high performance computing on graphics processing units: hgpu.org

Strassen’s matrix multiplication algorithm is an efficient and widely used practical algorithm for matrix multiplication. In its basic form, the algorithm is a series of recursive steps to decompose the matrices, multiply intermediate matrices and another set of recursive steps to recompose the product matrix. Implementing the algorithm on a GPU requires it to be converted into an iterative algorithm and choosing the right mode of execution to achieve maximum parallelism. The iterative algorithm has aspects of both task and data parallelism. Modern GPUs and OpenCL constructs help to program and execute algorithms in either data parallel mode or task parallel mode. Exploiting hybrid parallelism that handles both data as well as task parallelism will be beneficial. However, the onus is on the programmer to understand the underlying device architecture and APIs to extract maximum parallelism in either data parallel mode or task parallel mode. We present some results of such platform aware implementations of Strassen’s algorithm. We also present results of implementation of hybrid parallelism by programmatic tweaking of the features of a device that supports simultaneous execution of multiple independent kernels. In our implementation each kernel is a light-weight kernel that does a single-task and within each kernel data parallelism is achieved. We have evaluated the scope for efficient implementation of the iterative Strassen’s algorithm in different programming modes and based on the results we propose a hybrid task-and-data-parallel OpenCL API extension that reduces the burden on the programmer as well as the run-time synchronization overhead to execute multiple kernels. This proposed API extension will provide native support for hybrid parallelism which is the best among all programming modes.