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Amdahl’s Law Amdhal’s law quantifies the fact that

Amdahl’s Law Amdhal’s law quantifies the fact that the sequential portion of an application will put a lid on its potential scalability. This law is best illustrated by a matrix multiplication example that consists of three stages: . Initialization read in the matrices data values. . Multiplication multiply the two matrices. . Presentation present the resulting matrix. Let’s assume further that the whole computation takes 10 ms, broken down as follows (these numbers are completely fictitious but help illustrate the point): . Initialization 2 ms . Multiplication 6 ms . Presentation 2 ms Over the years, many clever parallel algorithms have been developed to exploit multiprocessor architectures to speed up the second phase, that of matrix multiplication. The initialization and presentation phases are a different story. Practically, these two stages in the computation are sequential. In the ideal world, an unlimited number of parallel processors could, in theory, reduce the multiplication stage to 0 ms. But they would not help at all with the other two sequential stages, as shown by Figure 7.4. Figure 7.4. Potential speedup is limited In the figure, an unlimited number of parallel processors has only reduced a 10 ms computation to 4 ms. The multiplication phase has been reduced to 0 ms but the initialization and presentation stages still take 2 ms each. Looks as if 2.5x is the speedup limit for this particular application on any SMP system regardless of the number of processors. Sequential computations are the major roadblock on the way to scalability. In the following sections we will enumerate ways to eliminate or at least minimize sequential computations. Before we go there, we need to briefly clarify some terminology. Page 150

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