Derivation of optimal input parameters for minimizing execution time of matrix-based computations on a GPU

As GPUs are continually being utilized as coprocessors, the demand for optimally utilizing them for various computations continues to grow. The goal of this work is to derive input parameters which yield the minimum execution time for matrix-based computations executing on a GPU. Input parameters are defined as the dimensions of the grid and blocks assigned for execution on the GPU. Since input parameters inadequately represent the executional behavior of the GPU, execution metrics are formulated as functions of the input parameters to represent the behavior. The execution metrics are architecture independent and are utilized to derive optimal input parameters, which are input parameters that yield the minimum execution time. Optimal input parameters are derived for the following matrix-based computations: matrix-vector multiplication (Mv), matrix-matrix multiplication (MM), and convolution. The derivation allows for selection of optimal input parameters without executing code. Results, for all matrix-based computations and sizes tested, show that utilizing the derived optimal input parameters often yields the minimum execution time, and, at worst, execution time within 13.6% of the minimum.