← All parts of this equation

Equation 7 · Part 1 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol P_max

Pmax⁡P_{\max}
Pmax⁡P_{\max}

What this part means

the peak arithmetic rate.

Its job in the formula

PmP_max is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

Written as an inequality, attainable performance P satisfies P \;≤\le\; min⁡\min(Pmax⁡,  I⋅B)\left(P_{\max},\; I \cdot B\right), with Pmax⁡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

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.

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

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