Amdahl’s law: definition · Chip Field Guide

Beginner

The rule that speeding up part of a job can only help so much, because the part you didn’t speed up still takes its time.

Novice

$\text{Speedup} = 1 / \bigl((1 - f) + f/s\bigr)$ , where $f$ is the fraction of the original run time that gets faster and $s$ is how much faster it gets. If $f = 0.8$ , the other 20% still takes its full time, so the speedup can never exceed 5×, however large $s$ is.

Expert

Applies to accelerators ( $f$ is the share of time that can be offloaded, and the cost of handing work over belongs in the part that isn’t sped up) and to multicore chips ( $s$ is the number of cores). It assumes a fixed job; Gustafson’s law covers jobs that grow with the machine.