Synergy User Manual and Tutorial. - THE CORE MEMORY

Synergy User Manual and Tutorial
Amdahl’s law for parallelization states that the sequential fraction F s of a task that cannot
be performed in parallel and the fraction F p = (1-F s ) that can gives the following formula
for maximum speedup by N p processors:
S
=
F
s
1
1−
F
+
N
p
s
As N approaches infinity, the maximal speedup approaches 1/F s . As the (1-F s )/N p value
becomes very small, the price paid for marginal performance increases. Assume that F s =
0.06. Then F p = 1-F s = 0.94. For 4 processors:
S
1
=
1−
0.06
0.06 +
4
1
=
0.06 +
0.94
4
1
=
=
0.06 + 0.235
1
0.295
= 3.3898
The table below shows the run time, speedup, efficiency and cost for processors
N p ={1,2,4,…,1024}, where F s = 0.06 and F p = 0.94. Notice that the speedup per
additional processor is much less as N p increases, causing greater cost and less efficiency.
The graphs show the effect on speedup (y-axis) with respect to F s (x-axis) with increasing
N p .
Processors(N p) 1 2 4 8 16 32 64 128 256 512 1024
Run Time 1024.00 542.72 302.08 181.76 121.60 91.52 76.48 68.96 65.20 63.32 62.38
Speedup 1.0000 1.8868 3.3898 5.6338 8.4211 11.1888 13.3891 14.8492 15.7055 16.1718 16.4155
Efficiency 100.00% 94.34% 84.75% 70.42% 52.63% 34.97% 20.92% 11.60% 6.13% 3.16% 1.60%
Cost 1.00 1.06 1.18 1.42 1.90 2.86 4.78 8.62 16.30 31.66 62.38
4
16
16
64
70
60
3.8
14
50
1
1
1
F
1 F 3.6
4
F
1 F
16
12
F
1 F
64
40
30
3.4
10
20
3.39 3.2
0 0.01 0.02 0.03 0.04 0.05 0.06
8.421
8
0 0.01 0.02 0.03 0.04 0.05 0.06
13.389
10
0 0.01 0.02 0.03 0.04 0.05 0.06
0 F
0.06
0 F
0.06
0 F
0.06
256
300
1200
1.024 . 10 3
250
1000
200
800
1
1
F
1 F 150
256
F
1 F 600
1024
100
400
50
103
200
15.706
0
0 0.01 0.02 0.03 0.04 0.05 0.06
16.416
0
0 0.01 0.02 0.03 0.04 0.05 0.06
0 F
0.06
0 F
0.06