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Equation 6 · Part 7 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

fraction

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

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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

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