Equation 11 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
superscript
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.
Full expression→superscript→Article meaning
The passage around this formula
Matrix multiplication is the canonical demonstration because it has enormous latent reuse and a naive schedule that throws almost all of it away. Multiplying two N N matrices performs about 2 operations on 3 words — an intensity proportional to N , which for large N is spectacularly compute-bound in principle. Executed as three nested loops in the obvious order, though, each element of one input is re-read from main memory on every pass, and the realised intensity collapses toward a small constant. The available reuse and the exploited reuse are different quantities, and only the second appears in the roofline.
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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