Equation 17 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
Symbol b
What this part means
the traffic falls linearly in.
Its job in the formula
b occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Symbol b→Article meaning
Where the article explains it
First, traffic falls linearly in b : doubling the tile halves the bytes moved, which is why tiling is the single highest-leverage transformation in dense linear algebra.
The passage around this formula
The repair is to restructure the loops so that the working set of the innermost computation is small enough to sit in a fast store and is used many times before being evicted. Partition the operands into b b blocks and compute block by block. Three such blocks — two inputs and an accumulator — must be resident simultaneously, so the tile size is bounded by the fast-store capacity M in words: . Taking b as large as the constraint allows gives
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.
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Sources cited in the article section
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