dolfin team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

On 02/06/11 15:21, Benjamin Kehlet wrote:
> On 2 June 2011 14:59, Garth N. Wells <gnw20@xxxxxxxxx> wrote:
>>
>>
>> On 02/06/11 12:10, Benjamin Kehlet wrote:
>>> On 2 June 2011 11:51, Anders Logg <logg@xxxxxxxxx> wrote:
>>>> On Thu, Jun 02, 2011 at 10:46:29AM +0100, Garth N. Wells wrote:
>>>>>
>>>>>
>>>>> On 02/06/11 10:26, Anders Logg wrote:
>>>>>> On Thu, Jun 02, 2011 at 10:07:59AM +0100, Garth N. Wells wrote:
>>>>>>>
>>>>>>>
>>>>>>> On 01/06/11 23:46, Anders Logg wrote:
>>>>>>>> Have you checked that there is no performance penalty?
>>>>>>>
>>>>>>> I just have - evaluating a Legendgre polynomial 10k times at the same
>>>>>>> point is just noise with both methods (of the order 10^-5 - 10^-4 s).
>>>>>>
>>>>>> It may be noise for some applications, but not for others. I'm not
>>>>>> sure this is a bottle-neck for the ODE code (Benjamin will know) but
>>>>>> we need to evaluate Legendre polynomials of degree > 100 many times
>>>>>> and then it may not be noise.
>>>>>>
>>>>>
>>>>> For very high degree (e.g. 200) Boost is marginally faster.
>>>>
>>>> Sounds promising then.
>>>>
>>>>>>> The Boost code is slightly slower because it doesn't cache the values
>>>>>>> (which is nice not to do), but may be faster if the call is inlined.
>>>>>>> It's not possible to inline it at the moment because of clashes between
>>>>>>> tr1:tuple and boost::tuple (Boost bug, I suspect). Old and new are the
>>>>>>> same when evaluating at different points.
>>>>>>
>>>>>> Let's wait for Benjamin to comment.
>>>>>>
>>>>>
>>>>> The speed is about the same (with scope to improve the speed for Boost)
>>>>> for unique values. The caller should be responsible for caching, if
>>>>> desired, since it can lead to memory blow out.
>>>>>
>>>>> Legendre does not appear in the ode code. It only appears in the
>>>>> computation of quadrature schemes.
>>>>
>>>> True, but the quadrature schemes are used in the ode code.
>>>>
>>>> --
>>>> Anders
>>>>
>>>>
>>>>> Garth
>>>>>
>>>>>
>>>>>
>>>>>>> Garth
>>>>>>>
>>>>>>>
>>>>>>>> Benjamin has
>>>>>>>> worked quite hard on optimizing some of the basic math routines (in
>>>>>>>> some cases by many many orders of magnitude).
>>>>>>>>
>>>>>>>> Benjamin, can you take a look that it still works?
>>>
>>> Yes, the performance seems to be about the same, but I'm unable to
>>> compile it with support for GMP.
>>>
>>> /usr/include/boost/math/special_functions/legendre.hpp:178:
>>> instantiated from ‘typename boost::math::tools::promote_args<RT,
>>> float, float, float, float, float>::type boost::math::legendre_p(int,
>>> int, T, const Policy&) [with T = __gmp_expr<__mpf_struct [1],
>>> __mpf_struct [1]>, Policy =
>>> boost::math::policies::policy<boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy,
>>> boost::math::policies::default_policy>]’
>>> /usr/include/boost/math/special_functions/legendre.hpp:185:
>>> instantiated from ‘typename boost::math::tools::promote_args<RT,
>>> float, float, float, float, float>::type boost::math::legendre_p(int,
>>> int, T) [with T = __gmp_expr<__mpf_struct [1], __mpf_struct [1]>]’
>>> /home/benjamik/fenics/dolfin-wells_gmp/dolfin/math/Legendre.cpp:42:
>>> instantiated from here
>>> /usr/include/boost/math/special_functions/legendre.hpp:167: error: no
>>> matching function for call to ‘pow(__gmp_expr<__mpf_struct [1],
>>> __gmp_binary_expr<long int, __gmp_expr<__mpf_struct [1],
>>> __gmp_binary_expr<__gmp_expr<__mpf_struct [1], __mpf_struct [1]>,
>>> __gmp_expr<__mpf_struct [1], __mpf_struct [1]>,
>>> __gmp_binary_multiplies> >, __gmp_binary_minus> >,
>>> __gmp_expr<__mpf_struct [1], __gmp_binary_expr<__gmp_expr<__mpf_struct
>>> [1], __mpf_struct [1]>, long int, __gmp_binary_divides> >)’
>>> /usr/include/bits/mathcalls.h:154: note: candidates are: double
>>> pow(double, double)
>>> /usr/include/c++/4.4/cmath:358: note:                 float
>>> std::pow(float, float)
>>> /usr/include/c++/4.4/cmath:362: note:                 long double
>>> std::pow(long double, long double)
>>> /usr/include/c++/4.4/cmath:369: note:                 double
>>> std::pow(double, int)
>>> /usr/include/c++/4.4/cmath:373: note:                 float std::pow(float, int)
>>> /usr/include/c++/4.4/cmath:377: note:                 long double
>>> std::pow(long double, int)
>>> [...]
>>>
>>> boost::math::legendre seems to rely on std::pow which is not
>>> templated, only implemented with the most common types.
>>>
>>
>> Looks like some tweaks are required to work with GMP:
>>
>> http://www.boost.org/doc/libs/1_43_0/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html
> 
> That's not a bad solution, but it requires changing the
> multi-precision type from mpf (provided by GMP) to mpfr (which is a
> library that extends the floating point functionality in GMP). For
> floating-point arithmetic MPFR is much better than pure GMP. I think
> CGAL depends on MPFR, so it wouldn't even introduce new dependencies.
> The problem is that MPFR doesn't ship with a C++-wrapper (as opposed
> to GMP). Although several independent wrappers exists, none of them
> are avalilable in Debian/Ubuntu through apt. The one Boost requires is
> not updated since 2008 (MPFR has gone from version 2.3 to 3.0.1 since
> then).
> 

I've just plonked a copy of gmpfrxx in the DOLFIN dirs to test - it's
licensed under GPL.

> (Another option would be to take the same approach as Boost ourself:
> Implement the few functions that are required (pow() plus possibly a
> few more) and place it in the global namespace before including
> boost::mat::legendre), but GMP does not provide pow() when the
> exponent is a floating point number, so this is not straight forward
> without switching to MPFR).
> 
> So I guess the question is whether we want to switch to MPFR now, to
> get rid of the few lines of code in Legendre.cpp (which performs
> reasonably well), when the code is likely to be thrown out pretty soon
> anyway. I vote for "no", but I have no problems with moving the entire
> ODE solvers to a separate project, then adding it back (without
> supporting extended precision) later in the form of code generation
> for time dependent problems.
> 

There are a few issues here - even if the ODE code is moved out, I think
that we should retain the polynomial and quadrature code in DOLFIN.

Garth

> Benjamin
> 
>>
>> Garth
>>
>>
>>> Benjamin
>>>
>>>>>>>>
>>>>>>>
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>>>>
>>>> _______________________________________________
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>>>>
>>
>>