Synergy User Manual and Tutorial. - THE CORE MEMORY

Synergy User Manual and Tutorial
S
=
performance _ with _ improvement
performance _ without _ improvement
100
= = 1.333
75
If a computation is improved such that it affects a proportion F p of the computation, then
the improvement will have a speedup S affecting F p . The improved time for a
computation will be equal to the unimproved time multiplied by the sum of the
unaffected portion (1-F p ) and the speedup reduced affected portion (F p ÷S) of the task. To
find the improved execution time we use:
⎡
improved _ time = unimproved _ time ×
⎣
F
p ⎤
⎢( 1−
Fp
) + ⎥ ⎦
Continuing the formula above with an affected portion of 40 percent and a speedup of
2.66 times on this portion, we have:
⎡ 0.4 ⎤
improved _ time = 4×
⎢
=
⎣ 2.66⎥
⎦
( 1−
0.4) + = 4×
( 0.6×
0.15) = 4×
0.75 3
This method states, assuming that the value for the speed of the unimproved computation
is 100 percent, the overall speedup for this computational improvement will be:
S
S
unimproved _ time
=
improved _ time
=
(1 − F
1
p
) +
F
S
p
Then plugging in the example proportional values:
S
1
=
(1 − 0.4) +
0.4
2.66
=
1
0.75
= 1.33
Using time values instead of proportions, we have:
4sec
S =
1.6sec
(4sec−1.6sec)
+
2.66
=
4sec
3sec
= 1.33
102