Amdahl’s Law CPS 5401 Fall 2013 Shirley Moore

Amdahl’s Law The performance improvement to be realized from using some faster mode of execution is limited by the fraction of time the faster mode can be used. “The performance improvement to be realized from improving some feature of a design is limited by the amount of time that feature is used and by the amount of improvement to the feature.” “Make the common case fast.”

Speedup What is speedup? Performance for entire task using enhancement Speedup = ______________________________________ Performance for entire task without enhancement OR Execution Time without enhancement _______________________________ Execution Time with enhancement Realizing that Performance is inversely related to execution time: e.g., to compare performance of two machines:

Amdahl’s Law provides a way to calculate the speedup to be realized from some design enhancement which depends on two factors: Fraction of computation time in original machine that will be affected by the enhancement. The amount of said enhancement, ie. “how much improvement did we make to the feature under consideration?” One might find that the desired speedup cannot be obtained by improving a single feature. Consider the following common riddle: You are traveling from Point A to Point C going through Point B. The distance from A-> B is 1 mile and the distance from B -> C is one mile. You travel from A to B at 30 mph, how fast must you go in traveling from Point B to Point C in order to average 60 mph? Amdahl’s Law and Speedup

A machine takes 100 sec to execute a given program 40 seconds for fp 60 seconds for everything else Question: Can I double the speed by enhancing fp? Suppose that I improve fp by a factor of 10, what is the speedup that can be realized? Example 1

Example 2 Amdahl’s Law expresses the Law of Diminishing Returns Suppose I have a choice of two improvements. Fp square root = 20% or all fp 50% Proposition 1 -- improve square root by a factor of 10 Proposition 2 --improve all fp by a factor of 2 Which would you choose? Prop 1. Speedup = 1 _______________ = /10 Prop 2. Speedup = 1 ________________ = /2 It is sometimes difficult to determine how much time is being used by particular components.