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Equation 3 · Part 2 · AI Datacenter Interconnects in Practice: An Advanced Technical Guide

subtraction

(n−1)/n(n-1)/n
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

That last point is the operational discipline this section is really about: a changed environment variable is a hypothesis, not a result, until it is measured against the fabric it was set on. The standard instrument for that measurement is bus bandwidth as reported by NCCL’s own test suite, which applies an operation-specific correction factor to the raw bytes-per-second figure — 2(n-1)/n for all-reduce, (n-1)/n for reduce-scatter, all-gather and all-to-all, and a factor of one for broadcast and reduce, where n is the participant count — specifically so the resulting number can be compared directly against the hardware’s rated peak bandwidth regardless of how many ranks are in the job [ 2 ]…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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