An improved reduction algorithm with deeply pipelined operators

Many scientific applications involve reduction or accumulation operations on sequential data streams. Examples such as matrix-vector multiplication include multiple inner product operations on different data sets. If the core operator of the reduction is deeply pipelined, which is usually the case, dependencies between the input data cause data hazards in the pipeline and ask for a proper design. In this paper, we propose a modified design of the reduction operation based on Sips and Lin´s method. We analyze the performance of the proposed design to prove the correctness of the timing and demonstrate its performance against previous methods.