The Amdahl's Law

In computer architecture, Amdahl's law is a formula that predicts the theoretical maximum speedup in latency of the execution of a task when multiple processors or processor cores are used. According to Amdahl's law, the maximum achievable speedup is limited by the fraction of the task that cannot be parallelized.

Formula

The formula for calculating the maximum theoretical speedup is as follows:

Speedup = 1 / (1 - P + (P / N))

Where:

• P = the proportion of the program that can be parallelized
• N = the number of processors

Explanation

The Amdahl's law shows that as the number of processors increase, the speedup gained from parallelization becomes less effective due to the sequential portion of the program that cannot be parallelized. In other words, adding more processors to a system will eventually reach a point of diminishing returns.

For example, if a program can be parallelized by 80%, and we have 10 processors, the maximum theoretical speedup that can be achieved is:

Speedup = 1 / (1 - 0.8 + (0.8 / 10)) = 4.38x

This means that the program would run 4.38 times faster on 10 processors compared to a single processor.

Conclusion

Amdahl's law is an important concept for programmers to understand when designing and optimizing parallel programs. It helps programmers determine the optimal number of processors to use in order to achieve maximum performance gain. However, it is important to note that Amdahl's law is only a theoretical model and the actual speedup achieved in practice may differ due to various factors such as overhead, communication costs, and load imbalance.