#12449: Improve the way that sage evaluates symbolic functions on basic types
---------------------------------------------+------------------------------
Reporter: bober | Owner: bober
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: symbolics | Keywords: gamma function
Work_issues: | Upstream: N/A
Reviewer: Burcin Erocal, Jonathan Bober | Author: Jonathan Bober,
Burcin Erocal
Merged: | Dependencies: #4498, #12507,
#9130
---------------------------------------------+------------------------------
Changes (by bober):
* status: needs_work => needs_review
Old description:
> Currently when a symbolic function (e.g. gamma(), exp(), sin()) gets a
> python float, it passes it off to ginac, and let's ginac evaluate it.
> This can be very slow, e.g.:
>
> {{{
> sage: timeit('exp(6.0r)')
> 625 loops, best of 3: 476 µs per loop
> }}}
>
> This also leads to possibly undesirable inconsistencies across different
> platforms: for example, ginac ends up calling the local libc tgammal to
> evaluate the gamma function, and even when this tgammal is evaluated by
> the same version of eglibc on two different platforms the answer varies
> depending on whether 80 bit doubles are available.
>
> To fix this, we make Sage check its types which correspond most closely
> to python type for the function that should be called, and use the
> functions for those types if available.
>
> Now we have
>
> {{{
> sage: timeit('exp(6.0r)')
> 625 loops, best of 3: 1.02 µs per loop
> }}}
>
> For the specific case of the gamma function, the is also a change here to
> make RDF use python's math.gamma(). It is more accurate than gsl. It is
> perhaps not as accurate as eglibc's gamma(), but it should give reliable
> results on different platforms.
>
> I think this will fix 3 of the 4 failing numerical accuracy doctests on
> ARM, though the test for binomial(.5r, 5) had to be weakened slightly.
> (see http://groups.google.com/group/sage-
> devel/browse_thread/thread/3c8c61ea113ea60c ) binomial() is currently not
> computed in a very good way, though, so it is reasonable to weaken this
> test temporarily. (see http://trac.sagemath.org/sage_trac/ticket/12448 )
>
> Finally, I'll remark that these improvements could probably be much
> better. The above timings should be compared to
> {{{
> sage: timeit('math.exp(6.0r)')
> 625 loops, best of 3: 112 ns per loop
> }}}
>
> Apply:
> - attachment:12449.patch
> - attachment:trac_12449-py_tgamma.patch
New description:
Currently when a symbolic function (e.g. gamma(), exp(), sin()) gets a
python float, it passes it off to ginac, and let's ginac evaluate it. This
can be very slow, e.g.:
{{{
sage: timeit('exp(6.0r)')
625 loops, best of 3: 476 µs per loop
}}}
This also leads to possibly undesirable inconsistencies across different
platforms: for example, ginac ends up calling the local libc tgammal to
evaluate the gamma function, and even when this tgammal is evaluated by
the same version of eglibc on two different platforms the answer varies
depending on whether 80 bit doubles are available.
To fix this, we make Sage check its types which correspond most closely to
python type for the function that should be called, and use the functions
for those types if available.
Now we have
{{{
sage: timeit('exp(6.0r)')
625 loops, best of 3: 1.02 µs per loop
}}}
For the specific case of the gamma function, the is also a change here to
make RDF use python's math.gamma(). It is more accurate than gsl. It is
perhaps not as accurate as eglibc's gamma(), but it should give reliable
results on different platforms.
I think this will fix 3 of the 4 failing numerical accuracy doctests on
ARM, though the test for binomial(.5r, 5) had to be weakened slightly.
(see http://groups.google.com/group/sage-
devel/browse_thread/thread/3c8c61ea113ea60c ) binomial() is currently not
computed in a very good way, though, so it is reasonable to weaken this
test temporarily. (see http://trac.sagemath.org/sage_trac/ticket/12448 )
Finally, I'll remark that these improvements could probably be much
better. The above timings should be compared to
{{{
sage: timeit('math.exp(6.0r)')
625 loops, best of 3: 112 ns per loop
}}}
Apply:
- attachment:trac_12449_rebase.patch
--
Comment:
I've attached a patch rebased to 5.0-beta5. I had no problem applying the
patches, so I just made sure all tests still pass.
Maybe I should just go ahead and put it back to positive review, but I'll
give Burcin a day or so to take a look at it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12449#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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