# Measure of Performance

The Speed-Up is the ratio of sequential time $T\left(1\right)$ and the parallel time on $P$ processors $T\left(P\right)$ :(1)
$S\left(P\right)=T\left(1\right)/T\left(P\right)$
The efficiency is defined as:(2)
$E\left(P\right)=S\left(P\right)/P\text{\hspace{0.17em}};\text{\hspace{0.17em}}E\left(P\right)\le 1$
The Amdahl’s law for multitasking is used to determine the speed-up:(3)
$S\left(P\right)=\frac{\left({T}_{Seq}+{T}_{Par}\right)}{\left({T}_{Seq}+{T}_{Par}}{P}\right)}$
Where, ${T}_{Par}$ and ${T}_{Seq}$ are the computation times respectively related to parallel and non-parallel parts. As ${T}_{Seq}+{T}_{Par}=1$ , write:(4)
$S\left(P\right)=\frac{1}{\left({T}_{Seq}+{T}_{Par}}{P}\right)}$
The limit value can be obtained when the process number tends to infinite:(5)
$S\left(\infty \right)=\frac{1}{{T}_{Seq}}$

Process Number

Seq / P

2 4 8 16 32 64 128 $\infty$
100% 2.0 4.0 8.0 16.0 32.0 64.0 128. $\infty$
99% 2.0 3.9 7.5 13.9 24.4 39.3 56.4 100.
98% 2.0 3.8 7.0 12.3 19.8 28.3 36.2 50.0
97% 1.9 3.7 6.6 11.0 16.5 22.1 26.6 33.3
96% 1.9 3.6 6.3 10.0 14.3 18.2 21.1 25.0
95% 1.9 3.5 5.9 9.1 12.5 15.4 17.4 20.0
90% 1.8 3.0 4.7 6.4 7.8 8.7 9.3 10.0
50% 1.3 1.6 1.8 1.9 1.9 2.0 2.0 2.0