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.

) Amdahl's law states that the overall speedup of applying the improvement will be:

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.

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.

* Gene Amdahl ( b. 1922 ) computer architect known for Amdahl's Law

The maximum possible speed-up of a program as a result of parallelization is known as Amdahl's law.

* Amdahl's law, a. k. a. Amdahl's argument – Gene Amdahl

The potential speed-up of an algorithm on a parallel computing platform is given by Amdahl's law, originally formulated by Gene Amdahl in the 1960s.

Gustafson's law is another law in computing, closely related to Amdahl's law.

Both Amdahl's law and Gustafson's law assume that the running time of the sequential portion of the program is independent of the number of processors.

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:.

Gene Amdahl's seminal 1964 article on IBM System / 360 used 1K to mean 1024.

* Gene Amdahl, formulator of Amdahl's law of parallel computing and founder of Amdahl Corporation

With Gene Amdahl's departure, and increasing influence from Fujitsu, Amdahl broke into large system multi-processor design in the mid-80's with the 5870 ( attached processor ) and 5880 ( full multiprocessor ) models.

Amdahl owed some of its success to antitrust settlements between IBM and the U. S. Department of Justice, which ensured that Amdahl's customers could license IBM's mainframe software under reasonable terms.

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

By the time IBM introduced its breakthrough 64-bit zSeries 900 in 2000, it was all over for Amdahl's hardware business, which only had 31-bit-addressing Millennium and OmniFlex servers to sell.

The IPL function in the System / 360 and its successors, and its compatibles such as Amdahl's, reads 24 bytes from an operator-specified device into main storage starting at real address zero.

A graphical representation of Amdahl's law.

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