fraction

The passage around this formula

while the useful work performed is r $\cdot$ c $\cdot$ L multiply-accumulates — one per cell, once per streamed step, in steady state. Dividing useful work by the total cell-cycles available, r $\cdot$ c $\cdot$ T , gives an idealised utilization $\eta \approx \frac{L}{L + r + c - 2}$. As the streamed sequence L grows large relative to the array’s dimensions, $\eta$ approaches one and the fill-and-drain overhead becomes negligible. But when L is comparable to r and c — a small batch, a short sequence, a matrix dimension that barely exceeds the array’s own size — the overhead is not a rounding error, it is a large fraction of every pass through the array. This is a simplified model, not a specification of any one…

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