Equation 17 · Part 4 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
Symbol N^2
What this part means
The square of N: multiply N by itself.
Its job in the formula
is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.
Full expression→Symbol N^2→Article meaning
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
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
See this notation across published equations →
Sources cited in the article section
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