Equation 17 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol Q
Q is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol N^3
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol M
M is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
superscript
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.
See an illustrated explanation →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.
What the article says around this equation
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
Sources cited in the article section
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