Fundamentals of Quantitative Design and Analysis - Computer Architecture: A Quantitative Approach - page 44

FIGURE 1.17 SPECfp2000 execution times (in seconds) for the Sun Ultra 5—the refer-
ence computer of SPEC2000—and execution times and SPECRatios for the AMD Opter-
on and Intel Itanium 2 . (SPEC2000 multiplies the ratio of execution times by 100 to remove
the decimal point from the result, so 20.86 is reported as 2086.) The final two columns show
the ratios of execution times and SPECRatios. This figure demonstrates the irrelevance of the
reference computer in relative performance. The ratio of the execution times is identical to the
ratio of the SPECRatios, and the ratio of the geometric means (27.12/20.86 = 1.30) is identic-
al to the geometric mean of the ratios (1.30).
Because a SPECRatio is a ratio rather than an absolute execution time, the mean must be
computed using the geometric mean. (Since SPECRatios have no units, comparing SPECRatios
arithmetically is meaningless.) The formula is
In the case of SPEC, samplei i is the SPECRatio for program i . Using the geometric mean en-
sures two important properties:
1. The geometric mean of the ratios is the same as the ratio of the geometric means.
2. The ratio of the geometric means is equal to the geometric mean of the performance ratios,
which implies that the choice of the reference computer is irrelevant.
Hence, the motivations to use the geometric mean are substantial, especially when we use per-
formance ratios to make comparisons.