Loop Reordering

This is a simple example of matrix multiplication (Row x Col) to demonstrate how to achieve better pipeline II factor by loop reordering.

KEY CONCEPTS: Kernel Optimization, Loop reorder to improve II

KEYWORDS: #pragma HLS ARRAY_PARTITION

This example demonstrates how changing the order of loop can improve the performance of the kernel. In this case, loop reordering helps us achieve better Initiation Interval(II).

If matrix multiplication is performed with the commented code as shown below, Initiation Interval achieved is 64.

// lreorder1: for (int i = 0; i < size; i++) {
//     lreorder2: for (int j = 0; j < size; j++) {
//         lreorder3: for (int k = 0; k < MAX_SIZE; k++) {
//             int result = (k == 0) ? 0 : temp_sum[j];
//             result += A[i][k] * B[k][j];
//             temp_sum[j] = result;
//             if (k== size -1) C[i][j] = result;
//         }
//     }
// }

With the reordered loop as shown below, II achieved is 1. Reordering avoids the adder tree for the sum(output) of a single output element.

lreorder1:
    for (int i = 0; i < size; i++) {
       #pragma HLS LOOP_TRIPCOUNT min=c_size max=c_size
    lreorder2:
        for (int k = 0; k < size; k++) {
           #pragma HLS LOOP_TRIPCOUNT min=c_size max=c_size
        lreorder3:
            for (int j = 0; j < MAX_SIZE; j++) {
                int result = (k == 0) ? 0 : temp_sum[j];
                result += A[i][k] * B[k][j];
                temp_sum[j] = result;
                if (k == size - 1)
                    C[i][j] = result;
            }
        }
    }

EXCLUDED PLATFORMS:

• 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.cpp

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

./loop_reorder <mmult XCLBIN>