Output-stationary and other dataflows

Ask which value remains local

A systolic array performs parallel work while operands move through neighboring processing elements. “Stationary” describes a value retained nearby for reuse during a computation. Different choices change PE registers, partial-sum paths and the boundary schedule even when the mathematical operation is identical.

In this course's output-stationary design, PE(i,j) retains the partial sum for C(i,j). A and B move as k advances. After all K terms arrive, the result is collected; clear starts a new output tile. A values are reused across a row and B values down a column. In the 2×2 example, A(0,0)=1 contributes to both C(0,0) and C(0,1).

Weight-stationary designs preload weights such as B into PEs and reuse them across incoming activations. Partial sums must move or collect elsewhere. Renaming ports does not transform the OS controller into WS: the stored value, preload sequence and result path all change. Input-stationary designs retain activations for reuse across weights or output calculations. We compare that idea without implementing an IS array here.

Keep three traffic measurements separate

Consider two 2×2 products using the same B. Our OS boundary model feeds four A and four B values per job: sixteen operand values across two jobs. A local B buffer can avoid rereading B from external memory for the second job, while still supplying its four boundary tokens. Weight preload reuse offers a different tradeoff and requires a different partial-sum path.

External reads, boundary injections and PE-to-PE transfers are separate measurements. The UC Berkeley Gemmini README provides a primary-source example of configurable OS and WS dataflows. Our learning array has its own contract and does not reproduce Gemmini's implementation or instruction interface.

For a design review, identify what stays local, where sums accumulate and which values cross each boundary. Reuse alone does not guarantee adequate memory ports or sustained throughput.