#12121: floor/ceil can be very slow at integral values
--------------------------------+-------------------------------------------
Reporter: dsm | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: basic arithmetic | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Reported (in slightly different form) on
[http://ask.sagemath.org/question/964/lenlist-ceillog42-bugs
ask.sagemath.org]:
{{{
sage: %timeit floor(log(3)/log(2))
625 loops, best of 3: 586 µs per loop
sage: %timeit floor(log(4)/log(2))
5 loops, best of 3: 3.79 s per loop
sage: %timeit ceil(log(3)/log(2))
625 loops, best of 3: 586 µs per loop
sage: %timeit ceil(log(4)/log(2))
5 loops, best of 3: 3.79 s per loop
}}}
This happens because ceil and floor first try to increase the precision of
a coercion of the input argument to a `RealInterval` by 100 bits from 53
to 20000 before finally trying a full_simplify, which succeeds.
One possible solution would be to try
{{{
sage: %timeit bool(log(4)/log(2) == round(log(4)/log(2)))
125 loops, best of 3: 5.57 ms per loop
}}}
after some number (maybe even 1?) of `RealInterval` attempts, and then get
back to increasing the precision. Trying to think of use cases, ceil and
floor are probably called 95%+ of the time on things which only require a
round or two at most to determine the answer, so it makes sense to
optimize that end.
As well, the "+100 bits" approach (rather than going up by some factor
each time, say) probably penalizes numbers requiring lots of bits too much
relative to those requiring only a few, but the integer case is probably
more important.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12121>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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