====================================
GEMM (General Matrix-Matrix Product)                                        [TOC:2]
====================================

The benchmark tests the GEMM Operation

---- LATEX ---------------------------------------------------------------------
C \leftarrow \beta C + \alpha\,A\,B
--------------------------------------------------------------------------------

where

 - $\alpha$ and $\beta$ are scalars,
 - $C$ is a $m \times n$ matrix,
 - $A$ is a $m \times k$ matrix and
 - $B$ is a $k \times n$ matrix.

In the benchmarks we used $m = n = k$ and $\alpha = \beta =1$.  However, these
can easily be modified to more general cases by setting macros in the compile
command:

    - `-DMIN_M=<m>`, `-DMIN_K=<k>`, `-DMIN_N=<n>` defines the minimal
      dimensions.
    - `-DMAX_M=<m>`, `-DMAX_K=<k>`, `-DMAX_N=<n>` defines the maximal
      dimensions.
    - `-DINC_M=<m>`, `-DINC_K=<k>`, `-DINC_N=<n>` defines the increment
      of dimensions in the benchmark.
    - `-DALPHA=<alpha>`, `-DBETA=<beta>` defines the scalar values being used.

Also the element types for $A$, $B$, $C$ and the scalars $\alpha$ and $\beta$
can be set through

    - `-DTYPE_A=<type>`, `-DTYPE_B=<type>`, `-DTYPE_C=<type>`,
      `-DTYPE_ALPHA=<type>`, `-DTYPE_BETA=<type>`

In this benchmarks we only test homogeneous types, e.g. `type` is `double`.


Single Precision
================

---- IMAGE -----------------
BLAS3/bench.sgemm.mflops.svg
----------------------------

Double Precision
================

---- IMAGE -----------------
BLAS3/bench.dgemm.mflops.svg
----------------------------

Complex Single Precision
========================

---- IMAGE -----------------
BLAS3/bench.cgemm.mflops.svg
----------------------------

Complex Double Precision
========================

---- IMAGE -----------------
BLAS3/bench.zgemm.mflops.svg
----------------------------


Raw Results from Benchmarks
===========================

---- SHELL (path=BLAS3,hostname=heim) ------------------------------------------
make BLAS_FUNCTIONS=gemm clean
make BLAS_FUNCTIONS=gemm
./sgemm_MKL > report.sgemm_MKL
./dgemm_MKL > report.dgemm_MKL
./cgemm_MKL > report.cgemm_MKL
./zgemm_MKL > report.zgemm_MKL
./sgemm_Eigen > report.sgemm_Eigen
./dgemm_Eigen > report.dgemm_Eigen
./cgemm_Eigen > report.cgemm_Eigen
./zgemm_Eigen > report.zgemm_Eigen
./sgemm_openBLAS > report.sgemm_openBLAS
./dgemm_openBLAS > report.dgemm_openBLAS
./cgemm_openBLAS > report.cgemm_openBLAS
./zgemm_openBLAS > report.zgemm_openBLAS
./sgemm_BLIS > report.sgemm_BLIS
./dgemm_BLIS > report.dgemm_BLIS
./cgemm_BLIS > report.cgemm_BLIS
./zgemm_BLIS > report.zgemm_BLIS
gnuplot plot.sgemm.mflops
gnuplot plot.dgemm.mflops
gnuplot plot.cgemm.mflops
gnuplot plot.zgemm.mflops
--------------------------------------------------------------------------------


Single Precision
----------------

---- SHELL (path=BLAS3,hostname=heim) ------------------------------------------
cat report.sgemm_MKL
cat report.sgemm_Eigen
cat report.sgemm_openBLAS
cat report.sgemm_BLIS
--------------------------------------------------------------------------------


Double Precision
----------------

---- SHELL (path=BLAS3,hostname=heim) ------------------------------------------
cat report.dgemm_MKL
cat report.dgemm_Eigen
cat report.dgemm_openBLAS
cat report.dgemm_BLIS
--------------------------------------------------------------------------------


Complex Single Precision
------------------------

---- SHELL (path=BLAS3,hostname=heim) ------------------------------------------
cat report.cgemm_MKL
cat report.cgemm_Eigen
cat report.cgemm_openBLAS
cat report.cgemm_BLIS
--------------------------------------------------------------------------------


Complex Double Precision
------------------------

---- SHELL (path=BLAS3,hostname=heim) ------------------------------------------
cat report.zgemm_MKL
cat report.zgemm_Eigen
cat report.zgemm_openBLAS
cat report.zgemm_BLIS
--------------------------------------------------------------------------------