$$R_{\mathrm{attainable}} = \min(R_{\mathrm{peak}}, B \cdot I)$$

Equation 1 · Small & Edge Models

The Deployment Envelope: Small Models Where the Power Is Not

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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: $R_{\mathrm{attainable}} = \min(R_{\mathrm{peak}}, B \cdot I)$. with $R_{\mathrm{peak}}$ 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.

Meanings in this article

• $R_{\mathrm{peak}}$: the peak arithmetic rate.
• $B$: the achievable memory bandwidth and I the operational intensity of the kernel.
• $I$: the operational intensity of the kernel.

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