00 s
Wall time: 7.03
sage: time n=number_of_partitions(10^9)
CPU times: user 94.71 s, sys: 0.28 s, total: 94.99 s
Wall time: 95.56
MATHEMATICA:
sage: time s=mathematica.eval('PartitionsP[10^7]')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 8.65
sage: time s=mathematica.eval('PartitionsP[10^8]')
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 48.08
sage: time s=mathematica.eval('PartitionsP[10^9]')
CPU times: user 0.04 s, sys: 0.00 s, total: 0.05 s
Wall time: 350.30
Yep -- Mathematica 5.2 interestingly totally sucks at
computing the number of partitions on an Intel OSX
machine... and SAGE rocks.
-- William
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