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Equation 6 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol P_max

I∗=Pmax⁡/BI^{*} = P_{\max}/B
Pmax⁡P_{\max}

What this part means

the peak arithmetic rate.

Its job in the formula

PmP_max appears in the objective or constraint used by the optimization on the right.

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

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 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 article section

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