Equation 17 · Part 12 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Numerator: 2N^3

Q(b) \;\approx\; \frac{2N^3}{b} + N^2, \qquad \text{subject to} \quad 3b^2 \le M .

2N^3

What this part means

The complete quantity above the fraction bar.

Its job in the formula

2 $N^3$ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionNumerator: 2N^3Article 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 $\times$ 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: $Q(b) \;\approx\; \frac{2N^3}{b} + N^2, \qquad \text{subject to} \quad 3b^2 \le M$ . Taking b as large as the constraint allows gives

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

[13] TVM: An Automated End-to-End Optimizing Compiler for Deep Learning ↗

These citations provide research context; check each source for the exact claim it supports.