Using Amdahls law Suppose we enhance a machine to make all f

Using Amdahl\'s law: Suppose we enhance a machine to make all floating point instructions run four times faster. Look at how speedup behaves when we incorporate faster floating point hardware. If the execution time of some benchmark before floating point enhancement is 15 seconds total, what is the speedup if one-third of the 15 seconds was spent executing floating point instructions?

Solution

speed up chieved = 4 times faster

so if previously floating point instruction took x seconds previously

now it will be x/4 seconds

Time in benchmarking = 15 second

out of 15 one third = 15/3 = 5 seconds in floating point instructions)

Let for y operation it took 5 seconds

so per instruction it took = 5/y seconds

Now with new hardware as it is 4 times faster

per instruction time will be = (5/y)/4 = 5/(4*y)

Total time for y instruction = y*5/(4*y) = 5/4 = 1.25

So total time is time without floating point + time for floating point instruction

= (15 -5) + 1.25

= 10+1.25

= 11.25