Amdahl's Law is a computing principle that states that the speedup of a parallel program is limited by the fraction of the program that cannot be parallelized. It is named after its author, Gene Amdahl, who first presented it in a 1967 paper.
The formula for Amdahl's Law is as follows:
S = 1 / (1 - f + f / p)
Where:
S is the speedup, which is the ratio of the parallel execution time to the serial execution time
f is the fraction of the program that can be parallelized
p is the number of processors
The meaning of Amdahl's Law is as follows:
In parallel computing, the speedup is limited by the fraction of the program that cannot be parallelized.
Even if the number of processors increases to infinity, it cannot completely compensate for the impact of a small parallel fraction.
Applications of Amdahl's Law
Amdahl's Law can be used to analyze the performance bottlenecks of parallel computing systems. For example, if the parallel fraction of a system is 2/3, then even if the number of processors increases to infinity, the speedup can only reach 3/2. This means that even if the parallel performance of the system is greatly improved, it is still impossible to compensate for the impact of a small parallel fraction.
Amdahl's Law can also be used to guide the design of parallel computing systems. For example, if a system wants to achieve a higher speedup, it needs to maximize the parallel fraction. This can be done in the following ways:
Divide the parallelizable part into smaller parts so that they can be executed in parallel.
Use more efficient parallel algorithms.
Optimize the communication and synchronization mechanisms of the parallel system.
Limitations of Amdahl's Law
Amdahl's Law is based on a fixed-sized task model. In practice, the size of tasks is often variable. If the size of the task increases with the increase in the number of processors, the speedup may be further improved.
Summary
Amdahl's Law is an important theory in the field of parallel computing. It can help us understand the performance bottlenecks of parallel computing systems and guide the design of parallel computing systems.
Examples of Amdahl's Law
Here are some examples of how Amdahl's Law can be applied:
A computer program that has a 50% parallel fraction will only achieve a speedup of 2x, even if the number of processors increases to infinity. This is because the program will still spend half of its time executing the serial fraction.
A parallel computing system that is designed to solve a problem that is 90% parallelizable can achieve a speedup of 10x with 10 processors. This is because the parallel fraction of the problem is large enough to be able to take advantage of the increased number of processors.
A parallel computing system that is designed to solve a problem that is only 10% parallelizable will only achieve a speedup of 1.1x, even if the number of processors increases to infinity. This is because the parallel fraction of the problem is too small to be able to significantly improve the performance of the system.