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Equation 2 · Part 1 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol P

P  ≤  min⁡(Pmax⁡,  I⋅B),P \;\le\; \min\left(P_{\max},\; I \cdot B\right),
PP

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

Its job in the formula

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

The passage around this formula

…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  ≤  min⁡(Pmax⁡,  I⋅B)P \;\le\; \min\left(P_{\max},\; I \cdot B\right). with Pmax⁡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∗I^{*} = Pmax⁡P_{\max}/B . Below it a kernel is memory-bound and its runtime is set…

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