Matrix multiplication based on dynamic distributed arithmetic

Abstract

Distributed arithmetic is a technique developed for the real-time computation of the inner product of the vector with constant elements and the vector with varying coefficients. The inner product is computed without splitting into operations of multiplication and addition. At calculation, operations of summation and shift of inner products of an unchangeable vector and a bit-slice of a changeable vector are carried out. All possible values of partial inner products are calculated offline and written down in Look Up Table (LUT). In this paper, it is offered to apply technology of the distributed arithmetic to calculation in real time of product of changeable matrices. Thus, content of LUT is computed dynamically in the online mode. Contents of this memory remain invariable for the period of multiplication of the left matrix by a column of the right matrix. Despite need of calculation of contents of LUT total number of microoperations of addition decreases in comparison with a classical way of calculation of matrix product. The analysis of computational complexity of the offered approach depending on an order of matrices and word length of elements is provided in paper. The offered approach is intended for realization of the advanced algorithms of digital signal processing with application of FPGA.