Measuring Performance

Amdahl's (Heartbreaking) Law

Speedup due to enhancement E:

$$\text{Speedup w/ E}=\frac{\text{Exec time w/o E}}{\text{Exec time w/ E}}$$

If the enhancement E do not affect a portion s (s < 1) of a task, and accelerate the remainder (1 - s) by a factor P (P > 1):

• Exec time w/ E = Exec time w/o E * (s + (1 - s) / P)

$$\text{Speedup w/ E}=\frac{1}{s+{\displaystyle \frac{1-s}{P}}}\stackrel{P\to +\mathrm{\infty }}{\to }\frac{1}{s}$$

Consequence of Amdahl's Law: The amount of speedup that can be achieved through parallelism is limited by the serial portion of the program