Equation 6 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
Symbol P_max
What this part means
the peak arithmetic rate.
Its job in the formula
ax appears in the objective or constraint used by the optimization on the right.
Full expression→Symbol P_max→Article meaning
Where the article explains it
with 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
with 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 = /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.
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 →
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Sources cited in the article section
- [5] Roofline: An Insightful Visual Performance Model for Floating-Point Programs and Multicore Architectures ↗
- [4] AI and Memory Wall ↗
- [1] FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness ↗
- [9] Data Movement Is All You Need: A Case Study on Optimizing Transformers ↗
These citations provide research context; check each source for the exact claim it supports.