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Equation 9 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

superscript

I∗I^{*}
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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

These citations provide research context; check each source for the exact claim it supports.