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INTRODUCTION ============ M4RI is a library for fast arithmetic with dense matrices over F2. The name M4RI comes from the first implemented algorithm: The "Method of the Four Russian"” inversion algorithm published by Gregory Bard. This algorithm in turn is named after the "Method of the Four Russians" multiplication algorithm which is probably better referred to as Kronrod's method. M4RI is available at http://m4ri.sagemath.org FEATURES ======== * basic arithmetic with dense matrices over F2 (addition, equality testing, stacking, augmenting, sub-matrices, randomisation); * asymptotically fast O(n^log_2(7)) matrix multiplication via the "Method of the Four Russians" (M4RM) & Strassen-Winograd algorithm; * asymptotically fast O(n^log_2(7)) PLE factorisation (Gaussian elimination, system solving, ...); * fast row echelon form computation and matrix inversion via the "Method of the Four Russians" (M4RI, O(n^3/log(n))); * support for the x86/x86_64 SSE2 instruction set where available; * preliminary support for parallelisation on shared memory systems via OpenMP; * and support for Linux, Solaris, and OS X (GCC) and limited support for Windows (Visual Studio 2010). OPENMP SUPPORT ============== OpenMP support for parallel multiplication and elimination is enabled with the --enable-openmp configure switch. If GCC is used to compile the library it is advised to use at least GCC 4.3 since earlier versions have problems with OpenMP in shared libraries. OpenMP support was introduced in GCC 4.2. Both MSVC and SunCC support OpenMP but we have no experience with these yet. Generally speaking better performance improvements can be expected on multi-core AMD CPUs than on multi-core Intel CPUs. This is because the later has a shared L2 cache which is already almost fully utilised in the single-core implementation. Overall, the speed-up is considerably but sublinear. See http://m4ri.sagemath.org/performance.html for details. INSTALL ======= If you downloaded M4RI as a compressed tarball from its website, installation instructions are contained in the file INSTALL. If you downloaded M4RI by cloning the mainline tree at https://bitbucket.org/malb/m4ri you need to first run the following command: $ autoreconf --install Then follow the instructions in the file INSTALL. DOCUMENTATION ============= To build the reference manual, ensure that you have Doxygen installed. The HTML version of the reference manual can be built as follows: $ cd src/ $ doxygen The built documentation is contained under the doc subdirectory of m4ri/. Once the HTML version is built, you can build the PDF version as follows: $ cd doc/latex/ $ make