#17157: Improve formula for Bell numbers
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Reporter: jdemeyer | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/17157 | 0266cef42895b095b8c7eca5718a1466300e1304
Dependencies: | Stopgaps:
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Comment (by fredrik.johansson):
Replying to [comment:7 jdemeyer]:
> Replying to [comment:6 fredrik.johansson]:
> > Sage's current bell_number(n, algorithm='dobinski')
> With or without this patch?
Without. The difference is bigger for smaller n of course. Here is a more
accurate comparison:
flint:
100 cpu/wall(s): 2.6e-05 2.68e-05
200 cpu/wall(s): 8.2e-05 8.57e-05
400 cpu/wall(s): 0.00039 0.000403
1000 cpu/wall(s): 0.004 0.00441
2000 cpu/wall(s): 0.023 0.026
4000 cpu/wall(s): 0.16 0.172
10000 cpu/wall(s): 0.91 0.949
20000 cpu/wall(s): 4.02 4.173
40000 cpu/wall(s): 18.12 21.109
sage (without patch):
100 5 loops, best of 3: 1.05 ms per loop
200 625 loops, best of 3: 1.52 ms per loop
400 125 loops, best of 3: 1.96 ms per loop
1000 125 loops, best of 3: 7.39 ms per loop
2000 5 loops, best of 3: 38 ms per loop
4000 5 loops, best of 3: 216 ms per loop
10000 5 loops, best of 3: 2.17 s per loop
20000 1 loops, best of 3: 13 s per loop
40000 1 loops, best of 3: 68 s per loop
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Ticket URL: <http://trac.sagemath.org/ticket/17157#comment:9>
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