Amdahl's law, also known as Amdahl's argument, is named after computer architect Gene Amdahl, and is used to find the maximum expected improvement to an overall system when only part of the system is improved.

Amdahl's law is a model for the relationship between the expected speedup of parallelized implementations of an algorithm relative to the serial algorithm, under the assumption that the problem size remains the same when parallelized.

For example, if for a given problem size a parallelized implementation of an algorithm can run 12 % of the algorithm's operations arbitrarily quickly ( while the remaining 88 % of the operations are not parallelizable ), Amdahl's law states that the maximum speedup of the parallelized version is times as fast as the non-parallelized implementation.

In the case of parallelization, Amdahl's law states that if P is the proportion of a program that can be made parallel ( i. e., benefit from parallelization ), and ( 1 − P ) is the proportion that cannot be parallelized ( remains serial ), then the maximum speedup that can be achieved by using N processors is

P estimated in this way can then be used in Amdahl's law to predict speedup for a different number of processors.

Amdahl's law is often conflated with the law of diminishing returns, whereas only a special case of applying Amdahl's law demonstrates ' law of diminishing returns '.

Amdahl's law does represent the law of diminishing returns if you are considering what sort of return you get by adding more processors to a machine, if you are running a fixed-size computation that will use all available processors to their capacity.

* Amdahl's law

These systems faced initial skepticism, based on the assumption that applications do not have significant parallelism, because of Amdahl's law, but the success of early systems such as nCUBE and the fast progress in microprocessor performance following Moore's law led to a fast replacement.

However, for supercomputing, the low latency of Myrinet is even more important than its throughput performance, since, according to Amdahl's law, a high-performance parallel system tends to be bottlenecked by its slowest sequential process, which in all but the most embarrassingly parallel supercomputer workloads is often the latency of message transmission across the network.

The result was rather disappointing real-world performance, something that could, perhaps, have been forecast by Amdahl's law.

Amdahl's law –

The achievable reduction is governed primarily by the ( somewhat obvious ) law known as Amdahl's law, that essentially states that the improvement from parallel processing is determined by its slowest sequential component.

If is the fraction of a calculation that is sequential, and is the fraction that can be parallelized, the maximum speedup that can be achieved by using P processors is given according to Amdahl's Law:.

Amdahl's law assumes that the entire problem is of fixed size so that the total amount of work to be done in parallel is also independent of the number of processors, whereas Gustafson's law assumes that the total amount of work to be done in parallel varies linearly with the number of processors.

As such, the original STAR proved to be a great disappointment when it was released ( see Amdahl's Law ).

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For example if 50 % of the total execution time ( or path length ) is absorbed in a subroutine whose speed can be doubled by programmer optimization, an overall saving of around 25 % might be expected ( Amdahl law ).

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