Amdahl's Law

  Various interpretations are in use. Originally defined for showing that vectorizing of a program can only affect that part of the program which lends itself to vectorizing. The ``law'' can be written as

where f is the fraction of the program that can be improved, S_f is the improvement factor on this fraction, and is the overall improvement achieved. Obviously, for small f, , whatever the value of S_f, i.e. insignificant overall gain is achieved.

The generalization to the parallelizing of programs is obvious, although the effect of diminishing returns there is enhanced because of the introduction of communication overheads, synchronization effects, etc. A further generalization could be to a rule of thumb like work only on problems with good returns.

Another accepted meaning is that of diminishing returns for parallel systems as the number of processors increases: according to this rule of thumb, the effective capacity scales not with the number of processors (N), but with .