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The quantity that decides which of these limits binds is arithmetic intensity : the number of arithmetic operations a kernel performs per byte it moves across a given level. Williams, Waterman and Patterson formalised the consequence as the roofline model, which relates attainable floating-point performance to operational intensity and memory bandwidth in a single visual bound [ 5 ] . Written as an inequality, attainable performance P satisfies $P \;\le\; \min\left(P_{\max},\; I \cdot B\right)$. with $P_{\max}$ the peak arithmetic rate, I the arithmetic intensity in operations per byte, and B the achievable bandwidth at the level that dominates. The two terms cross at a ridge point $I^{*}$ = $P_{\max}$/B . Below it a kernel is…

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