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Equation 2 · Part 7 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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  ≤  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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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