Multiple Precision Toolbox for MATLAB

This toolbox defines a new mp class allowing multiple precision objects in MATLAB.

Description

The mp toolbox defines a new class, the mp class, which holds arbitrary precision quantities. Many common numerical functions are overloaded for this class and therefore work without modification to source code. Look at the @mp directory under the MATLAB directory for a list of mp supported functions. If the function is not specifically written for mp objects, it still may work if the function in question relies only on functions in the @mp directory. Precompiled and builtin function from TMW like eig, etc. will not work with mp objects unless specifically written using overloaded functions from the @mp directory.A simple script, mp_makeall.m looks through the current variables,and converts all doubles to mp objects.The mp toolbox is only implemented for base 10 quantities, and the rounding mode is fixed to be GMP_RNDN (unless you change it in all the /private/*.c files and recompile).The overloaded functions sum, min, and max only work for 1 or 2 dimensional mp objects right now.mp random numbers can be generated using rand() if rand at least 1 of the input arguments is an mp object. However, the seed given to gmp_randseed_ui is only in the range 0<seed<1000000, but this can be adjusted in @mp/rand.mA zeta function using m arithmetic is provided, whereas native MATLAB has no such function except for sym objects.

• Acknowledgements: This submission has inspired the following:; Variable Precision Integer Arithmetic
• MATLAB release: MATLAB 7 (R14)
• Other requirements: GMP (GNU Multiple Precision Arithmetic Library): http://www.swox.com/gmp/ and the MPFR (multiple-precision floating-point computations with exact rounding): http://www.mpfr.org/

Other Files

@mp/.emacs.desktop,
@mp/.emacs.desktop.lock,
@mp/abs.m,
@mp/acos.m,
@mp/acosh.m,
@mp/acot.m,
@mp/acoth.m,
@mp/acsc.m,
@mp/acsch.m,
@mp/all.m,
@mp/and.m,
@mp/any.m,
@mp/asec.m,
@mp/asech.m,
@mp/asin.m,
@mp/asinh.m,
@mp/atan.m,
@mp/atan2.m,
@mp/atanh.m,
@mp/ceil.m,
@mp/colon.m,
@mp/complex.m,
@mp/conj.m,
@mp/cos.m,
@mp/cosh.m,
@mp/cot.m,
@mp/coth.m,
@mp/csc.m,
@mp/csch.m,
@mp/ctranspose.m,
@mp/cumprod.m,
@mp/cumsum.m,
@mp/diag.m,
@mp/disp.m,
@mp/display.m,
@mp/double.m,
@mp/eps.m,
@mp/eq.m,
@mp/erf.m,
@mp/exp.m,
@mp/eye.m,
@mp/factorial.m,
@mp/find.m,
@mp/fix.m,
@mp/floor.m,
@mp/gamma.m,
@mp/ge.m,
@mp/gt.m,
@mp/imag.m,
@mp/install_mac,
@mp/inv.m,
@mp/isfinite.m,
@mp/isinf.m,
@mp/isnan.m,
@mp/isreal.m,
@mp/le.m,
@mp/length.m,
@mp/log.m,
@mp/log10.m,
@mp/log2.m,
@mp/logical.m,
@mp/lt.m,
@mp/lu.m,
@mp/max.m,
@mp/min.m,
@mp/minus.m,
@mp/mldivide.m,
@mp/mp.m,
@mp/mp_Defaults.m,
@mp/mpEuler.m,
@mp/mpLog2.m,
@mp/mpower.m,
@mp/mpPi.m,
@mp/mrdivide.m,
@mp/mtimes.m,
@mp/ne.m,
@mp/norm.m,
@mp/not.m,
@mp/num2str.m,
@mp/ones.m,
@mp/or.m,
@mp/plot.m,
@mp/plus.m,
@mp/power.m,
@mp/private/getVals.m,
@mp/private/gmp_prototype.c,
@mp/private/hasimag.m,
@mp/private/mp_compile_all.m,
@mp/private/mp_defaults.m,
@mp/private/mpAddDecimal.m,
@mp/private/mpeuler.m,
@mp/private/mpExpForm.m,
@mp/private/mpfr_absc.c,
@mp/private/mpfr_add.c,
@mp/private/mpfr_atan2.c,
@mp/private/mpfr_ceil.c,
@mp/private/mpfr_const_log2.c,
@mp/private/mpfr_construct_cd.c,
@mp/private/mpfr_construct_dd.c,
@mp/private/mpfr_cos.c,
@mp/private/mpfr_cosc.c,
@mp/private/mpfr_div.c,
@mp/private/mpfr_divc.c,
@mp/private/mpfr_eq.c,
@mp/private/mpfr_erf.c,
@mp/private/mpfr_euler.c,
@mp/private/mpfr_exp.c,
@mp/private/mpfr_expc.c,
@mp/private/mpfr_factorial.c,
@mp/private/mpfr_fix.c,
@mp/private/mpfr_floor.c,
@mp/private/mpfr_gamma.c,
@mp/private/mpfr_ge.c,
@mp/private/mpfr_get_d.c,
@mp/private/mpfr_gt.c,
@mp/private/mpfr_isinf.c,
@mp/private/mpfr_isnan.c,
@mp/private/mpfr_le.c,
@mp/private/mpfr_log.c,
@mp/private/mpfr_log10.c,
@mp/private/mpfr_log10c.c,
@mp/private/mpfr_log2.c,
@mp/private/mpfr_log2c.c,
@mp/private/mpfr_logc.c,
@mp/private/mpfr_lt.c,
@mp/private/mpfr_mul.c,
@mp/private/mpfr_mul_d.c,
@mp/private/mpfr_mulc.c,
@mp/private/mpfr_mulc_d.c,
@mp/private/mpfr_pi.c,
@mp/private/mpfr_pow.c,
@mp/private/mpfr_powc.c,
@mp/private/mpfr_rand.c,
@mp/private/mpfr_round.c,
@mp/private/mpfr_sin.c,
@mp/private/mpfr_sinc.c,
@mp/private/mpfr_sqrt.c,
@mp/private/mpfr_sqrtc.c,
@mp/private/mpfr_tan.c,
@mp/private/mpfr_zeta.c,
@mp/private/mplog2.m,
@mp/private/mppi.m,
@mp/private/precAndSize.m,
@mp/prod.m,
@mp/qr.m,
@mp/rand.m,
@mp/rdivide.m,
@mp/real.m,
@mp/rem.m,
@mp/round.m,
@mp/sec.m,
@mp/sech.m,
@mp/sign.m,
@mp/sin.m,
@mp/sinh.m,
@mp/sort.m,
@mp/sprintf.m,
@mp/sqrt.m,
@mp/subsasgn.m,
@mp/subsindex.m,
@mp/subsref.m,
@mp/sum.m,
@mp/svd.m,
@mp/tan.m,
@mp/tanh.m,
@mp/times.m,
@mp/TODO,
@mp/transpose.m,
@mp/tril.m,
@mp/triu.m,
@mp/uminus.m,
@mp/uplus.m,
@mp/zeros.m,
@mp/zeta.m,
license.txt,
mp_changelog,
mp_dvec_sort_bubble_a.m,
mp_euler.m,
mp_gausscpp.m,
mp_gausscppSolve1.m,
mp_gausscppSolve2.m,
mp_log2.m,
mp_makeall.m,
mp_makeallDouble.m,
mp_myqr.m,
mp_mysvd.m,
mp_pi.m,
mp_README,
mp_set_defaults.m,
mp_TESTING.m,
mp_TESTING2.m,
mp_WindowsBinaries2006a.zip

[Zhiyi Li]

I can not compile the C files in it using mex. The compiler can't find mpfr.h

[Tim Eakin]

I have the same problems encountered by Zhiyi when attempting installation on a Windows XP platform. It looks like there may need to be some sort of -I or -L mex switch in a mexopts.bat file. I use Lcc for the C compiler.

[Leo da Li]

It really seams that this toolbox, as it is, was made to work uniquely under matlab for linux. I tried many diferent things to compile it in matlab for windows (xp) and i couldn't! It could be realy helpfull if instructions/modifications for matlab in windows were provided! I used gcc of cygwin to compile gmp and mpfr, but i can't make a mexopts.bat to gcc on matlab for windows!

[Leo da Li]

Well, in Linux (Fedora Code 4 and Ubuntu) the installation was successful. Actually, on the line 7 of the file mp_compile_all.m:

mex([dd(ii).name,' mpfr_atan2.c'],'-lmpfr -lgmp');

i had to delete ",' mpfr_atan2.c'", otherwise an error is produced. But well, it works pretty great ;) But it would be nice if some functins were included or completed. For exemple, the mrdivide.m function is not fully functional, so we can't accomplish operations where inv of a matrix is required. Usually, mrdivide(A,B) does the same as A*inv(B), but hugely faster and more accurate (inv is neither included).

But, well, this toolbox works really fine. I rate 4 just because it is not fully functional (yet).

[Jarek Grzegogrze³kowski]

 

[Egemen Kolemen]

For those who are interested in using gcc of cgywin please see:

http://gnumex.sourceforge.net/

[Carlos López]

I were able to compile it for R13 under Windows, but failed miserably to do so for 7.0 and 7.2.
If anyone needs such version contact me to describe what I did.
I added some other test to the toolbox, and overall it appears to run fine.

[Umberto .]

Really excellent. However it can be improved, e.g.: (i) some functions are really slow when applied to large matrices (e.g. the overloaded function "prod") and (ii) it worked for me under Matlab 7.3 (2006b) but not under Matlab 6.5. I give a five star rating since this toolbox fills a serious gap into the Matlab numeric representation capabilities.

[Christoph Krautz]

Installation fails on Windows! Documentation is more than bad!

[Martin Andersson]

I got this system working well on xp-based Matlab, R13 but I never got the compilation to work, an error about missing h-files came up. Anyway, there is no need to compile it as it worked fine using the dll files from Lopes. Before I could use it, I needed to put some work on it a bit and rewrite a few of the m-files, but now it seems OK.

Yes, like other pointed out already, the calculations do become very, very slow, but at least I became able to see what happens when using more digits.

Slower as expected, but still an Excellent tool. (But the Windows installation guide is difficult to understand).

Thanks

[Laszlo Sragner]

Some small precisions (1-2) can cause Matlab to break. Some operations cause memory dump errors , maybe this is due to passing illegal arguments somewhere to mex functions.
The GMP mex wrapper functions work well with the supported dlls on a windows XP for these it is worth using it and writing your own m-class around them.

[Andrew Wildes]

Installed on windows, and works well. It's slow, so it would be difficult to use with any fitting program. We found a couple of bugs and contacted Mr. Barrowes, who was very receptive and replied quickly and enthusiastically. Recommended!

[Ronan Fleming]

When installing in suse 10.1, I found it necessary to explicitly provide the path '/usr/local/lib' in the mp_compile_all.m file as that is where my lmpfr libraries were

e.g. If you get the error
mex: link of 'mpfr_something.mexglx' failed.

Then change lines 12 & 13 to

disp(['compiling: mex ',dd(ii).name,' -L/usr/local/lib -lmpfr -lgmp'])
    mex([dd(ii).name],'-L/usr/local/lib -lmpfr -lgmp');

[Nikolai Zolotykh]

It's really useful and greate soft

[Zolotykh Nikolai]

 

[grat c]

can anyone tell me how exactly to install the binaries in windows? thanks

[HH VD]

Windows version here: http://www.thedigitalmap.com/~carlos/software/index.htm

[Kevin Mitchell]

 

[Kevin Mitchell]

Beautiful! This rivals laprint.m (http://www.mathworks.com/matlabcentral/fileexchange/4638) for packages that really should be included with Matlab by default.

[Brent Ware]

Anyone had any luck getting this to work with recent versions of OS X? The old instructions don't seem to work.

[Nigel Delaney]

I just reinstalled this package for a windows 7 64 bit computer (running 64 bit matlab). It was a bit of work so I thought I would share the process, or offer to email anyone the binaries/toolbox as I have it.
The first issue is that building mpfr/gmp for x64 is quite hard. Apparently, there is a new ming compiler out for 64 bit, but no one has had it work so far (and I didn't try it). The second option, SUA is also useless as there is no gcc compiler for x64 with it, and you would be forced to make a 32 bit version. So, in order to get the libraries I had to use MPIR (which can substitute for GMP) and then compile mpfr with this instead of gmp. To do this, you need to do the following:
Download MPFR ad MPIR :
http://www.mpfr.org/
http://www.mpir.org/
Now, both of these are hard to build, but someone has setup a way to build them with either visual studio or visual studio express that is reasonably painless. Go here to get the build instructions.
http://gladman.plushost.co.uk/oldsite/computing/gmp4win.php
Note that in order to get the visual studio build to work, you have to install a yasm assembler program and integerate it into visual studio (follow the 3 step instructions on their website).
 http://www.tortall.net/projects/yasm/
One you are setup to go, first build mpir using visual studio. Note that there is a vcbuild directory included with the mpir program that you can use directly to make the files. This program can substitute for gmp in the next linking step, so use the gmp.h header file that comes with it next. With that done, you can now open the VS project from the gladman site and get ready to compile mpfr. Note that the project files he hands out do not include the actual code, so you will have to move the mpfr source files and reference mpir library files around to make sure they appear in their correct locations relative to the what is in the .sln file gladwell gives out. Once this is done, you are all set to build and things should compile just fine.
Next, compile the .mex files (which should be pretty straightforward now that the libraries are built). Now the package is up and running, however it did not work right away for me. It appears that for whatever reason if matlab saw this type of code:
length(x)==1
in the toolbox .m files, it would call the eq.m method of this toolbox instead of the builtin method, and this broke the dang thing as it would not know how to work with two double types. The same was true for <, >, etc.. This seemed very strange to me and I am not sure if it is due to matlab upgrades or to some odd system setting on my machine. In any event, changing the relevant files to check for a double and go to the builtin method seemed to work around the problem okay, and so far the code is working fine.

Great package overall!!! Certainly a lot of work must have gone into it, only giving it 4 out of 5 because I just spent 6 hours getting it to work, but I am sure if I had gone the 32 bit route it would have been much easier.

[Dmitry Savransky]

Absolutely fantastic. Exactly what I needed - many thanks. Quick note for anyone installing on RHEL5. The default rpms that may be pre-installed for GMP don't seem to work when it comes time to compile the c files. However, if you get rid of these and compile GMP and MPFR from source, everything works great.