# Amdahl’s Law and Gustafson’s Law

**Amdahl’s law** states that the speedup achieved through parallelisation of a program is limited by the percentage of its workload that is inherently serial. We can get no more than a maximum speedup equal to *1 / (s + p / N ) *where

*s = *the length of the serial part of the problem

*p = the length of the parallel part of the problem*

*N = number of processors used
*

**Gustafson’s law*** *states that , with increasing data size, the speedup obtained through parallelisation increases, because the parallel work increases(scales) with data size.

To those who took Amdahl’s law as an argument against Massively Parallel Processing, Gustafson’s law proves they are wrong.

1. Today, Amdahl’s presumption of fixed data size is obviously a restriction which does not map into reality for many problems.

2. Both laws are in fact different perspective over the same truth – one sees data size as fixed and the other sees the relation as a function of data size.* *