No Zero Padded Sparse Matrix-Vector Multiplication on FPGAs

Sparse Matrix-Vector Multiplication (SpMxV) algorithms suffer heavy performance penalties due to irregular memory accesses. In this paper, we introduce a novel compressed element storage (CES) format, in which the additional data structures for indexing are abandoned, and each location associated with the non-zero element of the matrix is now indicated by the name of a variable multiplied by the corresponding element of the vector. To ensure fastest access and parallel access without data hazards, on-chip registers are used exclusively to replace the BRAM or off-chip DRAM/SRAM to hold all the SpMxV data. On-chip DSP resources are fully utilized so as to ensure a maximum number of multipliers concurrently working.