Algorithm Design for Tensor Units

Toward accelerated stencil computation by adapting tensor core unit on GPU

“…However, summing up T a [1][1] and T b [1][1] will lead to incorrect result. This is because the first column of P b are the coefficients required by the reduction of the second row in [5] is excepted), other than the first row. Thus, the matrix A ′ cannot be multiplied directly by parameter matrix as in star stencil.…”

“…As shown in Figure 9, after each GEMM operation, we move A ′ one row down along the input mesh. For example, to update point M [5][3], the first GEMM operation starts at the first row of the input mesh, where T a [3] Similar to star stencil (Figure 4 and Figure 5), all points of the inner region with size of L + 2r × L can be calculated by 2r + 1 GEMMs operations on TCU for box stencil, as shown in Figure 9, and the points of the boundary region can be updated with partial weighted reductions through GEMMs operations (the other partial weighted reductions are calculated using FMA on CUDA cores).…”

“…These works fail to consider the characteristics of stencil computation when using TCU, and thus cannot fully utilize the computation resources of TCU. For example, Chowdhury et al [5] transform each stencil computation into convolution between weight matrix (stencil coefficients) and data matrix (stencil mesh). However, most values of the weight matrix are zero and each convolution can only update one point, which leads to low efficiency for optimizing the performance of stencil computation.…”