squarePacked GEMM.

[madanm3]

• squarePacked(sqp) GEMM framework is mainly targeted for real and complex GEMM operation for square and small matrix sizes (where, m=k=n <= 512 and m is multiple of 8).
• First level implementation is done for double precision & double complex precision only.
• Framework uses set of column major dgemm kernels. mx8: {8mx6n, 8mx5n, 8mx4n, 8mx3n, 8mx2n, 8mx1n}
• In dgemm, by default A matrix is always packed and for AtxB operations A transpose is done while packing.
• These real dgemm kernels are re-used in induced zgemm implementation with 3m algorithm.
• 3m implementation in sqp, packs all matrix (A, B & C) and its real and imaginary component.
• New 3m method offers up-to 25% gain over other zgemm implementation in blis for the targeted sizes.
• Though PR implementation is efficient for square and smaller matrix sizes, implementation allows tuning for parameters for other sizes and shapes.
• Replacing multiplication with add and sub when alpha, beta = +/-1 is done in the implementation for both real and complex GEMM.
• Basic multithreading implementation of threading work items along m dimension is done, which could be useful for large m and relatively smaller n and k sizes. This method is currently disabled since more generic implementation with further framework modification is in progress.
• By default, k partition is not done since focus was for small matrix sizes. This does single load and store of C matrix.
• But there is provision in the implementation to do k partition by changing kx parameter.
• Complete implementation is lightweight and limited to 2 c files. One file for framework and another for kernels.
• There is provision to add new kernel set, apart from mx8 kernel set, which is currently used. (new kernel sets - WIP)