Equation 6 · Part 3 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol B

I^{*} = P_{\max}/B

B

What this part means

the achievable bandwidth at the level that dominates.

Its job in the formula

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

Full expressionSymbol BArticle meaning

Where the article explains it

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 passage around this formula

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 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 article section

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