amdahl's law

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Gene Amdahl was a great computational architect, recognized worldwide for his advances in the area of computer science, his work with IBM (IBM 360 and IBM 704) and the creation of several technology companies, including the Amdahl Corporation. One of his greatest legacies is the famous Amdahl Law, which he enunciated in the year of 1967 and would change a bit the perspective with respect to the improvement of the processors, determining the maximum performance that these can offer when an improvement is implemented to a part of them.


This law gets its name thanks to the person who enunciated it, the computational architect Gene Amdahl. This law dictates that the improvement that can be obtained in the performance of a system in which any of its parts or components is altered, is limited by the fraction of time that said part or component is used. The speed increase of some program using multiple processors in parallel is limited by the sequential fraction of the program.

This law was used to determine the maximum performance that an information system could achieve when only one part of said system is improved. We can say that Amdahl’s law can be separated into two parts:

  1. Amdahl’s first Law says that the increase in performance due to the improvements made in the system with a new resource, is limited by the time that said improvement is used in carrying out the task and not by the amount of improvements.
  2. The second Amdahl’s Law dictates that when a computer was previously improved and a new improvement is introduced, the performance increase will be much lower than if the same improvement were introduced in an unimproved system, that is, the more improvements are introduced, the lower the acceleration achieved with the new improvements.

Formula of Amdahl’s Law

The original formula of Amdahl’s law is as follows:

F = Fa ((1-Fm) + Fm / Am)


  • Fm the improved runtime
  • Fa the old execution time.
  • Am the improvement factor that has been introduced in the improved subsystem.

With Amdahl’s formulation, the percentage of improvement in the performance of a processor is limited by the percentage of the impact of the element that is to be modified. The law of Amdahl, generalizing is applicable to any problem that has an improvable part and another that cannot be improved.

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