Amdahl's Law

The performance rule that tells how much speed-up a program can gain when only part of it can run in parallel.

All programs have a serial portion and a parallel portion. Addition of CPU cores only speeds up the parallel portion. The performance improvement gained is limited by the fraction of time that the improved part is actually used.

$$\text{Speedup}(N) = \cfrac{1}{S + \frac{1 - S}{N}}$$

Here:

• $N$ - number of processing cores
• $S$ - serial portion of the task
• $P = 1- S$ - parallel portion of the task

Serial portion of an application has disproportionate effect on performance gained by adding additional cores.

If $S$ is large, speedup is small even with many cores. As $N$ increases, the speedup approaches $\frac{1}{S}$, which is the maximum.