Equation 5 · Part 1 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
Symbol B
What this part means
the achievable bandwidth at the level that dominates.
Its job in the formula
B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol B→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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value 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.