In this section, systolic arrays are designed for matrix-matrix multiplication . The DG for this problem corresponds to a three-dimensional (3D) space representation. Linear projection is used to design 2D systolic arrays for matrix-matrix multiplication.
Given 2 matrices A and B, we can denote their product as C = AB, where A, B, and C are n × n matrices. For n = 2, we have
These equations can be represented in a space representation as shown in Fig. 7.17.
From the space diagram, we can write the iteration in standard output RIA form as follows:
The corresponding RDG is shown in Fig. 7.18. Now, applying the scheduling inequality for each edge in the RDG sTe + γy − γx ≥ Tx and assuming
Tmult−add = 1 and Tcom = 0, we have,
For linear scheduling, γa = γb = γc = 0. Consider ...