Re: [eigen] Arbitrary precision arithmetic support in Eigen

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

On Thu, Jul 15, 2010 at 8:37 AM, Pavel Holoborodko
<pavel@xxxxxxxxxxxxxxx> wrote:
> Hi Gael!
>
> I am very thankful for your warm acceptance of MPFR C++.
> Thank you for your support!
>
> 1.
> I've added 3 new functions to MPFR C++ library:
> mpfr::machine_epsilon(prec) // the smallest eps such that 1+eps != 1 for the
> precision prec
> mpfr::mpreal_min(prec)         // the largest positive number presentable in
> precision prec and current exponent range
> mpfr::mpreal_max(prec)        // the smallest positive number presentable in
> precision prec and current exponent range
>
> They do not use pow, only simple and fast operations.
> Also I've changed mpreal_eigen.h to embed updated MPFR C++.

excellent! seems to work well. I'm currently only testing high-level
operation such LU, LLT, and symmetric eigenvalues, that indirectly
already covers a large part of Eigen !!


To Eigen people: maybe this is an opportunity to add new accuracy
oriented unit tests that would compares the results obtained with
float or double to the ones obtained with a much higher accuracy?

>
> MPFR C++:
> http://www.holoborodko.com/pavel/wp-content/plugins/download-monitor/download.php?id=4
>
> mpreal_eigen.h:
> http://www.holoborodko.com/pavel/wp-content/plugins/download-monitor/download.php?id=9
>
> I would appreciate any tests, or further suggestions.
>
> 2.
> I am very glad you fixed bug in ei_aligned_delete().
> I believe that was the bug users complain about in KDE forum.
> (crash on memory deallocation for dynamic matrices using mpreal)
> http://forum.kde.org/viewtopic.php?f=74&t=43643.

indeed, that was exactly it.

> 3.
> On where to put such a header file.
> I agree with you that it would be convenient for users to include
> MpfrSupport.h into Eigen itself.
> Please do it.

ok, done :) To be more precise I've currently added it as a
MPRealSupport module which currently lives in the unsupported/ folder
to not distract us too much for Eigen3. I've also added a
FindMPFR.cmake file and to ease testing I've included a copy of
mpfrc++ (the 2 files) in our test folder.

Since mpfrc++ it is quite lightweight and not packaged in common
distro, I'm even tempted to put these two files in the MPRealSupport
module. We would update them every new release of mpfrc++. This way we
can guarantee that the trio  MPFRC++/MPRealSupport/Eigen always work
fine, and people would only have to install MPFR and #include
<Eigen/MPRealSupport> and basta! Of course if you're OK for that we'll
make it crystal clear that's come from MPFRC++ with link to your
website everywhere it is appropriate (website, documentation, etc.).

gael

> One issue is maintenance of MpfrSupport.h upon changes in MPFR C++.
> I think we can manage to do that properly and timely.
>
> Thank you! And please keep me updated.
>
> All the best,
> Pavel Holoborodko
> http://holoborodko.com/pavel/
>
> On Thu, Jul 15, 2010 at 5:27 AM, Gael Guennebaud <gael.guennebaud@xxxxxxxxx>
> wrote:
>>
>> while trying to write proper unit tests, I hit the following issue:
>>
>> mpfr::pow(2,-mpfr::mpreal::get_default_prec())
>>
>> which is used to compute the epsilon takes forever... Is it "normal" ??
>>
>> The following runs fine though:
>>
>> mpfr::mpreal x = 1;
>> for(int i=0; i<mpfr::mpreal::get_default_prec(); ++i)
>>  x = x/2;
>>
>>
>> Also is there an easy way to get the highest and lowest representable
>> values ? They are needed for some operations in Eigen3.
>>
>> cheers,
>>
>> gael.
>>
>> On Wed, Jul 14, 2010 at 9:24 PM, Gael Guennebaud
>> <gael.guennebaud@xxxxxxxxx> wrote:
>> > ok, I could not resit to adapt it for Eigen3. Actually this is very
>> > useful to stress Eigen with scalar types having non trivial ctor/dtor
>> > (i.e., allocating/freeing memory), and bingo (!) there was a bug in
>> > ei_aligned_detete() for null pointers ;)
>> >
>> > gael
>> >
>> >
>> > On Wed, Jul 14, 2010 at 4:06 PM, Gael Guennebaud
>> > <gael.guennebaud@xxxxxxxxx> wrote:
>> >> Hi Pavel,
>> >>
>> >> thank you for your email. This is excellent!
>> >>
>> >> Actually, the possibility to use arbitrary precision scalar types is
>> >> one of the main argument I often use to sell Eigen. So having an
>> >> officially supported module for your lib with extensive testing is
>> >> something I wanted to do for a while, but you know there are always so
>> >> many things to do.
>> >>
>> >> So I'm really glad to see you added support for Eigen ;) I will add a
>> >> word on the website.
>> >>
>> >> What to do next?
>> >>
>> >> You said there is a lack of extensive testing. Since all our efforts
>> >> are now focused on the next Eigen version, Eigen3 which should be
>> >> release within a few months I'd rather spend time testing MPFR support
>> >> on Eigen3 than Eigen2. However, the way to add support for custom
>> >> scalar types slightly change. Fortunately, based on your current
>> >> support header file this should not be difficult. I can have a look at
>> >> it myself.
>> >>
>> >> One leading question is where to put such an header file? Within Eigen
>> >> as a (MpfrSupport module) or as a standalone file as it is currently
>> >> the case? The main advantage I see in having it in Eigen itself is
>> >> that should simplify to had full and continuous testing What do you
>> >> think?
>> >>
>> >> Finally, once MPFR C++ will use expression template, adding a good
>> >> support for Eigen-MPFR C++ that leverages ET at both the matrix and
>> >> scalar type level will be more tricky because Eigen will have to know
>> >> about the returned expression types of the mpreal operations. We
>> >> currently do not have an easy solution for that but this is something
>> >> we have to workout anyway for many other use cases (e.g., to nest
>> >> Eigen's Matrix/Array types, for automatic differentiation, etc.)
>> >>
>> >> cheers,
>> >>
>> >> gael
>> >>
>> >>
>> >>
>> >>
>> >>
>> >> On Wed, Jul 14, 2010 at 7:01 AM, Pavel Holoborodko
>> >> <pavel@xxxxxxxxxxxxxxx> wrote:
>> >>> Hello Everyone!
>> >>>
>> >>> First of all I would like to thank all the developers for the this
>> >>> beautifully designed and implemented library!
>> >>> I've learned a lot looking over it.
>> >>>
>> >>> I'm developer of C++ interface for the arbitrary precision floating
>> >>> point
>> >>> arithmetic library MPFR: http://www.holoborodko.com/pavel/?page_id=12.
>> >>>
>> >>> During last year I've received couple of questions from the users on
>> >>> how to
>> >>> use my wrapper together with Eigen. There was discussion in KDE forum
>> >>> on the
>> >>> topic but it seems that not all problems were solved:
>> >>> http://forum.kde.org/viewtopic.php?f=74&t=43643.
>> >>>
>> >>> Recently the most complete (hopefully:)) bridge for embedding mpreal
>> >>> type
>> >>> into Eigen was created.
>> >>> Please check home page under "Software using MPFR C++" for header file
>> >>> mpreal_eigen.h:
>> >>> http://www.holoborodko.com/pavel/?page_id=12.
>> >>>
>> >>> So, now user can equip Eigen with arbitrary precision arithmetic by:
>> >>> 1. Installing  MPFR and GMP libraries.
>> >>> 2. Using MPFR C++ interface (mpreal.h, mpreal.cpp) along with header
>> >>> file
>> >>> mpreal_eigen.h
>> >>> 3. Using mpreal type (provided by MPFR C++) instead of built-in type
>> >>> double
>> >>> or float.
>> >>>
>> >>> Precision (number of bits used for significant) can be setup globally
>> >>> by
>> >>> mpreal::set_default_prec().
>> >>> For instance double has only 53 bits precision with machine epsilon
>> >>> 1e-16
>> >>> (maximum 16 correct digits).
>> >>> Using mpreal user can do calculations with any precision, e.g. 1024
>> >>> bits
>> >>> with machine epsilon 1e-309 (309 correct digits).
>> >>>
>> >>> I would appreciate if someone who intensively use/develop Eigen would
>> >>> test
>> >>> how MPFR C++ works with Eigen.
>> >>>
>> >>> Any suggestions for improvement, test reports, etc.  are very very
>> >>> welcome.
>> >>>
>> >>> Also I would appreciate if Eigen webpage or documentation will
>> >>> reference
>> >>> such possibility on using arbitrary precision arithmetic.
>> >>> I think, this option could be very useful for the users.
>> >>>
>> >>> Besides reference on my site would give me huge support and motivation
>> >>> for
>> >>> further improvement.
>> >>>
>> >>> All the best,
>> >>>
>> >>> Pavel Holoborodko.
>> >>> http://holoborodko.com/pavel/
>> >>>
>> >>> P.S.
>> >>> I'm planning to release new version of MPFR C++ soon based on
>> >>> expression
>> >>> templates inspired by Eigen.
>> >>>
>> >>>
>> >>
>> >
>>
>>
>
>