Start by clearly stating Amdahl's Law and deriving the speedup formula S(N) = 1 / ((1-p) + p/N). Then discuss the asymptotic limit as N → ∞, its implications for GPU design, contrast with Gustafson's Law, and compute the numeric example for p=0.95 at N=10 and N=1000.
Pro tip: Emphasize that Amdahl's Law assumes fixed problem size, while Gustafson's Law assumes scaled problem size—this distinction is crucial for GPU workloads where problem sizes often grow with available parallelism.
Define the serial and parallel fractions, then derive S(N) = 1 / ((1-p) + p/N) by considering total time as serial time plus parallel time divided by N.
Take the limit as N → ∞ to show S_max = 1/(1-p), and explain that even infinite processors yield finite speedup due to the serial portion.
Discuss how Amdahl's Law highlights the need to minimize serial bottlenecks and maximize parallelizable fraction in GPU kernels; mention that GPU design aims to reduce serial overhead.
Explain Gustafson's Law: scaled speedup S(N) = N - (1-p)(N-1) or S(N) = (1-p) + pN, which assumes problem size grows with N, leading to linear speedup for parallelizable parts.
For p=0.95, calculate S(10) = 1 / (0.05 + 0.95/10) ≈ 6.9 and S(1000) = 1 / (0.05 + 0.95/1000) ≈ 19.6, showing diminishing returns.
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