Using Amdahls Law calculate the speedup gain of an applicati

Using Amdahl\'s Law, calculate the speedup gain of an application that has a 90% parallel component

for the following:

a) Four processing cores.

b) Sixteen processing cores.

Solution

Parallelization Formula given by Amdahl\'s Law

S(n) = 1 / ((1-p) + p/n)

where n is the number of cores

p is the fraction of algorithm that can be made parallel

a) Four processing cores.

here n =4, p = 0.9

S(n) = 1 / (0.1 + 0.9/4) = 4/1.3 = 3.07 is the speed up

b) Sixteen processing cores

here n =16, p =0.9

S(n) = 1 / (0.1 + 0.9/16) = 16/2.5 = 6.4 is the speed up