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MPLAPACK constitutes a multi-precision linear algebra package, predicated upon the foundational structures of BLAS and LAPACK.

This particular package has undergone a comprehensive conversion into the C++ programming language, further accommodating an array of high-precision libraries, inclusive of GMP, MPFR, and QD. Such a versatile feature enables users to selectively opt for the library most congruous with their specific requirements. MPLAPACK represents a freely accessible software, disseminated under a 2-clause BSD-style license, supplemental to the original license ascribed by LAPACK.

News

  • 2022-09-12, MPLAPACK 2.0.1 was released, featuring CUDA versions of Rgemm (dd) and Rsyrk (dd) for use on Vota and Ampere, and on Tesla V100, with performance reaching approximately 450 GFlops. Support for V100 and A100 was also reintroduced by Nakazato (aizu-u). We also provide DLLs provided for MINGW mplapack.
  • 2022-07-26, MPLAPACK 2.0.0 was released, with all routines, with the exception of mixed precision routines, now functional and extensively tested for all multiple precisions.

Capabilities

  • MPBLAS: All BLAS routines can be done in multiple precision arithmetic.
  • MPLAPACK: All LAPACK routines can be done in multiple precision arithmetic; except for mixed precision routines.
  • Linear Equations
  • Linear Least Squares (LLS) Problems
  • Generalized Linear Least Squares (LSE and GLM) Problems
  • Standard Eigenvalue and Singular Value Problems
  • Symmetric Eigenproblems (SEP)
  • Nonsymmetric Eigenproblems (NEP)
  • Singular Value Decomposition (SVD)
  • Generalized Eigenvalue and Singular Value Problems
  • Generalized Symmetric Definite Eigenproblems (GSEP)
  • Generalized Nonsymmetric Eigenproblems (GNEP)
  • Generalized Singular Value Decomposition (GSVD)

Supported multiple precision libraries and floating point formats

We use MPFR + MPC as the primary arithmetic class.

Supported platforms

  • Ubuntu 22.04, 20.04, 18.04 (amd64, AArch64)
  • CentOS 7,8 (amd64, AArch64)
  • Ubuntu 20.04 (amd64) + Intel oneAPI
  • macOS (Intel) + gcc via macports (you may use homebrew instead, small modification of build script req'ed)
  • Windows (64bit; mingw64 on Ubuntu with wine64)

MPLAPACK test results

MPLAPACK benchmark results

Manual

@misc{2109.13406v2,
Author = {Maho Nakata},
Title = {MPLAPACK version 2.0.1 user manual},
Year = {2022},
Eprint = {arXiv:2109.13406v2},
}

Movies

Slides

Setting up docker environment for CUDA

The following link provides a comprehensive guide for installation: https://docs.nvidia.com/datacenter/cloud-native/container-toolkit/install-guide.html#install-guide

Building on Linux and Windows via Docker (Recommended)

The construction process necessitated a duration of approximately 3.5 hours, utilizing an Apple Mac mini (2018) equipped with a Core i5-8500B processor, comprising 6 cores operating at a frequency of 3 GHz. The instructions are designed for the Ubuntu 22.04 operating system. Please execute the following commands:

Ubuntu 22.04

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:ubuntu2204 -f Dockerfile_ubuntu22.04 . 2>&1 | tee log.ubuntu2204

Ubuntu 20.04

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:ubuntu2004 -f Dockerfile_ubuntu20.04 . 2>&1 | tee log.ubuntu2004

Ubuntu 20.04 + Intel oneAPI

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:ubuntu2004intel -f Dockerfile_ubuntu20.04_inteloneapi . 2>&1 | tee log.ubuntu2004.intel

Windows 64bit (using cross compiler on Ubuntu)

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:mingw -f  Dockerfile_ubuntu20.04_mingw64 . 2>&1 | tee log.mingw

CentOS 7 (amd64)

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:centos7 -f Dockerfile_CentOS7_amd64 . 2>&1 | tee log.CentOS7

CentOS 7 (aarch64)

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:centos7 -f Dockerfile_CentOS7_AArch64 . 2>&1 | tee log.CentOS7

CentOS 8

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:centos8 -f Dockerfile_CentOS8 . 2>&1 | tee log.CentOS8

Ubuntu 18.04

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:ubuntu1804 -f Dockerfile_ubuntu18.04 . 2>&1 | tee log.ubuntu1804

How to build and install from source tarball

  • on Linux: prerequiesties: gcc, g++ and gfortran
$ rm -rf $HOME/tmp $HOME/MPLAPACK
$ mkdir $HOME/tmp
$ cd $HOME/tmp
$ wget https://github.com/nakatamaho/mplapack/releases/download/v2.0.1/mplapack-2.0.1.tar.xz
$ tar xvfz mplapack-2.0.1.tar.xz
$ cd mplapack-2.0.1
$ CXX="g++" ; export CXX
$ CC="gcc" ; export CC
$ FC="gfortran"; export FC
$ ./configure --prefix=$HOME/MPLAPACK --enable-gmp=yes --enable-mpfr=yes --enable-_Float128=yes --enable-qd=yes --enable-dd=yes --enable-double=yes --enable-test=yes --enable-benchmark=yes #--enable-_Float64x=yes 
$ make -j4
$ make install
  • on macOS (using macports) FSF gcc is required (via macports, homebrew, or whatever); we don't test clang which doesn't support _Float128. There are two problems with building the mac version. We have to downgrade the command line tools to 13.4. See #60 and /opt/local/bin/ginstall is somewhat broken. See #44 to workaround.
$ sudo port install gcc10 coreutils git gsed
$ rm -rf $HOME/tmp $HOME/MPLAPACK
$ mkdir $HOME/tmp
$ cd $HOME/tmp
$ wget https://github.com/nakatamaho/mplapack/releases/download/v2.0.1/mplapack-2.0.1.tar.xz
$ tar xvfz mplapack-2.0.1.tar.xz
$ cd mplapack-2.0.1
$ CXX="g++-mp-10" ; export CXX
$ CC="gcc-mp-10" ; export CC
$ FC="gfortran-mp-10"; export FC
$ INSTALL="/usr/bin/install"; export INSTALL
$ ./configure --prefix=$HOME/MPLAPACK --enable-gmp=yes --enable-mpfr=yes --enable-_Float128=yes --enable-qd=yes --enable-dd=yes --enable-double=yes --enable-test=yes --enable-benchmark=yes #--enable-_Float64x=yes 
$ make -j4
$ make install

Note: Float64x is supported only on Intel CPUs, you can enable this by uncomment "#--enable-_Float64x=yes" -> "--enable-_Float64x=yes" as follows:

$ ./configure --prefix=$HOME/MPLAPACK --enable-_Float64x=yes --enable-gmp=yes --enable-mpfr=yes --enable-_Float128=yes --enable-qd=yes --enable-dd=yes --enable-double=yes --enable-test=yes

Docker build for developemnt (+ FABLE; Automatic Fortran to C++ converter)

https://github.com/cctbx/cctbx_project/tree/master/fable FABLE: Automatic Fortran to C++ conversion (https://doi.org/10.1186/1751-0473-7-5).

How to build

$ git clone https://github.com/nakatamaho/mplapack/
$ cd mplapack
$ /usr/bin/time docker build -t mplapack:fable -f Dockerfile_fable . 2>&1 | tee log.fable

How to convert a sample Fortran to C++

$ docker run -it mplapack:fable
$ cd ; fable.cout sample.f

MPLAPACK Release process

MPLAPACK 3.0.0 Release process

This is the release process for MPLAPACK 3.0.0

Action Date Status Description
optimized implementations should be the default
add template version mockup https://github.com/nakatamaho/mplapack-template
add gmpfrxx https://math.berkeley.edu/~wilken/code/gmpfrxx/
add openblas for benchmark of double
update to LAPACK 3.10.1
FMA for QD, DD
add more benchmarks, Rsyev, Rgesvd etc
optimized implementations
add qa program of BLAS
Take benchmark on A100 (Rgemm, Rsyrk dd)
python integration?
octave integration?
Drop GMP version Since trigonometric functions req'ed
Impliment mixed precision version
cleanup pow (REAL, long int)
Get rid of compiler warnings
lp64 ilp64 llp64 ilp32 lp32 cleanup

MPLAPACK 4.0.0 Release process

This is the release process for MPLAPACK 3.0.0

Action Date Status Description

old schedules

History

  • 2022/6/14 MPLAPACK 2.0.0 alpha released. Complex version and RFP version are now working. If you find problems feel free to raise issues.
  • 2022/05/24 2.0 All tests for complex and RFP have passed! alpha version is merged into HEAD.
  • 2022/03/21 2.0 (develoment ongoing). Now complex lin tests have passed for all precisions.
  • 2021/11/1 1.0.1 release. Fixing dd and qd arithmetic by Inte One API.
  • 2021/10/1 1.0.0 release. Huge improvement; all real LAPACK routines are available; SVD, eigenproblem solver for non symmetric matrices are added. manual is available: https://raw.githubusercontent.com/nakatamaho/mplapack/master/doc/manual/manual.pdf
  • 2021/4/11 0.9.3 release. CentOS7 AArch64 support
  • 2021/4/6 0.9.1 release. CentOS support
  • 2021/4/1 0.9.0 release. Rename to mplapack. You must rename include files, etc. Rewrite and recompilation required.
  • 2012/12/25: MPACK 0.8.0 NVIDIA C2050 support for Rgemm in double-double, and preliminary support for Intel Xeon Phi. ANNOUNCE
  • 2012/12/20: MPACK 0.8.0-RC2 Build fixes on various platforms.
  • 2012/12/05: Our Rgemm dd paper "A Fast implementation of matrix-matrix product in double-double precision on NVIDIA C2050 and application to semidefinite programming" is selected as the Best Papers of The Third International Conference on Networking and Computing. Slide is here.
  • 2012/11/29: MPACK 0.8.0-RC1 CUDA version of Rgemm in double-double precision is integrated.
  • 2012/10/13: CUDA 4.2 or later version of accelerated Rgemm in double-double precision on NVIDIA C2050 GPU is now available. Note it does not work on CUDA 4.1. Original release announce is here., and preprint is available from here, and it will be presented at The Third International Conference on Networking and Computing Okinawa, Japan, December 5-7, 2012 .
  • 2012/06/16: MPACK 0.7.0! Announcement
  • 2012/06/16: Development has been migrated to SVN repository.
  • 2011/10/28: Rgemm acceleration in double-double precision on NVIDIA C2050 GPU is now available. Even though papers are not published, you can just try by "make". Note that only CUDA 3.2 is supported. Origial release announce is here.
  • 2011/08/24: Rgemm acceleration on NVIDIA C2050 GPU is coming. Unfortunately paper are rejected, so please wait... Here is a pdf slide.
  • 2010/08/20: MPACK 0.6.7! Includes condition number estimators; Rgecon and Rpocon. Now 100 MLAPACK routines, and license has been changed to 2-clause BSD style license. No longer use LGPLv3.
  • 2010/08/6: MPACK 0.6.6! Build fix release. Tested on various Linux distributions.
  • 2010/05/31: A paper for MPACK (0.6.4) in Japanese has been uploaded.
  • 2010/05/21: MPACK 0.6.5! MPFR support, and MBLAS license has been changed to BSD style. Still MLAPACK part is LGPLv3. I'll replace hopefully soon.
  • 2010/01/13: MPACK 0.6.4! BUILD FIX RELEASE! PLEASE CHECK ON YOUR ENVIRONMENT! THANKS! ALSO WINDOWS IS SUPPORTED!
  • 2009/12/18: POSTER and SLIDE ARE UPLOADED; MPACK (MBLAS/MLAPACK) poster at HPCS2010 in English, and slide in Japanese, and I did two seminars about MPACK (MBLAS/MLAPACK) @NII and @Tokyo Univ; here is the slide.
  • 2009/11/24: MPACK 0.6.0!
  • 2009/11/7: Add example page.
  • 2009/10/9: MPACK 0.5.2, build fix on Intel Mac.
  • 2009/10/6: The cvs version has faster Raxpy using OpenMP parallelism.
  • 2009/10/5: MPACK 0.5.1, just minor updates.
  • 2009/9/24: MPACK 0.5.0!
  • 2009/9/17: GMP/QD/DD integration is going very well; now builds the mlapack part as well.
  • 2009/9/11: Now CVS version of MBLAS supports QD and DD. I abandoned "explicit generation of instances" for bad performance.
  • 2009/5/25: Now I switched to template programming so that the library will be most portable. We automatically generate GMP, QD and DD versions via "explicit generation of instances". For real calculations, source code level compatibility is retained and also we can made some optimized version as well, whereas complex code we need a small changes. Typically 2-3 percent performance loss have been observed.
  • 2009/3/21: QD and DD version of SDPA (SDPA-QD, DD) have been uploaded. These packages include some part of MPACK in QD and DD.
  • 2009/2/10: mpack-devel ML has been launched.
  • 2009/2/10: mpack-0.0.9.tar.gz.
  • 2009/2/5: SDPA-GMP 7.1.2 has been released now is supported by MPACK (MBLAS/MLAPACK!)
  • 2009/1/8: mpack-0.0.8.tar.gz. Moved to souceforge.net.
  • 2008/8/22: mpack-0.0.6.tar.gz. Build fix release.
  • 2008/8/14: mpack-0.0.5.tar.gz. Eighteen LAPACK routines (Rlamch, Rlae2, Rlaev2, Rlassq, Rlanst, Rlansy, Rlapy2, Rlarf, Rlarfg, Rpotf2, Rlarfb, Rlaset, Rlarft, Rlartg, Rlascl, Rlasrt, Rlasr, Rlatrd) with check programs and complete "blas.h" and "lapack.h" (prototypes for the BLAS and LAPACK) have been made.
  • 2008/7/23: mpack-0.0.4.tar.gz. All test cases are imported.
  • 2008/7/18: mpack-0.0.3.tar.gz. Fix copyright issues, make check partially works, except for MacOSX.
  • 2008/7/17: mpack-0.0.2.tar.gz. Installation instructions on Fedora9 and Ubuntu 8.04 are now available. Build fix with gcc-4.3.
  • 2008/7/15: mpack-0.0.1.tar.gz. Now configurable and installable :)
  • 2008/7/11: Change GPL to LGPLv3 and upload mpack-0.0.0.tar.gz.
  • 2008/6/27: Add mBSD header of original authors.
  • 2008/6/26: Tar ball has been provided. All sources for MBLAS have been uploaded.
  • 2008/6/24: This page has been created.

Oldpage

http://mplapack.sourceforge.net/

Acknowledgment:

This work has been supported by: The Special Postdoctoral Researchers' Program of RIKEN (2008, 2009) Grant-in-Aid for Scientific Research (B) 21300017 from the Japan Society for the Promotion of Science (2009, 2010, 2011). Microsoft Research CORE6 (2010), and the Japan Society for the Promotion of Science (JSPS KAKENHI Grant no. 18H03206) and TIS inc.

Also the M.N would like to thank Dr. Imamura Toshiyuki. Dr. Nakasato Naohito, Dr. Fujisawa Katsuki, Dr. Kouya Tomonori, Dr. Takahashi Daisuke, Dr. Goto Kazushige, Dr. Himeno Ryutaro, Dr. Hishimuna Toshiaki, Dr. Katagiri Takahiro, Dr. Ogita Takeshi, Dr. Kashiwagi Masahide, Dr. Yuasa Fukuko, Dr. Ishikawa Tadashi, Dr. Geshi Masaaki and Mr. Minato Yuichiro for warm encouragement.

Citation

@misc{2109.13406v2,
Author = {Maho Nakata},
Title = {MPLAPACK version 2.0.1 user manual},
Year = {2022},
Eprint = {arXiv:2109.13406v2},
}

contact

NAKATA Maho [email protected] [email protected]