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Law

Gustafson's Law

Fixed time: how big a job can I finish in the same time?

Serial fraction
fraction of a job that is serial
Processors
number of processors

How it behaves

One input on the horizontal axis, the others held fixed.

s = 5%s = 20%
Data table
Scaled speedup by processors (the parallel part grows with N)
Processors NseriesSpeedup
1s = 5%1×
1.09s = 5%1.09×
1.19s = 5%1.18×
1.3s = 5%1.28×
1.41s = 5%1.39×
1.54s = 5%1.51×
1.68s = 5%1.64×
1.83s = 5%1.79×
2s = 5%1.95×
2.18s = 5%2.12×
2.37s = 5%2.3×
2.59s = 5%2.51×
2.82s = 5%2.73×
3.07s = 5%2.97×
3.35s = 5%3.23×
3.65s = 5%3.52×
3.98s = 5%3.83×
4.34s = 5%4.17×
4.73s = 5%4.54×
5.16s = 5%4.95×
5.62s = 5%5.39×
6.13s = 5%5.87×
6.68s = 5%6.4×
7.29s = 5%6.97×
7.94s = 5%7.6×
8.66s = 5%8.28×
9.44s = 5%9.02×
10.3s = 5%9.83×
11.2s = 5%10.7×
12.2s = 5%11.7×
13.3s = 5%12.7×
14.5s = 5%13.9×
15.8s = 5%15.1×
17.3s = 5%16.5×
18.8s = 5%17.9×
20.5s = 5%19.6×
22.4s = 5%21.3×
24.4s = 5%23.2×
26.6s = 5%25.3×
29s = 5%27.6×
31.6s = 5%30.1×
34.5s = 5%32.8×
37.6s = 5%35.8×
41s = 5%39×
44.7s = 5%42.5×
48.7s = 5%46.3×
53.1s = 5%50.5×
57.9s = 5%55×
63.1s = 5%60×
68.8s = 5%65.4×
75s = 5%71.3×
81.8s = 5%77.7×
89.1s = 5%84.7×
97.2s = 5%92.4×
106s = 5%101×
115s = 5%110×
126s = 5%120×
137s = 5%130×
150s = 5%142×
163s = 5%155×
178s = 5%169×
194s = 5%184×
211s = 5%201×
230s = 5%219×
251s = 5%239×
274s = 5%260×
299s = 5%284×
325s = 5%309×
355s = 5%337×
387s = 5%368×
422s = 5%401×
460s = 5%437×
501s = 5%476×
546s = 5%519×
596s = 5%566×
649s = 5%617×
708s = 5%673×
772s = 5%733×
841s = 5%799×
917s = 5%871×
1Ks = 5%950×
1s = 20%1×
1.09s = 20%1.07×
1.19s = 20%1.15×
1.3s = 20%1.24×
1.41s = 20%1.33×
1.54s = 20%1.43×
1.68s = 20%1.54×
1.83s = 20%1.66×
2s = 20%1.8×
2.18s = 20%1.94×
2.37s = 20%2.1×
2.59s = 20%2.27×
2.82s = 20%2.45×
3.07s = 20%2.66×
3.35s = 20%2.88×
3.65s = 20%3.12×
3.98s = 20%3.38×
4.34s = 20%3.67×
4.73s = 20%3.99×
5.16s = 20%4.33×
5.62s = 20%4.7×
6.13s = 20%5.1×
6.68s = 20%5.55×
7.29s = 20%6.03×
7.94s = 20%6.55×
8.66s = 20%7.13×
9.44s = 20%7.75×
10.3s = 20%8.43×
11.2s = 20%9.18×
12.2s = 20%9.99×
13.3s = 20%10.9×
14.5s = 20%11.8×
15.8s = 20%12.9×
17.3s = 20%14×
18.8s = 20%15.3×
20.5s = 20%16.6×
22.4s = 20%18.1×
24.4s = 20%19.7×
26.6s = 20%21.5×
29s = 20%23.4×
31.6s = 20%25.5×
34.5s = 20%27.8×
37.6s = 20%30.3×
41s = 20%33×
44.7s = 20%35.9×
48.7s = 20%39.2×
53.1s = 20%42.7×
57.9s = 20%46.5×
63.1s = 20%50.7×
68.8s = 20%55.2×
75s = 20%60.2×
81.8s = 20%65.6×
89.1s = 20%71.5×
97.2s = 20%77.9×
106s = 20%84.9×
115s = 20%92.6×
126s = 20%101×
137s = 20%110×
150s = 20%120×
163s = 20%131×
178s = 20%142×
194s = 20%155×
211s = 20%169×
230s = 20%185×
251s = 20%201×
274s = 20%219×
299s = 20%239×
325s = 20%261×
355s = 20%284×
387s = 20%310×
422s = 20%338×
460s = 20%368×
501s = 20%401×
546s = 20%437×
596s = 20%477×
649s = 20%520×
708s = 20%567×
772s = 20%618×
841s = 20%673×
917s = 20%734×
1Ks = 20%800×

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Error falls as one over the square root

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