Equation 17 · Part 5 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
Symbol b^2
What this part means
the square of b; the traffic falls linearly in.
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 b^2→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
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
These citations provide research context; check each source for the exact claim it supports.