multiplication

The passage around this formula

It is tempting to compare these four families by a single number — peak operations per second, or operations per watt — and the rest of this article explains why that number, alone, is close to meaningless. A more useful decomposition separates what a device can theoretically do from what a piece of software actually gets it to do, and splits that gap into two distinct causes: $T_{\mathrm{achieved}} = T_{\mathrm{peak}} \cdot U_{\mathrm{hw}} \cdot U_{\mathrm{compiler}}$. Here $T_{\mathrm{peak}}$ is the arithmetic identity fixed at design time, $U_{\mathrm{hw}}$ $\in$ (0,1] is the fraction of cycles the hardware keeps its arithmetic units genuinely busy on whatever workload is thrown at it, and $U_{\mathrm{compiler}}$ $\in$ (0,1] is the fraction of a program’s theoretically…

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