Computer Systems Architecture Problems

1. Consider a machine running a program with four categories of instructions: Floating Point (FP), Integer (INT), Load/Store(L/S), and Branch (BR). The execution time for the individual categories are included in the table below:

Instruction FP INT L/S BR

Time (sec) 90 75 120 60

a. By how much is the total execution time changed if the time for FP instructions is reduced by 20% and the time for INT instructions is increased by 40% (assuming no other changes)?

b. If we want to reduce the total execution time by 20% by optimizing L/S instructions only, what is the target execution time of L/S instructions in order to achieve the reduction (assuming all other instructions are not changed)?

c. Can the total time be reduced by 20% by reducing only the time for branch instructions? Use calculations to justify your answer.

2. Assume that we compile and run a program with two different compilers on the same machine. Compiler A results in a dynamic instruction count of 2.0 x 109 and has an execution time of 4 s, while compiler B results in a dynamic instruction count of 2.5 x 109 and an execution time of 3s.

a. Find the average CPI for the executable generated by compiler A and compiler B respectively given that the processor is 2GHz.

b. Now suppose that we run the compiled programs on two different processors of the same ISA and get the same execution time. Compare the clock of the processor running compiler As code versus the clock of the processor running compiler Bs code, which clock is faster? By how much?

3. Assume for arithmetic, load/store, and branch instructions, a processor has CPIs of 1, 10 and 3, respectively. Also assume that we are checking a program that requires the following number of instructions of different categories if run on a single processor:

Arithmetic instructions: 2.56 x 109

Load/store instructions: 1.28 x 109

Branch instructions: 6.40 x 108

a. Find the total execution time for this program on a single processor of 4GHz.

b. Find the average CPI of all instructions for this program.

c. Assume that we try to parallelize this program to run over multiple processors of the same CPI and clock rate as above. Suppose the parallelized version requires the same number of branch instructions as the original version per processor, while the number of arithmetic and load/store instructions per processor is divided by p (where p is the number of processors). Find the speedup for this program on 4 processors over the original execution from Q3.a.