Amdahl\'s Law. On a uniprocessor, perfectly serial portion A of program P1 consu
ID: 3784241 • Letter: A
Question
Amdahl's Law. On a uniprocessor, perfectly serial portion A of program P1 consumes 15 s, while perfectly parallel portion B consumes 95 s. he theoretical maximum speed up for P1 is obtained by using an infinite number of processors. What integral number of processors is required to achieve at least half the theoretical maximum speedup for P1? Perfectly serial portion A of large program P2 consumes 15 s, while perfectly parallel portion B consumes 950 s. What integral number of processors is required to achieve, for P2, at least the theoretical maximum speed up for P1? Perfectly serial portion A of even large program P3 consumes 15 s, while perfectly parallel portion B consumes 9, 500 s. What integral number of processors is required to achieve, for P3, at least the theoretical maximum speedup for P1?Explanation / Answer
Solution :
Execution time for Portion A (ETP1) = 15 s
Execution time for Portion B (ETP2) = 95 s
To obtain maximum speedup = (ETP1) +(ETP2)
= 15 + 95
= 110 s
So, to reduce this means we need to minimize the time taken by Portion B= 15 + 0 =15 s
Smax = 110 / 15 = 7.333
a)
Execution time (ETP1) = 15 s
To achieve the maximum speed up, it will be 1.5 P processor will be required to achieve the maximum speed up.
b)
Now,
(ETP1) = 15 s
(ETP2) = 950 s
Theoretical maximum speedup of P1 = 7.3333 (in 15 s)
So, to achieve this, let’s calculate current execution time of P2 = 15 + 950 = 965 s
Maximum speedup of P2 = 965 / 7.33 = 131.65
To achieve this speed, P2 needs 7.33 number of processor.
c)
Same as P2.
let’s calculate current execution time of P3 = 15 + 9500 = 9515 s
Maximum speedup of P2 = 9515 / 7.33 = 1298.65
To achieve this speed, P3 needs 7.33 number of processor.
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