Compute the CPU time of each (note that IC and clock rate (CCT) remain the same)
Understand the Problem
The question is asking to compute CPU times for different enhancement options for the floating point (FP) units in a machine, and evaluate the speedup achieved based on the provided CPI (cycles per instruction) values and instruction breakdown.
Answer
The speedup for enhancing all FP units is approximately 1.23, while for enhancing just the FP sqrt. unit, it is approximately 1.22.
Answer for screen readers
The speedup enhancing all FP units is approximately 1.23, while enhancing just the FP sqrt. unit gives a speedup of approximately 1.22.
Steps to Solve
- Calculate the original CPI for the machine
The original CPI is calculated based on the instruction breakdown.
[ CPI_{\text{original machine}} = 0.25 \times 4.0 + 0.75 \times 1.33 = 2.00 ]
- Determine the new CPI for enhancing all FP units
If all FP units are enhanced, the new CPI for FP operations is 2.5.
[ CPI_{\text{all FP}} = 0.75 \times 1.33 + 0.25 \times 2.5 = 1.625 ]
- Compute speedup from enhancing all FP units
The speedup can be calculated using the original CPI and the new CPI after enhancement.
[ \text{Speedup}_{\text{all FP}} = \frac{IC \times 2.00 \times CCT}{IC \times 1.625 \times CCT} = \frac{2.00}{1.625} \approx 1.23 ]
- Calculate the new CPI for enhancing just the FP sqrt. unit
For enhancing just the FP sqrt. unit, we adjust the original CPI by subtracting the improvement from the FP sqrt. operations.
The improvement can be computed as:
[ CPI_{\text{FP sqrt.}} = CPI_{\text{original}} - 0.02 \times (20 - 2) = 1.64 ]
- Compute speedup from enhancing just the FP sqrt. unit
Calculate the speedup for enhancing only the FP sqrt. unit using the new CPI.
[ \text{Speedup}_{\text{FP sqrt.}} = \frac{IC \times 2.00 \times CCT}{IC \times 1.64 \times CCT} = \frac{2.00}{1.64} \approx 1.22 ]
- Compare the speedups
To determine which enhancement is better, compare the two speedups:
- Speedup enhancing all FP units: 1.23
- Speedup enhancing FP sqrt. unit: 1.22
The speedup enhancing all FP units is approximately 1.23, while enhancing just the FP sqrt. unit gives a speedup of approximately 1.22.
More Information
Enhancing all FP units yields a slightly better performance improvement than enhancing only the FP sqrt. unit. Both enhancements improve the CPU performance, but optimizing all FP units is more efficient in this case.
Tips
- Forgetting to apply the correct instruction counts when calculating CPIs can lead to incorrect speedup calculations.
- Misinterpreting the breakdown of instructions (such as the percentages of FP operations) can skew results.
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