Amdahl

Amdahl

Amdahl's Law is a formula used to find the maximum improvement possible by enhancing a particular part of a system. In computing, it is often used to predict the theoretical maximum speedup for program processing using multiple processors compared to a single processor. The law is named after Gene Amdahl, who presented it in 1967.

Overview

Amdahl's Law addresses the issue of speedup in a system that results from increasing the resources of a particular part of the system. The law is particularly significant in the field of parallel computing, where it is used to predict the potential speedup of a task by dividing it among multiple processors. The essence of Amdahl's Law can be summarized by the formula:

\[S = \frac{1}{(1 - P) + \frac{P}{N}}\]

where:

• \(S\) is the theoretical speedup of the execution of the whole task,
• \(P\) is the proportion of the task that can be parallelized (0 ≤ P ≤ 1),
• \(N\) is the number of processors, and
• \(1 - P\) is the proportion of the task that must be performed serially.

Implications

Amdahl's Law has significant implications for computer architecture and software development. It suggests that there is a diminishing return on adding more processors because the serial portion of a task limits the overall speedup achievable. This has led to a focus on not just adding more processors, but also on optimizing software to minimize the serial components and maximize the parallelizable components.

Limitations

While Amdahl's Law provides a useful framework for understanding the potential speedup from parallel processing, it has limitations. It assumes that the problem size remains constant and does not take into account the overhead of coordinating multiple processors, such as communication and synchronization costs. Furthermore, it does not address the issue of scalability beyond a certain number of processors.

See Also

• Parallel computing
• Computer architecture
• Scalability
• Gene Amdahl