Question

Assume that a design team is considering enhancing a machine by adding MMX (multimedia extension instruction) hardware to a processor. When a computation is run in MMX mode on the MMX hardware, it is 10 times faster than the normal mode of execution. Call the percentage of time that could be spent using the MMX mode the percentage of media enhancement.

(a)What percentage of media enhancement is needed to achieve an overall speedup of 2 ?
(b) What percentage of the run-time is spent in MMX mode if a speedup of 2 is achieved? (Hint: You will need to calculate the new overall time.)
(c) What percentage of the media enhancement is needed to achieve one-half the maximum speedup attainable from using the MMX mode?

Answer 1

Using Amdahl's Law, 18% of media enhancement is needed to achieve an overall speedup of 2, and 18% of the runtime would be spent in MMX mode for this speedup. To achieve one-half the maximum speedup of the MMX mode, around 44% of media enhancement is needed.

Step-by-step explanation:

The question deals with the concept of speedup in computer processor performance with the addition of multimedia extension instruction hardware (MMX). To calculate the percentage of media enhancement required to achieve an overall speedup of 2, we can use Amdahl's Law, which states that the overall speedup of a system from using some faster mode of execution is limited by the fraction of the time the faster mode can be used.

Part a

Let the fraction of time the system could spend using MMX mode be represented as X, and the speedup for that fraction be 10 times (since MMX is 10 times faster). According to Amdahl's Law, the formula for the overall speedup (S) is S = 1 / ((1 - X) + X/10). To achieve an overall speedup of 2, this equation can be solved for X—resulting in 0.18 or 18% of media enhancement needed.

Part b

If a speedup of 2 is achieved, the run-time percentage spent in MMX mode can be determined. Since we've calculated X to be 18%, this means 18% of the runtime will be spent in MMX mode for a speedup of 2.

Part c

To achieve one-half the maximum speedup from using MMX mode, we need to look at the case where 100% of runtime is MMX, which would yield a speedup of 10. Half of this is a speedup of 5, which we calculate in a similar fashion to part a, finding that it requires a percentage of media enhancement of roughly 0.44 or 44%.