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 port