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Published equation contexts

T≈(r+c−2)+LT \approx (r + c - 2) + L

Why this formula appears here

Consider an idealised r ×\times c array holding one operand stationary, with a second operand streamed through in a sequence of length L — for instance, L activation vectors passed through a weight-stationary array of r input rows and c output columns. Before the first result emerges, the data has to propagate across the array’s diagonal, costing roughly r + c - 2 cycles; after the last input enters, the same number of cycles is needed to drain the pipeline. Total latency is therefore approximately T≈(r+c−2)+LT \approx (r + c - 2) + L. 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…

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TT

Symbol T

T is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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rr

Symbol r

r is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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cc

Symbol c

c is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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T≈(r+c−2)+L,T \approx (r + c - 2) + L,

Equation 10 · Semiconductors

How AI Accelerator Architecture Actually Works

This equation gives an approximation: it relates the quantities while allowing an approximation.

Consider an idealised r ×\times c array holding one operand stationary, with a second operand streamed through in a sequence of length L — for instance, L activation vectors passed through a weight-stationary array of r input rows and c output columns. Before the first result emerges, the data has to propagate across the array’s diagonal, costing roughly r + c - 2 cycles; after the last input enters, the same number of cycles is needed to drain the pipeline. Total latency is therefore approximately T≈(r+c−2)+LT \approx (r + c - 2) + L. 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…

Meanings in this article

  • LL: the number of positions in each sequence.
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