Question

Suppose a computer M3 has an average CPI of 2.7 and a clock rate of 3.7 GHz. Please answer the following: (a) Calculate the runtime for a program P with 22,933 instructions, which uses an accelerating co-processor 45 percent of the time. (b) determine how much faster (or slower) the accelerator needs to run for P to run 1.5 times (1.5X) as fast on M3 with the faster (resp. slower) accelerator. Hint: First set up your equation for Amdahl’s Law, and see if it can indeed be solved… a negative result means that the requested improvement is infeasible…

Answer 1

a)

Rin tine = CPI*Instruction count*/Clock rate

2.7 * 22933/(3.7*10^9)

= 16734.8918919 * 10^-9

= 16.7 micro seconds

b)

To make the system run 1.5 times faster we have to make sure that 45% is covering that speed

first of all system to be 1.5 times faster needs to run in = 16.7/1.5 = 11.1333333333 microseconds

so, 11.1333333333 = (2.7 * 22933/(3.7*10^9)) * 0.55 + 0.45 * x

so x = (11.133333-9.20419054054)/0.45 = 4.28698324324

which means the co processor needs to be 4.28698324324 times faster.