Fundamentals of Quantitative Design and Analysis - Computer Architecture: A Quantitative Approach - page 49

root (FPSQR) is responsible for 20% of the execution time of a critical graphics
benchmark. One proposal is to enhance the FPSQR hardware and speed up this
operation by a factor of 10. The other alternative is just to try to make all FP in-
structions in the graphics processor run faster by a factor of 1.6; FP instructions
are responsible for half of the execution time for the application. The design
team believes that they can make all FP instructions run 1.6 times faster with
the same effort as required for the fast square root. Compare these two design
alternatives.
Answer
We can compare these two alternatives by comparing the speedups:
Improving the performance of the FP operations overall is slightly beter be-
cause of the higher frequency.
Amdahl's law is applicable beyond performance. Let's redo the reliability example from
page 35 after improving the reliability of the power supply via redundancy from 200,000-hour
to 830,000,000-hour MTTF, or 4150X beter.
Example
The calculation of the failure rates of the disk subsystem was
Therefore, the fraction of the failure rate that could be improved is 5 per million
hours out of 23 for the whole system, or 0.22.