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Equation 1 · Part 2 · The Deployment Envelope: Small Models Where the Power Is Not

Symbol R_peak

Rattainable=min⁡(Rpeak,B⋅I)R_{\mathrm{attainable}} = \min(R_{\mathrm{peak}}, B \cdot I)
RpeakR_{\mathrm{peak}}

What this part means

the peak arithmetic rate.

Its job in the formula

RpR_peak appears in the objective or constraint used by the optimization on the right.

Where the article explains it

with RpeakR_{\mathrm{peak}} the peak arithmetic rate, B the achievable memory bandwidth and I the operational intensity of the kernel.

The passage around this formula

The general form of the argument is old and well posed. Williams, Waterman and Patterson built the roofline model on the premise that “for the recent past and foreseeable future, off-chip memory bandwidth will often be the constraining resource”, and defined operational intensity as operations per byte of DRAM traffic [ 1 ] . Their bound is one line, and it is the single most useful line in this whole subject: Rattainable=min⁡(Rpeak,B⋅I)R_{\mathrm{attainable}} = \min(R_{\mathrm{peak}}, B \cdot I). with RpeakR_{\mathrm{peak}} the peak arithmetic rate, B the achievable memory bandwidth and I the operational intensity of the kernel. If I is small, the second term wins and the accelerator’s headline throughput is irrelevant.

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Sources cited in the surrounding passage

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