Equation 20 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
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the traffic falls linearly in. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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What the article says around this equation
Two things in that expression matter more than the constant. 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. Second, and less often noticed, traffic falls only as . Quadrupling the fast store buys a factor of two in traffic, not a factor of four. That square root is the reason architects cannot simply spend their way out of the problem with more SRAM, and it is worth holding on to when reading any claim that a larger cache will fix a bandwidth-bound kernel.
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