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62 CHAPTER 2 / COMPUTER EVOLUTION AND PERFORMANCE

2.15. To clarify the results of the preceding problem, we look at a simpler example.

Processor
Benchmark
X Y Z
1 20 10 40
2 40 80 20

a. Compute the arithmetic mean value for each system using X as the reference ma-
chine and then using Y as the reference machine. Argue that intuitively the three
machines have roughly equivalent performance and that the arithmetic mean
gives misleading results.
b. Compute the geometric mean value for each system using X as the reference ma-
chine and then using Y as the reference machine. Argue that the results are more
realistic than with the arithmetic mean.
2.16. Consider the example in Section 2.5 for the calculation of average CPI and MIPS
rate,which yielded the result of CPI = 2.24 and MIPS rate = 178.Now assume that the
program can be executed in eight parallel tasks or threads with roughly equal number
of instructions executed in each task. Execution is on an 8-core system with each core
(processor) having the same performance as the single processor originally used.
Coordination and synchronization between the parts adds an extra 25,000 instruction
executions to each task. Assume the same instruction mix as in the example for
each task, but increase the CPI for memory reference with cache miss to 12 cycles
due to contention for memory.
a. Determine the average CPI.
b. Determine the corresponding MIPS rate.
c. Calculate the speedup factor.
d. Compare the actual speedup factor with the theoretical speedup factor deter-
mined by Amdhal’s law.
2.17. A processor accesses main memory with an average access time of T 2 . A smaller
cache memory is interposed between the processor and main memory.The cache has
a significantly faster access time of T 1 6 T 2 . The cache holds, at any time, copies of
some main memory words and is designed so that the words more likely to be ac-
cessed in the near future are in the cache. Assume that the probability that the next
word accessed by the processor is in the cache is H, known as the hit ratio.
a. For any single memory access, what is the theoretical speedup of accessing the
word in the cache rather than in main memory?
b. Let T be the average access time. Express T as a function of T 1 , T 2 , and H.What is
the overall speedup as a function of H?
c. In practice, a system may be designed so that the processor must first access the
cache to determine if the word is in the cache and, if it is not, then access main
memory, so that on a miss (opposite of a hit), memory access time is T 1 + T 2 . Ex-
press T as a function of T 1 , T 2 , and H. Now calculate the speedup and compare to
the result produced in part (b).