Suppose that a design teamwants to enhance a machine by adding MMX (multimedia e

Question

Suppose that a design teamwants to enhance a machine by adding MMX (multimedia extensioninstruction) hardware to a processor. When a computation is run inMMX mode on the MMX hardware, it is 10 times faster than the normalmode of execution. Call the percentage of time that could be spentusing the MMX mode the percentage of media enhancement.

1. What percentage of mediaenhancement is needed to achieve an overall speedup of2?
2. What percentage of therun-time is spent in MMX mode if a speedup of 2 is achieved? (Hint:You will need to calculate the new overall time.)

Explanation / Answer

a) Using Amdahl’s Law

       Execution time with MediaEnhancement =

(Execution time improved by Media enhancement)/ (Amount ofImprovement) +Execution time unaffected

Let x be the percent of media enhancement needed for achievingan overall speedup of 2.

Then, (100)/2 = (x)/10 + (100-x)

          100/2 = x+ (100-x) 10/10

           100*10 = 2(x+ (100-x) 10)

          (100*10)/2= x+ (1000-10x)

            (100*5) = x+(1000-10x)

               500   = x + 1000 -10x

               500 = 1000-9x

                9x= 1000-500

                    = 500

                 x = 55.55

b) The new overall time is 100/2 = 50.

                  MMX time = 55.55/10 = 5.55

                    The rest 1 – 55.55 = 44.45

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