Sequences of Sparse Matrix-Vector Multiplication on Fugaku’s A64FX processors

Abstract

We implement parallel and distributed versions of the sparse matrix-vector product and the sequence of matrixvector product operations, using OpenMP, MPI, and the ARM SVE intrinsic functions, for different matrix storage formats. We investigate the efficiency of these implementations on one and two A64FX processors, using a variety of sparse matrices as input. The matrices have different properties in size, sparsity and regularity. We observe that a parallel and distributed implementation shows good scaling on two nodes for cases where the matrix is close to a diagonal matrix, but the performances degrade quickly with variations to the sparsity or regularity of the input.

Memory-aware Optimization for Sequences of Sparse Matrix-Vector Multiplications

“…Therefore, the dataset can be useful in testing the generalization ability of our approach. We also include some of the same matrix inputs used in prior work for optimizing SpMV [14], [36] and MPK [37] for a fair comparison.…”

“…Thirdly, LB-MPK requires significantly higher preprocessing overhead than our approach. Finally, [14] reports the performance of SSpMV vector addition, A(Ax + x) + x, on the Fugaku's A64FX processor using a standard SSpMV implementation. However, it does not provide memory optimization like our work.…”

“…These prior optimizations have primarily focused on the computation of a single, isolated SpMV invocation. While important, they ignore the optimization opportunities for a sequence of SpMV (SSpMV) operations [14], [15]. An SSpMV pattern involves performing a series of SpMV operations, such as Ax, A 2 x, A 3 x, • • • , A k x, and their linear combinations, such as A 2 x + Ax, where the same sparse matrix A is reused across invocations.…”

“…FBMPK is designed to support generic sequence sparse matrix-vector multiplication (SSpMV) of the form y = k i=0 α i A i x, where α i are real or complex constants. We evaluate our approach by applying it to the sparse matrix-power-vector kernel (MPK) [14], [15], which represents an instance of SSpMV. We test the performance of our system on four multi-core systems: three ARM systems, including Phytium (FT) 2000+ [24], Kunpeng (KP) 920 [25], and Thunder X2 [26], as well as an Intel platform.…”