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51Performance

Gustafson's Law

Scaled speedup for growing problems.

If

For a fixed time budget, a larger machine lets you solve a proportionally larger problem, so the serial fraction shrinks with scale and speedup grows near-linearly — the optimistic counterpart to Amdahl's fixed-workload pessimism.

Then

Before justifying more cores, ask whether the problem size grows with the hardware. If the workload is fixed, reason with Amdahl; if it scales, Gustafson applies.

Unless

Amdahl's Law — for a fixed-size workload, the serial fraction still hard-caps speedup

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