Understanding Amdahl's law

Question

I am trying to understand the following slide

The definition is kind of unclear to me. Sources like wikipedia say that Amdahl's measures the speedup in latency of the execution of a task at fixed workload that can be expected of a system whose resources are improved. To me speedup is basically how faster a task runs over other task. Speedup in this case is used in a different way. Can you clarify what Amdahl's law measures in an easier way and what speed up really is?

Answer 1

The definition of speedup here is:

Speedup = Baseline Running Time / New Running Time

This means that if the running time is BRT and the parallelizable portion is P, then:

BRT = (1 - P) * BRT + P * BRT

Now if a speedup of S was obtained on the P portion of the running time, then the new improved running time (IRT) is:

IRT = (1 - P) * BRT + P * (BRT / S)
    = (1 - P) * BRT + (P / S) * BRT
    = ((1 - P) + (P / S)) * BRT

Therefore:

BRT / IRT = 1 / ((1 - P) + (P / S))

This is the overall speedup. This is Amdahl's law.

To me speedup is basically how faster a task runs over other task.

Yes, speedup can be defined in different ways. This can be a little confusing.