Amdahl's Law

Consider a program which takes 1000 seconds to execute, broken into 5 phases: A, B, C, D, E. Without any optimizations, each phase takes one-fifth of the total execution time.

Suppose that Phase A and B are both 60% parallelizable, and Phase C, D, and E are each 20% parallizable.

a. Assuming that there are 100 processors, and zero overhead from parallelization, what is the maximum speedup that can be obtained?
b. Wat is the speed up achieved (w. r.t to the initial) if we had 1000 processors instead of 100?
c. Based on this program alone, does hte speedup increase warrant the additional 900 processors?

Part a: The speed up in case of the 100 processors is 400/21.

Part b: The speed up in case of the 1000 processors is 4000/21.

Part c: Yes in case of 1000 processors the speedup will increase eventually, and it will be 4000/21 Time

Explanation:

Each Phase Take 1\5 of Total Execution Time.

Total Execution Time is : 1000 Seconds.

A Time = 200 Seconds

B Time = 200 Seconds

C Time = 200 Seconds

D Time = 200 Seconds

E Time = 200 Seconds

T = [A + B] + [C+D+E]

As A and B are parallelizable 60%, the individual time of A and B is

Phase A[40%] total Time = A/40

Phase B [40%] Time = B/40

Similarly the pase C, D & E are parallelizable for 20% so the remaining time for individual process is

Phase C[80%] Time = C/80

Phase D[80%] Time = D/80

Phase E[80%] Time = E/80

Phase A + Phase B [60%] Time = 6*A/40 = 6*B/40

Phase C+Phase D+Phase E [20%] time= 2*C/80= 2*D/80 =2*E/80

T' = A' + B' + C' + D' + E'

  = A/40 + B/ 40 + C / 80 + D/80 + E/80 + 6*B / 40 + 2*D/80

T' = T/(5*40) + T/(5*40) + T/(5*80) + T/(5*80)+ T/(5*80) + 6*T/(5*40) + 2*T/(5*80)

We know that A, B, C, D, AND E are 1/5 of T. So:

T' =T/200 + T/ 200 + T/ 400 + T/400 + T/400 + 6*T/ 200 + 2*T/400

  = 21/400*T

The speed-up is

T / T' = T / (21/400 T) = 400/21 Time

In case of 1000 processors the time is given as

T/T'=T / (21/400 T) = 400/21 Time*1000/100=400/21 Time*10=4000/21 time

Yes in case of 1000 processors the speedup will increase eventually, and it will be 4000/21 Time

well people will have to mark your answer as the best answer. and from that u receive crowns.

~batmans wife dun dun

gilgamesh is a hero by birth as the epic explains it. in the epic the birth is explained in the way which tells us that gilgamesh’s creation was made perfect by the contribution of various god and that signifies the goal in his life, which was to become a hero and save mankind. an example from the text says. "the glorious sun shamash bestowed upon him glory; adad the terrible god of storms bestowed upon him courage. the great gods perfected his magnificence beyond all others, terrible like the great wild bull. two thirds god they made him; one third man they made him." a man born with superhuman qualities and partly god is destined to be a hero.

the heroic deeds carried by him later in his life also prove the heroic character of gilgamesh. for example hi battle with the ultimate beast humbaba is a proof of his bravery and characteristic heroism. gilgamesh was warned about the beast as the text says about humbaba “whose roar is a flood, whose mouth is fire, whose breath is death". but with the superhuman strength gilgamesh did the job