Upload a pdf file containing your solutions to the problems below to Learning Suite before 11:00pm on the assigned date.

1. Problem 6.24 from the text

2. Problem 424-4:
   Chapter 5 presents a series of performance measurements showing the performance benefits of a sequence of optimizations to the original combine1() function. For this problem, you will repeat that sequence of optimizations starting with this function:

       void dotproduct1(vec_ptr u, vec_ptr v, data_t *dest)
       {
           long int i;
           *dest = 1.0;
           for (i = 0; i < vec_length(u); i++)
           {
   	    data_t val1;
   	    data_t val2;
   	    get_vec_element(u, i, &val1);
   	    get_vec_element(v, i, &val2);
   	    *dest = *dest + val1 * val2;
           }
       }
     

   Start with with this tar file that includes dotproduct1() and a version of the getcpe timing code used in the previous homework set. Compiling and running the initial getcpe program should give you the CPE for the original code. Consistent with the treatment in the text, you should create a different version of the function for each of the six required optimizations listed below. Follow the naming conventions of the test -- dotproduct5() should be the version with 2x loop unrolling. For this assignment, you need only consider the cose where data_t is a double.
   • 2. Move the call to vec_length out of the loop
   • 3. Directly access the vector data
   • 4. Accumulate results in a local variable
   • 5. Unroll the loop by 2
   • 6. Unroll the loop by 2 with 2-way parallelism
   • 7. Unroll the loop by 2 and reassociate
   Your submission should include the C source code for all 6 new versions of the dotproduct function along with the reported CPE of each. (No other source code needs to be submitted.)
   After you obtain all 7 required CPE measurements, you should write a paragraph comparing your results with those in the book and, where possible, explaining the differences. Finally, state what can be inferred from your results about the functional units in the processor of the system you used. (Can you determine both latency and throughput bounds, for example?)

3. Problem 424-5:
   You are to determine the branch misprediction penalty for at least one machine that you have access to. The technique employed is described on pages 215-216 of the text. The absdiff() and measurement code in this tar file will serve as a good starting point. First, you should write a short paragraph describing the technique used to measure the branch misprediction penalty. (Study the code and read the book.) Secondly, report the penalty you calculated and identify the platform you obtained it on. Finally, find a compiler option that generates code for the absdiff() function that uses a conditional move instruction rather than a branch. (Compile getbrpen.c with the -S option and examine the code generated for absdiff().) Report the optimization level you used and results from running the brnchpen program with this version of absdiff(). How much is performance improved when the conditional move instruction is used?

Clarifications

Problem 424-4: You may or may not see performance boosts at every step. Make a few runs for each data-point and discuss your results in your submission. Once you have the file dotprod.tar, place it in your directory of choice. From within that directory, typing "tar xvf *" will create a new "dotprod" subdirectory with all the files required to build the getcpe executable. Typing "make" within that subdirectory should produce an executable named getcpe. It should compile correctly under Linux or Mac OS X. The initial version will measure the performance of the dotproduct1(). As you add each new version of the function to getcpe.c, you'll need to change the measurement code (in measure() in getcpe.c) so that the new version of your function is called.

Problem 424-5: Copy the tar file to your working directory, and type "tar xvf *" to create a "brnchpen" subdirectory, and type "make" to produce a "brnchpen" executable. It should compile correctly under Linux or on a Mac. You are strongly encouraged to try this measurement on systems with different processors -- you might be surprised how different the results can be.