Homework 1 examples

Purposes:
   (1) perform calculations with different units and prefixes;
   (2) perform calculations using CPI values and the execution time
         equation;
   (3) perform calculations using Amdahl's Law;
   (4) perform calculations to determine MIPS and MFLOPS.

Note:
   For main memory size, interpret K, M, and G as powers of two.
   Otherwise, interpret K, M, and G as powers of ten.



1. For a processor with 100 MHz clock frequency (a.k.a. clock rate),
   what is the clock cycle time?

   CCT = 1 / clock rate = 1 / ( 100 * 10^6 cycles per sec )
       = 10 / 10^9 secs per cycle = 10 nsec


2. Consider making a complete backup of a full 40 GB hard drive using a
   250 MB zip drive.  How many 250 MB zip disks will be needed?

   Use powers of ten for capacities other than cache or main memory.

   # of zip disks = 40 GB / 250 MB = 4*10^10 / 2.5*10^8 = 160

   
3. Find the execution time for a program that executes 30 million
   instructions on a processor with an avg. CPI of 2.0 and a clock
   cycle time of 33.3 nsec.

   exec. time = IC * CPI * CCT
              = 30M insts. * 2 cycles/inst * 33.3 nsec/cycle
              = 1.998 seconds = 2 seconds (rounded)


4. For the following instruction set workload and cycle values, find the
   average CPI.

      type   |  freq  cycles
      -------+--------------
      alu    |  0.5     2
      branch |  0.2     6
      ld/st  |  0.3     6

   avg. CPI = (0.5 * 2) + (0.2 * 6) + (0.3 * 6) = 4.0


5. Consider enhancing a scalar machine by providing a vector mode, which
   is 4 times faster than the normal mode of operation.

   (a) If the percentage of vectorization is 25%, what is the overall
       speedup?

                         1               1          1
       speedup = ----------------- = ---------- = ----- = 16/13 = 1.23
                 (1-1/4) + (1/4)/4   3/4 + 1/16   13/16

   (b) What percent of vectorization is needed to achieve an overall
       speedup of 2?

                 1
       2 = -------------  =>  (1-f) + (f/4) = 1/2 
           (1-f) + (f/4)
                          =>  4-4f+f = 2
                          =>  -3f = -2
                          =>  f = 2/3  so % vectorization needed is 67%


6. Consider a program that executes 100 million instructions in 5 seconds.
   What is the MIPS rating for this program?

            100*10^6 insts
     MIPS = -------------- = 20 MIPS
            5 secs * 10^6

   Consider a processor with a CPI value of 10 cycles/inst. and a clock
   frequency of 200 MHz.  What is the MIPS rating for this processor?

              200 M cycles/sec
     MIPS = --------------------- = 20 MIPS
            10 cycles/inst * 10^6


7. Consider the program in question 2 that executes 100 million instructions
   in 5 seconds.  If 15% of these instructions are floating-point operations,
   what is the MFLOPS rating for this program?

            0.15 flops/inst * 100*10^6 insts
     MIPS = -------------------------------- = 3 MFLOPS
                     5 secs * 10^6