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Equation 9 · Part 1 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol I^*

I∗I^{*}
I∗I^{*}

What this part means

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

Its job in the formula

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

The passage around this formula

Everything else in this article follows from one observation about that ridge point: because Pmax⁡P_{\max} has been growing at roughly twice the rate of B [ 4 ] , I∗I^{*} has been climbing steadily. A kernel whose intensity was comfortably compute-bound on one generation can be memory-bound on the next without a single line of it changing. Hardware progress moves operations across the boundary in only one direction.

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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 surrounding passage

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