Recall that speedup is defined as T1/T2 where T1 is the execution time for a program before some modification is made and T2 is the execution time after the modification. A certain program contains four different classes of instructions. The CPI for each instruction in the program is 4. The total number of instructions in the program is IC and the fixed cycle time for the processor on which the program runs is C nano-seconds.  

a) A single change that does not affect the instruction count, but that reduces the CPI for only one of the instruction classes in the program and yields a speedup for the program of  2.5. If 80% of the instructions in the program are from the modified class, what is the new CPI for instructions in the modified class?  

  b) As a different case, suppose that the class of instructions to be modified had accounted for only 22% of the total number of instructions in the program. What speedup factor would be provided for the original program by cutting the CPI for the modified class of  instructions from 4 down to 2 ? Round your answer to two decimal places.  

2. A program containing twenty million instructions is executed on a uni-processor system with a fixed clock cycle time of 250 pico-seconds (250*10-12seconds). All instructions are executed one at a time and each instruction requires an integral (i.e., whole) number of clock cycles.  The divide instruction on this machine requires 12 clock cycles and accounts for 10% of the total number of instructions executed in the program. The other 90% of the instructions in the program require an average of 5 clock cycles per instruction. The fastest instruction has a CPI of 2. Complete the following statements:

 a)  The total number of clock cycles consumed by the entire program is_              .

b)  What speedup (expressed to two decimal places) would be obtained for this program by reducing the CPI for divide instructions by 6?  Speedup=  _          _.

c)  What speedup relative to the original unmodified system would be obtained for this program by making the maximum possible improvement in only the divide instructions?  Express your answer to two decimal places.  Speedup= _            _.

d) How many of the fastest instructions could be executed in a one-second time interval?  

3. Consider two different implementations of the same instruction set architecture.  The instructions can be divided into four classes according to the CPI (class A, B, C, and D).  Processor P1 has a clock rate of 2 GHz and CPIs of 4, 2, 1, and 3.  Processor P2 has a clock rate of 2.5 GHz and CPI of 2 for each of the four instruction classes.  Given a program with a dynamic instruction count of 1.0E6 instructions divided into classes as follows: 10% class A, 20% class B, 50% class C, and 20% class D.

a)What is the CPI for each implementation?                                                                

  b)How many clock cycles are required for each implementation?

c)Find the total time for each implementation to execute the program.

4. Consider a computer running a program that requires 250 seconds, with 70 seconds spent executing floating point instructions, 85 seconds executing load/store instructions, and 40 seconds spent executing branch instructions.

a) By how much is the total time reduced if the time for floating point instructions is reduced by 20%?

b) What speedup would be achieved for the program if the only improvement made is to reduce the time for the branch instructions by 30%?

5. Compiler A translates a program that results in 2.6E9 (2.6 billion) instructions.  The program executes in 1733.3 milli-seconds (1.7333 seconds). The clock cycle time for the processor that runs the program is 1 ns (1.0*10-9seconds). 

a)What is the CPI?

b)  Compiler B translates the same program and results in 5.5E8 (550 million) instructions and has an average CPI of 1.1.  What is the speedup for the program produced by Compiler B relative to that produced by Compiler A?