Equation 13 · Part 9 · How AI Accelerator Architecture Actually Works
Denominator: L + r + c - 2
What this part means
The complete quantity below the fraction bar; it must be nonzero for this division.
Its job in the formula
L + r + c - 2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Denominator: L + r + c - 2→Article meaning
The passage around this formula
while the useful work performed is r c L multiply-accumulates — one per cell, once per streamed step, in steady state. Dividing useful work by the total cell-cycles available, r c T , gives an idealised utilization . As the streamed sequence L grows large relative to the array’s dimensions, 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…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
- [2] In-Datacenter Performance Analysis of a Tensor Processing Unit ↗
- [6] SCALE-Sim: Systolic CNN Accelerator Simulator ↗
These citations provide research context; check each source for the exact claim it supports.