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Amdahl's law: the slowest unimproved part of a task caps how much faster a whole system can get
Amdahl's law says that the overall speedup from improving one part of a system is capped by how much of the work that part handles. If a program spends 90 percent of its time on a task that you make infinitely fast, the whole program can at most become ten times faster, because the remaining 10 percent still takes the same time. The unimproved part becomes the bottleneck. Gene Amdahl presented the idea in 1967 at a major computing conference, in an argument about the limits of parallel processors. It is why adding more processor cores eventually stops helping: the parts of a job that must run one step after another set the ceiling. The law applies to any system, not just computers.
Suppose a fraction p of a task can be sped up by a factor s. The total time becomes (1 minus p) plus p divided by s, in units of the original time. As s grows large, the time never falls below the fraction that cannot be sped up, so the total speedup is capped at one divided by that fraction.
Amdahl's law sets realistic expectations for performance upgrades, from faster chips to parallel software. It explains why engineers spend effort on the slowest step rather than the step that already works well.
Gene Amdahl was a chief architect of IBM's System/360 mainframe family before founding his own computer company.
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