Systolic Array Implementation (OpenCL Kernel)

This is a simple example of matrix multiplication (Row x Col) to help developers learn systolic array based algorithm design. Note: Systolic array based algorithm design is well suited for FPGA.

This example demonstrates how Systolic array algorithm can be used in FPGAs to perform matrix operations efficiently.

Matrix multiplication is performed in the mmult kernel. Local matrices A and B are partitioned using attribute xcl_array_partition along rows and columns respectively for computation of each element of the matrix C requires a row of matrix A and a column of matrix B. Matrix C is partitioned completely.

int localA[MAX_SIZE][MAX_SIZE]  __attribute__((xcl_array_partition(complete, 1)));;
   int localB[MAX_SIZE][MAX_SIZE]  __attribute__((xcl_array_partition(complete, 2)));;
   int localC[MAX_SIZE][MAX_SIZE]  __attribute__((xcl_array_partition(complete, 0)));;

This allows the multiply and accumulate operations in the below code to be performed in parallel thus speeding up the operation as innermost loop is unrolled to provide for the pipelining in the outer loops. However, the number of these parallel operations is limited by the number of DSPs available in the FPGA.

systolic1: for(int k = 0; k < a_col; k++) {
        __attribute__((xcl_loop_tripcount(c_size, c_size)))
        systolic2: for(int i = 0; i < MAX_SIZE; i++) {
            __attribute__((xcl_loop_tripcount(c_size, c_size)))
            systolic3: for(int j = 0; j < MAX_SIZE; j++) {
                int last = (k==0) ? 0 : localC[i][j];
                int a_val = (i < a_row && k < a_col)? localA[i][k] : 0;
                int b_val = (k < b_row && j < b_col)? localB[k][j] : 0;
                int result = last + a_val*b_val;

                localC[i][j] = result;
            }
        }
    }

EXCLUDED PLATFORMS:

• Embedded ZC702

• All NoDMA Platforms, i.e u50 nodma etc

DESIGN FILES

Application code is located in the src directory. Accelerator binary files will be compiled to the xclbin directory. The xclbin directory is required by the Makefile and its contents will be filled during compilation. A listing of all the files in this example is shown below

src/host.cpp
src/mmult.cl

Access these files in the github repo by clicking here.

COMMAND LINE ARGUMENTS

Once the environment has been configured, the application can be executed by

./cl_systolic_array <mmult XCLBIN>