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Equation 6 · Part 10 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

Numerator: 2mnk

Igemm=2mnks (mk+kn+mn),I_{\mathrm{gemm}} = \frac{2mnk}{s\,(mk + kn + mn)},
2mnk2mnk

What this part means

The complete quantity above the fraction bar.

Its job in the formula

2mnk occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Multiplying an m ×\times k matrix by a k ×\times n matrix performs 2mnk floating-point operations while touching mk + kn + mn elements. If each element occupies s bytes, the ratio of work done to bytes moved is Igemm=2mnks (mk+kn+mn)I_{\mathrm{gemm}} = \frac{2mnk}{s\,(mk + kn + mn)}. which for large square matrices grows in proportion to the dimension. Double the matrix size and you roughly double the work performed per byte fetched. Almost nothing else in general-purpose computing behaves this way, and it is the entire economic basis for building a machine around one operation.

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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

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