Equation 6 · Part 1 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol I^*

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

I^{*}

What this part means

$I^*$ is the quantity selected or evaluated by the optimization written on the right.

Its job in the formula

$I^*$ is the quantity selected or evaluated by the optimization written on the right.

Full expressionSymbol I^*Article meaning

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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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