This is the core part of the implementation of HPL-AI mix-precision benchmark.

For the complete implementation of our HPL-AI benchmark, please go to:
https://github.com/wu-kan/HPL-AI

For the original implementation of HPL benchmark (HPL-2.3), which serves as the 
base of our work, please reference:
http://www.netlib.org/benchmark/hpl/index.html


This repository includes:

1. HPL_pir.c

    A mix-precision parallel iterative refinement ( IR ) implementation tuned for HPL-AI.

    based on the paper:

            A New  Analysis  Of Iterative Refinement And Its  Application To 
            Accurate Solution Of Ill Conditioned Sparse Linear Systems

        ---by Carson, Erin & Higham, Nicholas J., 2017

2. HPL_pgmres.c

    A parallel GMRES algorithm based on Householder transformation tuned for HPL-AI.

    based on the implementation of parallel GMRES:

            Parallelization Of The GMRES 

        ---by Morgan Görtz, Lund University.

    and the pioneer work implementing Householder Transformations into GMRES:

            Implementation Of The GMRES Method Using Householder Transformations Method

        ---by Homer F. Walker, 1988

3. HPL_pLdtrsv.c

    A parallel lower triangular system solver following the implementation of HPL_pdtrsv()
     of HPL-2.3, which is a parallel upper triangular system solver.

4. HPL_generate.c

    A parallel matrix generation implementation for HPL-AI.

    based on the paper:

            Matrices with Tunable Infinity-Norm Condition Number
            and No Need for Pivoting in LU Factorization

        --- by Fasi Massimiliano & Higham Nicholas J., 2020