Equation 19 · Part 2 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read
Symbol N^3
What this part means
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Its job in the formula
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Symbol N^3→Article meaning
The passage around this formula
Taking b as large as the constraint allows gives . 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.
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.