并行性的量化指标

Question

Some parameters have been described in the Advanced computer architecture book by Hwang, eg Speedup, Efficiency, Redundancy, Utilization and Quality as shown in the picture below.

I understand all and partially understand the last parameter, quality. The question is, why quality has inverse relationship with the redundancy. As said, redundancy shows the matching between software parallelism and the hardware. For example, one processor runs one unit instruction, therefore, O(1)=1.

By O(n) we are actually increasing the number of processors, so the unit operation increases and the upper bound is n. So, that is good! in't it?

But according to the quality metric, if we increase the redundancy, the quality decreases. Maybe some word definitions are ambiguous here.

Any thought?

Answer 1

I think misunderstood O(n), which is the total number of unit operations performed by all processors for the whole execution duration. This has no upper bound and O(1) is not necessarily (and realistically is not) 1; it depends on the application. If we had to do more operations to parallelize the application on n processors compared to executing it on a uniprocessor (ie, the redundancy is larger than 1), then this is bad a thing and the larger the redundancy the greater the mismatch between software and hardware parallelism. Ideally, the redundancy is 1. Therefore, if we want to combine the speedup, efficiency, and redundancy into a single quality metric, speedup and efficiency should be in the numerator and the redundancy should be in the denominator.

It's worth noting that most of the upper and lower bounds on these metrics as mentioned in the book are too simplistic on modern processors. They make most sense on simple (scalar) processors. However, on a modern multicore system, they don't capture accurately what may happen in reality. For example, the speedup on a 2-processor system could be lower than 1 or higher than 2. The redundancy depends not only on the ISA but also on the compiler. So it can be smaller than 1 or larger 2. Although the metrics themselves can still be very useful.