dolfin team mailing list archive

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

On 02/06/11 15:35, Benjamin Kehlet wrote:
> On 2 June 2011 16:31, Garth N. Wells <gnw20@xxxxxxxxx> wrote:
>>
>>
>> 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.
> 
> Agree, but I guess you don't need to support high precision?
> 

It would be nice to get it if we can.

Garth

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