An Integral-equation-oriented Vectorized SpMV Algorithm and its Application on CT Imaging Reconstruction

Sparse-matrix vector multiplication (SpMV) is a core routine in many applications. Its performance is limited by memory bandwidth, which is for matrix transport between processors and memory, and instruction latency in computations. Vectorized operations (SIMD) can dramatically improve the execution efficiency, but irregular matrices' sparsity pattern is not compatible with the style of SIMD execution. We present a new matrix format, Compressed Sparse Column Vector (CSCV), and a corresponding vectorized SpMV algorithm for matrices arising from integral equations. This SpMV algorithm can inherently suit wide SIMD instructions and reduce the memory bandwidth used. We implement this algorithm for Computed Tomography (CT) imaging reconstructions on both Intel and AMD x86 platforms and compare it with seven state-of-the-art SpMV implementations using different CT imaging matrices. Experimental results show that CSCV can achieve up to 96.9 GFLOP/s in single-precision tests, with speedup 3.70× to MKL and 3.48× to the second place implementation. Furthermore, the implementation of CSCV SpMV is performance portable, which excludes almost all SIMD assemble code and has promising performance with compiler-assisted vectorization. Code Availability: https://github.com/sysu-compsci/cscv