阿姆达尔定律

Strong scaling is a measure of how, for a fixed overall problem size, the time to solution decreases as more processors are added to a system. An application that exhibits linear strong scaling has a speedup equal to the number of processors used.

Strong scaling is usually equated with Amdahl's Law, which specifies the maximum speedup that can be expected by parallelizing portions of a serial program. Essentially, it states that the maximum speedup S of a program is:

S =1（1 -P）+PN

Here P is the fraction of the total serial execution time taken by the portion of code that can be parallelized and N is the number of processors over which the parallel portion of the code runs.

The larger N is(that is, the greater the number of processors), the smaller the P/N fraction. It can be simpler to view N as a very large number, which essentially transforms the equation into S=1/ (1-P). Now, if 3/4 of the running time of a sequential program is parallelized, the maximum speedup over serial code is 1 / (1 - 3/4) = 4.

In reality, most applications do not exhibit perfectly linear strong scaling, even if they do exhibit some degree of strong scaling. For most purposes, the key point is that the larger the parallelizable portion P is, the greater the potential speedup. Conversely, if P is a small number (meaning that the application is not substantially parallelizable), increasing the number of processors N does little to improve performance. Therefore, to get the largest speedup for a fixed problem size, it is worthwhile to spend effort on increasing P, maximizing the amount of code that can be parallelized.

并行计算中的加速比是用并行前的执行速度和并行后的执行速度之比来表示的，它表示了在并行化之后的效率提升情况。

阿姆达尔定律是固定负载（计算总量不变时）时的量化标准。可用公式：来表示。式中分别表示问题规模的串行分量（问题中不能并行化的那一部分）和并行分量，p表示处理器数量。

Read more at: http://docs.nvidia.com/cuda/cuda-c-best-practices-guide/index.html#ixzz322tn7J9x

Gustafson's Law

Gustafson's Law (also known as Gustafson–Barsis' law) is a law in computer science which says that computations involving arbitrarily large data sets can be efficiently parallelized. Gustafson's Law provides a counterpoint to Amdahl's law, which describes a limit on the speed-up that parallelization can provide, given a fixed data set size. Gustafson's law was first described ^[1] by John L. Gustafson and his colleague Edwin H. Barsis:

where P is the number of processors, S is the speedup, and the non-parallelizable fraction of any parallel process.

两者的形象的解释

Amdahl's Law approximately suggests:

“

Suppose a car is traveling between two cities 60 miles apart, and has already spent one hour traveling half the distance at 30 mph. No matter how fast you drive the last half, it is impossible to achieve 90 mph average before reaching the second city. Since it has already taken you 1 hour and you only have a distance of 60 miles total; going infinitely fast you would only achieve 60 mph.

”

Gustafson's Law approximately states:

“

Suppose a car has already been traveling for some time at less than 90mph. Given enough time and distance to travel, the car's average speed can always eventually reach 90mph, no matter how long or how slowly it has already traveled. For example, if the car spent one hour at 30 mph, it could achieve this by driving at 120 mph for two additional hours, or at 150 mph for an hour, and so on.