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Equation 2 · Part 3 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol I

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

What this part means

the arithmetic intensity in operations per byte.

Its job in the formula

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

Where the article explains it

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 passage around this formula

…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 by traffic; above it the kernel is compute-bound and traffic is hidden.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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