Amdahl's law bounds the speedup obtained by accelerating only part of a fixed computation. Let fraction of its original execution time remain serial, while fraction divides perfectly among identical processors. ThenThe terms add because the serial and accelerated parts still both have to finish. If , ten processors give ; even infinitely many cannot exceed speedup ten.
Gene M. Amdahl's 1967 argument emphasized sequential work and irregularities in real computations.[ref]
Validity of the single processor approach to achieving large scale computing capabilities by Gene M. Amdahl. printed p.483, sequential housekeeping and physical-problem irregularities
The displayed idealized formula follows from the stated time decomposition. Communication, synchronization, unequal work and limited memory bandwidth can reduce actual speedup. Increasing the problem size changes the serial fraction and asks a different scaling question. New to topics? Read the docs here!