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CHAPTER 11
RATIO GAMES

If you can’t convince them, confuse them.

—Truman’s Law

Ratios provide good opportunities for playing performance games with competitors. Ratios have a numerator and a denominator. The denominator is also called a base. Two ratios with different bases are not comparable. There are, however, many examples in published literature where computer scientists have knowingly or unknowingly compared ratios with different bases. The technique of using ratios with incomparable bases and combining them to one’s advantage is called a ratio game. There are many different ways in which ratios can be used. Some of these are explicit and others are implicit in the sense that it is not obvious that a ratio has been taken. Some of these techniques and the strategies that are used for winning such games are described in this chapter. Learning about such games is helpful, not because we recommend their usage, but because their knowledge will help us protect ourselves from being victimized by others.

11.1 CHOOSING AN APPROPRIATE BASE SYSTEM

The simplest way in which ratio games are played is by presenting the performance of two (or more) systems on a variety of workloads, taking a ratio of performance for each workload, and then using the average ratio to show that one’s proposed system is better than the alternative.

An example of such a case was presented in Section 1.2, where three ways to average the performance of two systems A and B were compared. To recapitulate, these three ways are as follows:

  Take an average of each individual system’s performance and then take a ratio.
  Normalize each system’s performance on each workload by that of system A and then take an average of ratios.
  Normalize each system’s performance on each workload by that of system B and then take an average of ratios.

It was shown that by appropriate choice of the base system one could reverse the conclusion about which of the two systems is better.

The following case study illustrates the game with real measurements.

Case Study 11.1 The performance of two processors, 6502 and 8080, was measured on two workloads called Block move and Sieve. The mean values of the 10 replications of each of the four experiments are shown in Table 11.1. The analysis of the data in using the average of totals, average of ratios with A as a base, and ratios with B as a base is also shown in the table. The three analyses lead to three different conclusions:
  Ratio of Totals: 6502 is worse. It takes 4.7% more time than 8080.
  With 6502 as a Base: 6502 is better. It takes 1% less time than 8080.
  With 8080 as a Base: 6502 is worse. It takes 6% more time.
TABLE 11.1 A Comparison of 6502 and 8080 Processors

Raw Measurements
With 6502 as a Base
With 8080 as a Base
System
System
System
Benchmark 6502 8080 6502 8080 6502 8080

Block 41.16 51.50 1.00 1.25 0.80 1.00
Sieve 63.17 48.08 1.00 0.76 1.31 1.00
             
Sum 104.33 99.58 2.00 2.01 2.11 2.00
Average 52.17 49.79 1.00 1.01 1.06 1.00

Ratio games can be played even when more than two systems or benchmarks are involved. The following case study illustrates one such case.

Case Study 11.2 Table 11.2 shows the measured code sizes for several workloads on a Reduced Instruction Set Computer (RISC) system and four other processors. This data has been adapted from those reported by Patterson and Sequin (1982). The sum of the code sizes is also shown in the table. RISC-I has the largest code size. The second processor, Z8002, requires 9% less code than RISC-I. Table 11.3 shows ratios of code sizes with RISC-I as a base. This table leads to the conclusion that Z8002 has the largest code size and that it takes 18% more code than RISC-I.


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