Cholesky

Name: Cholesky Factorization Kernel
Contact Person: OmpSs@FPGA Team, ompss-fpga-support@bsc.es
License Agreement: GPL 3.0
Platform: OmpSs@FPGA

Description

This application performs a cholesky decomposition/factorization over a square matrix. The matrix is distributed by blocks of contiguous memory.

The task implementation requires support for one external library that implements the mathematical operations. Supported ones are:

• Intel MKL
• Open BLAS

Build instructions

Clone the repository:

git clone https://github.com/bsc-pm-ompss-at-fpga/Cholesky.git
cd cholesky

Build the application binaries:

make BOARD=zedboard CROSS_COMPILE=arm-linux-gnueabihf-

Build variables

You can change the build process defining or modifying some environment variables. The supported ones are:

• CFLAGS
  • -DUSE_DMA_MEM. Defining the USE_DMA_MEM variable the blocked matrix is allocated in kernel memory instead of user-space memory.
  • -DUSE_DOUBLE. Defining the USE_DOUBLE variable the matix elements are of type double instead of float.
  • -DVERBOSE. Defining the VERBOSE variable the application steps are shown meanwhile executed.
• LDFLAGS
• GCC. If not defined, the default value is: gcc.
• MCC. If not defined, the default value is: mcc. However, for SMP machines we recommend the use of smpcc.
• CROSS_COMPILE
• MKL_DIR. Installation directory of MKL library. The default value is: $MKLROOT.
  • MKL_INC_DIR. Installation directory of includes for MKL library. The default value is: $MKL_DIR/include.
  • MKL_LIB_DIR. Installation directory of OS libraries for MKL library. The default value is: $MKL_DIR/lib.
• OPENBLAS_DIR. Installation directory of OpenBLAS library. The default value is: $OPENBLAS_HOME.
  • OPENBLAS_INC_DIR. Installation directory of includes for OpenBLAS library. The default value is: $OPENBLAS_DIR/include.
  • OPENBLAS_LIB_DIR. Installation directory of OS libraries for OpenBLAS library. The default value is: $OPENBLAS_DIR/lib.
• BOARD. Board option used when generating the bitstreams.
• FPGA_HWRUNTIME. Hardware Runtime used when generating the bitstreams. The default value is: POM.
• FPGA_CLOCK. Target frequency of FPGA accelerators in the bitstreams. The default value is: 200.
• FPGA_MEMORY_PORT_WIDTH. Bit-width of accelerators memory port to access main memory. The default value is: 128.
• BLOCK_SIZE. Dimension of matrix blocks that FPGA accelerators deal with. The default value is: 32.
• SYRK_NUM_ACCS. Number of FPGA accelerators for syrk task. The default value is: 1.
• GEMM_NUM_ACCS. Number of FPGA accelerators for gemm task. The default value is: 1.
• TRSM_NUM_ACCS. Number of FPGA accelerators for trsm task. The default value is: 1.
• FPGA_GEMM_II. Initiation interval, in cycles, for gemm middle loop. The default value is: 1.
• FPGA_OTHER_II. Initiation interval, in cycles, for syrk and trsm middle loop. The default value is: 1.
• POTRF_SMP. Use SMP arch for potrf tasks. The default value is: 1.

Note that in order to compile the application either MKL_DIR or OPENBLAS_DIR (or the derivate variables) must point to a valid installation.

For example, the build step to cross-compile the application for ARM using the smpcc profile and OpenBLAS library may be:

export MCC=smpcc
export CROSS_COMPILE=arm-linux-gnueabihf-
export OPENBLAS_DIR=/opt/install-arm/openblas
make

Run instructions

The name of each binary file created by build step ends with a suffix which determines the version:

• program-p: performance version
• program-i: instrumented version
• program-d: debug version

All versions use the same arguments structure:

./cholesky <matrix size> [<check>]

where:

• matrix size is the dimension of the matrices. (Mandatory)
• check defines if the result must be checked. Default is: TRUE. (Optional)