<s>
In	O
computer	B-General_Concept
architecture	I-General_Concept
,	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
(	O
or	O
Amdahl	O
's	O
argument	O
)	O
is	O
a	O
formula	O
which	O
gives	O
the	O
theoretical	O
speedup	B-Operating_System
in	O
latency	O
of	O
the	O
execution	O
of	O
a	O
task	O
at	O
fixed	O
workload	O
that	O
can	O
be	O
expected	O
of	O
a	O
system	O
whose	O
resources	O
are	O
improved	O
.	O
</s>
<s>
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
is	O
often	O
used	O
in	O
parallel	B-Operating_System
computing	I-Operating_System
to	O
predict	O
the	O
theoretical	O
speedup	B-Operating_System
when	O
using	O
multiple	O
processors	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
a	O
program	O
needs	O
20	O
hours	O
to	O
complete	O
using	O
a	O
single	B-Operating_System
thread	I-Operating_System
,	O
but	O
a	O
one-hour	O
portion	O
of	O
the	O
program	O
cannot	O
be	O
parallelized	B-Operating_System
,	O
therefore	O
only	O
the	O
remaining	O
19	O
hours	O
 '	O
(	O
)	O
execution	O
time	O
can	O
be	O
parallelized	B-Operating_System
,	O
then	O
regardless	O
of	O
how	O
many	O
threads	B-Operating_System
are	O
devoted	O
to	O
a	O
parallelized	B-Operating_System
execution	O
of	O
this	O
program	O
,	O
the	O
minimum	O
execution	O
time	O
cannot	O
be	O
less	O
than	O
one	O
hour	O
.	O
</s>
<s>
Hence	O
,	O
the	O
theoretical	O
speedup	B-Operating_System
is	O
limited	O
to	O
at	O
most	O
20	O
times	O
the	O
single	B-Operating_System
thread	I-Operating_System
performance	O
,	O
.	O
</s>
<s>
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
can	O
be	O
formulated	O
in	O
the	O
following	O
way	O
:	O
</s>
<s>
Slatency	O
is	O
the	O
theoretical	O
speedup	B-Operating_System
of	O
the	O
execution	O
of	O
the	O
whole	O
task	O
;	O
</s>
<s>
s	O
is	O
the	O
speedup	B-Operating_System
of	O
the	O
part	O
of	O
the	O
task	O
that	O
benefits	O
from	O
improved	O
system	O
resources	O
;	O
</s>
<s>
shows	O
that	O
the	O
theoretical	O
speedup	B-Operating_System
of	O
the	O
execution	O
of	O
the	O
whole	O
task	O
increases	O
with	O
the	O
improvement	O
of	O
the	O
resources	O
of	O
the	O
system	O
and	O
that	O
regardless	O
of	O
the	O
magnitude	O
of	O
the	O
improvement	O
,	O
the	O
theoretical	O
speedup	B-Operating_System
is	O
always	O
limited	O
by	O
the	O
part	O
of	O
the	O
task	O
that	O
cannot	O
benefit	O
from	O
the	O
improvement	O
.	O
</s>
<s>
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
applies	O
only	O
to	O
the	O
cases	O
where	O
the	O
problem	O
size	O
is	O
fixed	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
Gustafson	B-Operating_System
's	I-Operating_System
law	I-Operating_System
gives	O
a	O
less	O
pessimistic	O
and	O
more	O
realistic	O
assessment	O
of	O
the	O
parallel	O
performance	O
.	O
</s>
<s>
After	O
that	O
,	O
another	O
part	O
of	O
the	O
program	O
passes	O
each	O
file	O
to	O
a	O
separate	O
thread	B-Operating_System
for	O
processing	O
.	O
</s>
<s>
The	O
part	O
that	O
scans	O
the	O
directory	O
and	O
creates	O
the	O
file	O
list	O
cannot	O
be	O
sped	O
up	O
on	O
a	O
parallel	B-Operating_System
computer	I-Operating_System
,	O
but	O
the	O
part	O
that	O
processes	O
the	O
files	O
can	O
.	O
</s>
<s>
If	O
30%	O
of	O
the	O
execution	O
time	O
may	O
be	O
the	O
subject	O
of	O
a	O
speedup	B-Operating_System
,	O
p	O
will	O
be	O
0.3	O
;	O
if	O
the	O
improvement	O
makes	O
the	O
affected	O
part	O
twice	O
as	O
fast	O
,	O
s	O
will	O
be2	O
.	O
</s>
<s>
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
states	O
that	O
the	O
overall	O
speedup	B-Operating_System
of	O
applying	O
the	O
improvement	O
will	O
be	O
:	O
</s>
<s>
Notice	O
how	O
the	O
5	O
times	O
and	O
20	O
times	O
speedup	B-Operating_System
on	O
the	O
2nd	O
and	O
3rd	O
parts	O
respectively	O
do	O
n't	O
have	O
much	O
effect	O
on	O
the	O
overall	O
speedup	B-Operating_System
when	O
the	O
4th	O
part	O
(	O
48%	O
of	O
the	O
execution	O
time	O
)	O
is	O
accelerated	O
by	O
only	O
1.6	O
times	O
.	O
</s>
<s>
However	O
,	O
improving	O
part	O
B	O
by	O
a	O
factor	O
of	O
5	O
,	O
which	O
presumably	O
requires	O
more	O
effort	O
,	O
will	O
achieve	O
an	O
overall	O
speedup	B-Operating_System
factor	O
of	O
1.25	O
only	O
,	O
which	O
makes	O
it	O
20%	O
faster	O
.	O
</s>
<s>
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
is	O
often	O
conflated	O
with	O
the	O
law	O
of	O
diminishing	O
returns	O
,	O
whereas	O
only	O
a	O
special	O
case	O
of	O
applying	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
demonstrates	O
law	O
of	O
diminishing	O
returns	O
.	O
</s>
<s>
If	O
one	O
picks	O
optimally	O
(	O
in	O
terms	O
of	O
the	O
achieved	O
speedup	B-Operating_System
)	O
what	O
is	O
to	O
be	O
improved	O
,	O
then	O
one	O
will	O
see	O
monotonically	O
decreasing	O
improvements	O
as	O
one	O
improves	O
.	O
</s>
<s>
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
does	O
represent	O
the	O
law	O
of	O
diminishing	O
returns	O
if	O
one	O
is	O
considering	O
what	O
sort	O
of	O
return	O
one	O
gets	O
by	O
adding	O
more	O
processors	O
to	O
a	O
machine	O
,	O
if	O
one	O
is	O
running	O
a	O
fixed-size	O
computation	O
that	O
will	O
use	O
all	O
available	O
processors	O
to	O
their	O
capacity	O
.	O
</s>
<s>
Each	O
time	O
one	O
doubles	O
the	O
number	O
of	O
processors	O
the	O
speedup	B-Operating_System
ratio	O
will	O
diminish	O
,	O
as	O
the	O
total	O
throughput	O
heads	O
toward	O
the	O
limit	O
of	O
1/	O
( 1	O
−	O
p''	O
)	O
.	O
</s>
<s>
This	O
analysis	O
neglects	O
other	O
potential	O
bottlenecks	O
such	O
as	O
memory	B-General_Concept
bandwidth	I-General_Concept
and	O
I/O	O
bandwidth	O
.	O
</s>
<s>
An	O
implication	O
of	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
is	O
that	O
to	O
speed	B-Operating_System
up	I-Operating_System
real	O
applications	O
which	O
have	O
both	O
serial	O
and	O
parallel	O
portions	O
,	O
heterogeneous	O
computing	O
techniques	O
are	O
required	O
.	O
</s>
<s>
There	O
are	O
novel	O
speedup	B-Operating_System
and	O
energy	O
consumption	O
models	O
based	O
on	O
a	O
more	O
general	O
representation	O
of	O
heterogeneity	O
,	O
referred	O
to	O
as	O
the	O
normal	O
form	O
heterogeneity	O
,	O
that	O
support	O
a	O
wide	O
range	O
of	O
heterogeneous	O
many-core	O
architectures	O
.	O
</s>
