Hmm. Computing more in a fixed amount of time does not imply that we finish the overall computation faster, since we have not fix the problem size. Right? If I have a magic CPU that can compute twice as fast when handed 4 times the data, my magic cpu will compute more in a fixed amount of time, but will still take twice as long to finish the whole task.
kayvonf
@lament: In fact, this behavior of memory-constrained scaling is evident in the math on slide 24. Notice that the overall execution time goes up, even though the memory-constrained speedup is P.
Edit: I misunderstood your comment (I thought you were describing memory-constrained scaling). Time-constrained scaling is scaling the problem up as more processors are added so that execution time stays constant. Same execution time is part of the definition. (In your example, you're saying a bigger problem is more efficient on the same CPU. You're not increases the number of CPU resources.)
kayvonf
Question: If I say "I got a speedup of 2 using 2 CPUs via time-constrained scaling," what does that mean?
ghawk
In Time Constrained scaling, we assume that we get a fixed amount of execution time. Hence, your statement means that you have completed twice the amount of work with 2 CPUs compared to the amount of work you'd achieve with 1 CPU in the same time.
I think work here is measured in terms of the final output or result, instead of the amount of operations. @kayvonf, am I correct on this one?
And I guess, in context of the next slide lecture 9, slide 17 this would be something on the lines of how Assassin's Creed can render a frame with twice the detail than Half-Life in the same amount of time (say constant FPS) because of more computing power in terms of multiple cores.
kayvonf
@ghawk. Good answer. The definition of "work" in time-constrained scaling is problem specific. In the graphics example you referenced, it might be a metric like "triangles used in the scene". But it could also be a domain-agnostic metric like instructions performed.
Hmm. Computing more in a fixed amount of time does not imply that we finish the overall computation faster, since we have not fix the problem size. Right? If I have a magic CPU that can compute twice as fast when handed 4 times the data, my magic cpu will compute more in a fixed amount of time, but will still take twice as long to finish the whole task.
@lament: In fact, this behavior of memory-constrained scaling is evident in the math on slide 24. Notice that the overall execution time goes up, even though the memory-constrained speedup is P.
Edit: I misunderstood your comment (I thought you were describing memory-constrained scaling). Time-constrained scaling is scaling the problem up as more processors are added so that execution time stays constant. Same execution time is part of the definition. (In your example, you're saying a bigger problem is more efficient on the same CPU. You're not increases the number of CPU resources.)
Question: If I say "I got a speedup of 2 using 2 CPUs via time-constrained scaling," what does that mean?
In Time Constrained scaling, we assume that we get a fixed amount of execution time. Hence, your statement means that you have completed twice the amount of work with 2 CPUs compared to the amount of work you'd achieve with 1 CPU in the same time.
I think work here is measured in terms of the final output or result, instead of the amount of operations. @kayvonf, am I correct on this one?
And I guess, in context of the next slide lecture 9, slide 17 this would be something on the lines of how Assassin's Creed can render a frame with twice the detail than Half-Life in the same amount of time (say constant FPS) because of more computing power in terms of multiple cores.
@ghawk. Good answer. The definition of "work" in time-constrained scaling is problem specific. In the graphics example you referenced, it might be a metric like "triangles used in the scene". But it could also be a domain-agnostic metric like instructions performed.