The design of optimal planar systolic arrays for matrix multiplication

Forty-three ways of systolic matrix multiplication

“…[5,13,19,20,22]). Non-planar SAs of Class V and VI are obtained by the direction μ whose elements satisfy the condition μ i ∈ {−2, −1, 1, 2}, i = 1, 2, 3 with only one μ i = ±2.…”

“…Therefore, in order to obtain 2D SA with minimal number of PEs, defined by Corollary 3.1, it is necessary for G to have the form defined by Equation (13). Communication links between the PEs are determined as in Equation (12).…”

Matrix multiplication on bidirectional linear systolic arrays

“…According to Algorithm 1, orthogonal two-dimensional (2D) SAs can be synthesized (see, for example [3,4,9,10,15,17]). Orthogonal 2D SAs are obtained by the following projection direction vec-…”

“…2D orthogonal SAs degrade to 1D bidirectional SAs suitable for the implementation of matrix-vector products (see, for example [10,11,12,13]. This is valid only for the direction projections µ = [0 1 1] T and µ = [1 0 1] T .…”

“…N 2 ) times. Details concerning the synthesis of 1D bidirectional SAs for matrix-vector multiplication can be found in [10,11,12,13]. Here we will give some performance measures of bidirectional 1D SAs when used for computing matrix products.…”