Due to high parallelism, field-programmable gate arrays are widely used as accelerators in engineering and scientific fields, which involve a large number of operations of vector and matrix. High-performance accumulation circuits are the key to large-scale matrix operations. By selecting the adder as the reduction operator, the reduction circuit can implement the accumulation function. However, the pipelined adder will bring challenges to the design of the reduction circuit. To solve this problem, we propose a novel reduction circuit based on binary tree path partition, which can simultaneously handle multiple data sets with arbitrary lengths. It divides the input data into multiple groups and sends them to different iterations for calculation. The elements belonging to the same data set in each group are added to obtain a partial result, and the partial results of the same data set are added to achieve the final result. Compared with other reduction methods, it has the least area-time product.
The Hochschild Cohomology Group of a Class of Directed Tree-Path Algebras
