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GEMM: From Pure C to SSE Optimized Micro Kernels
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On the next pages we try to discover how __BLIS__ can achieve such a create
performance.  *For this journey we set up our own BLAS implementation!*

In our __ulmBLAS__ project we have implemented a simple matrix-matrix product
that follows the ideas described in __BLIS: A Framework for Rapidly
Instantiating BLAS Functionality__.

- __Page 1__ How to obtain the __ulmBLAS__ project.
- __Page 2__ Pure C implementation 
- __Page 3__ Naive Use of SSE Intrinsics.
- __Page 4__ Applying loop unrolling to the previous implementation.
- __Page 5__ Another SSE Intrinsics Approach which is based on the __BLIS__
  micro kernel for SSE architectures.
- __Page 6__ Improving pipelining by reordering SSE intrinsics.
- __Page 7__ Limitations of SSE intrinsics.
- __Page 8__ We go nuclear and translate the intrinsics to assember by ourself!
- __Page 9__ Unrolling the nuke: demo-asm-unrolled.
- __Page 10__ Fine-tuning the unrolled assembler kernel.
- __Page 11__ More fine-tuning of the unrolled assembler kernel.
- __Page 12__ Preparation for adding prefetching: Porting the rest of the micro
  kernel to assembler.
- __Page 13__ Adding prefetching.
- __Page 14__ Benchmarking!  Comparing the performance with __MKL__, __ATLAS__,
  __Eigen__ and the original __BLIS__ micro kernel.


Note that all benchmarks on these pages were generated when __doctool__
transformed the doc files to HTML.  All this happened on my MacBook Pro which
has a 2.4 GHz Intel Core 2 Duo (P8600, "Penryn").  The theoretical peak
performance of one core is 9.6 GFLOPS.

__Back__ to the main course


:links: BLIS           -> https://code.google.com/p/blis/
        BLIS: A Framework for Rapidly Instantiating BLAS Functionality -> http://www.cs.utexas.edu/users/flame/pubs/BLISTOMSrev2.pdf
        doctool        -> https://github.com/michael-lehn/DocTool
        Page (\d)      -> doc:page0$1/index
        Page (\d\d)    -> doc:page$1/index
        ulmBLAS        -> https://github.com/michael-lehn/ulmBLAS
        MKL            -> https://software.intel.com/en-us/intel-mkl
        ATLAS          -> http://math-atlas.sourceforge.net
        Eigen          -> http://eigen.tuxfamily.org/index.php?title=Main_Page
        Back           -> http://apfel.mathematik.uni-ulm.de/~lehn/sghpc