Assume that we make an enhancement to a computer that improves some mode of exec
ID: 666486 • Letter: A
Question
Assume that we make an enhancement to a computer that improves some mode of execution by a factor of 10. Enhanced mode is used 50% of the time, measured as a percentage of the execution time when the enhanced mode is in use. Recall that Amdahl’s law depends on the fraction of the original, unenhanced execution time that could make use of the enhanced mode. Thus, we can’t directly use the 50% measurement to compute speedup with Amdahl’s law.
1. What is the speedup we have obtained from fast mode?
2. What percentage of the original execution time has been converted to the fast mode?
Explanation / Answer
Amdahl’s Law
N
S = -----------------------
(B*N)+(1-B)
Where S is Speedup, N is Processor & B is % of algorithm that is serial
ANS: Assume that the time taken to execute some perfectly representative prrogram P on the computer in question is 100 seconds when the enhancement is in use. The amount of time during which enhanced mode is in use is 50% of this time, i.e. 50 seconds. Now the enhanced mode gives us a speedup factor of 10x. This means the original time (in unenhanced mode) to execute these 50 seconds would be 500 seconds. The total original time would therefore be 500 + 50 = 550 seconds.
Thus Original time 550
Speedup = --------------------- = -------- = 5.5
Enhanced time 100
2. What percentage of the original execution time has been converted to the fast mode?
ANS: The amount of original time converted to fast mode is 500 seconds. The total original time is 550 seconds. Thus the percentage of original time converted to fast mode is 90.91%,
N
S = -----------------------
(B*N)+(1-B)