## Homework #1

### CMSC 611, Fall 1998

Assigned: Tuesday, September 8, 1998

Due Tuesday, September 15, 1998 (in class)

1. We are considering the addition of a vector processing unit to a CPU. The vector unit speeds up vectorizable floating point computations but doesn't affect the speed of integer computation or non-vectorizable FP. Assume that the vector unit provides a speedup of 12 over normal floating point computations. Your measurements of scientific programs have shown that 90% of the time is spent doing floating point.
1. Assume that the FP computations are 100% vectorizable. How much speedup would be gained?
2. What fraction of FP computations must be vectorized to get a speedup of 4 over the unvectorized CPU?
3. You are given a choice between increasing the vector speedup by a factor of 2 (to 24x) or increasing the overall clock rate by a factor of 1.5, thus speeding up integer, floating point, and vector computations. Which results in a faster CPU, assuming that the FP code is 80% vectorizable?
2. You've built a new computer with multimedia (MM) instructions, and discover that MM instructions account for 30% of the run time of a set of benchmarks. You know that the MM instructions are 4 times faster than the "normal" instructions that they replaced.
1. How much faster does the CPU run with MM instructions relative to its original (without MM) speed?
2. What percentage of the original execution time was converted to MM instructions?
3. You have measured the "ideal" CPI of a program to be 0.5 (superscalar issue allows CPIs to be below 1). However, this doesn't include the memory system. Assume that cache hits cost nothing and that cache misses cost 50 cycles. If instruction references miss 1% of the time and data references miss 4% of the time, what is the overall average CPI? Assume the instruction frequencies shown in Figure 1.17 in the text.
4. Problem 1.12 in the text.
5. Problem 1.14 in the text.
6. Problem 1.15 in the text.

Last updated 9 Sep 1998 by Ethan Miller (elm@csee.umbc.edu)