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Equation 1 · Part 5 · The Deployment Envelope: Small Models Where the Power Is Not

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.