What is Amdahl's Law?

Amdahl's Law, named after computer architect Gene Amdahl, is a formula used to find the maximum theoretical improvement of an entire system when only a specific portion of the system is improved. In the world of high-performance computing, it is primarily used to predict the theoretical speedup when using multiple processors.

Understanding the Formula

The standard formula for Amdahl's Law is: S_latency = 1 / ((1 - P) + (P / S))

Where:

• P: The proportion of the execution time that the part benefiting from improved resources originally occupied. (Range: 0 to 1)
• S: The speedup factor of that specific part of the system.
• (1 - P): The serial portion of the task that cannot be improved.

How to Use This Calculator

To use the speedup calculator, first identify what percentage of your task can be parallelized (converted into decimal format). For example, if 80% of your code can run on multiple cores, enter 0.8. Then, enter the speedup factor (S). If you are using 8 processors, S would be 8. Click calculate to see the total system speedup and the step-by-step breakdown of the math.

Frequently Asked Questions

Why does speedup level off?

Amdahl's law demonstrates the law of diminishing returns. No matter how much you increase the speedup of the parallel portion (S), the overall speedup is limited by the serial fraction (1 - P). If 10% of a program is serial, the maximum speedup can never exceed 10x, even with an infinite number of processors.

Amdahl's Law vs. Gustafson's Law?

While Amdahl's Law assumes a fixed problem size, Gustafson's Law suggests that as more processing power becomes available, users tend to run larger and more complex problems. Thus, Gustafson's Law provides a more optimistic view of parallel scaling.