Synergy User Manual and Tutorial. - THE CORE MEMORY

Synergy User Manual and Tutorial
S =
F
sG
1
1−
F
+
N
p
sG
1
=
1−
0.05
0.05 +
1024
1
=
0.95
0.05 +
1024
1
=
0.05 + 0.0009277
Gustafson’s Law predicts:
=
1
0.0509277
= 19.635666
S
+ (1 − N
) × F
= N
p
p s
= 1024 + (1 −1024)
× 0.05
= 1024 −1023×
0.05 = 1024 − 51.15 = 972.85
However when the serial fraction F sA is calculated from F sG using the equation above, we
have:
F
sA
1
=
(1 − FsG
) × N
1+
F
sG
p
1
=
(1 − 0.05) × 1024
1+
0.05
1
=
972.8
1+
0.05
1
= =
1+
19456
1
19457
=
5.14E - 05
We substitute F sA for F sG and solve:
S =
1
1−
Fs
Fs
+
N
p
=
5.14E - 05
1
1−
5.14E - 05
+
1024
=
5.14E - 05
1
+
0.99994
1024
=
5.14E - 05
1
=
+ 9.7650E - 04
1
1.0279E - 03
= 972.85
For this situation, the claim of equivalent results with Gustafson’s Law by obtaining F sA
from F sG , as defined above, and substituting F sA for F sG in Amdahl’s Law is true. The
table below shows that this is true for all number of processors, where Np = {1, 2, 4, 8,
…, 1024} and F sG = 0.05.
107