Amdahl’s Law can be expressed mathematically as follows:
$$ \mathrm{Speedup}_{\max} = \frac{1}{(1-p) + \frac{p}{s}} $$- SpeedupMAX = maximum performance gain
- s = performance gain factor of p after implementing the enhancements.
- p = the part whose performance needs to be improved.
Let’s take an example. If the part that can be improved is 30% of the overall system and its performance can be doubled, then:
$$ \displaystyle \mathrm{Speedup}_{\max} = \frac{1}{(1-0.30)+\frac{0.30}{2}} = 1.18 $$
Oregon State University — Amdahl’s Law
If you buy a system with n cores, you should get n times Speedup (and 100% Speedup Efficiency), right? Wrong! There is always some fraction of the total operation that is inherently sequential and cannot be parallelized no matter what you do. This includes reading data, setting up calculations, control logic, storing results, etc.
Tutorialspoint — What is Amdahl’s Law?
La Ley de Amdahl dice que el rendimiento total está limitado por la parte del sistema que no podemos acelerar.
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