A program P running on a single$-$processor system takes time T to complete. Let us

assume that $30\%$ of the program$$s code is associated with $$data management

housekeeping$($according to Amdahl$)$ and, therefore, can only execute sequentially

on a single processor. Let us further assume that the rest of the program $(70\%)$ is

$$embarrassingly parallel$$ in that it can easily be divided into smaller tasks

executing concurrently across multiple processors $($without any interdependencies

or communications among the tasks$).$

a$.$ Calculate $2,4,8,$ which are the times to execute program P on a two$-,$

four$-,$ eight$-$processor system, respectively. $(9$ points$)$

b$.$ Calculate $$ on a system with an infinite number of processors. Calculate

the speedup of the program on this system, where speedup is defined as $$

$$

$.$

What does this correspond to$?(6$ points$)$

Problem $3(20$ points$)$:

Assume a program requires the execution of $40106$ FP $($Floating Point$)$

instructions, $70106$ INT $($integer$)$ instructions, $100106$ L$/$S $($Load$/$Store$)$

instructions, and $26106$ branch instructions. The CPI for each type of

instruction is $1,2,3,$ and $2,$ respectively. Assume that the processor has a $4$ GHz

clock rate.

a$.$ By how much must we improve the CPI of FP $($Floating Point$)$ instructions

if we want the program to run two times faster? $(9$ points$)$

b$.$ By how much must we improve the CPI of L$/$S $($Load$/$Store$)$ instructions if

we want the program to run two times faster? $(5$ points$)$

c$.$ By how much is the execution time of the program improved if the CPI of